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Research ArticleAdvanced Load Balancing Based on Network Flow Approach inLTE-A Heterogeneous Network
Shucong Jia Wenyu Li Xiang Zhang Yu Liu and Xinyu Gu
Beijing University of Posts and Telecommunications Beijing 100876 China
Correspondence should be addressed to Shucong Jia jiashucongjsc163com
Received 20 February 2014 Accepted 21 April 2014 Published 20 May 2014
Academic Editor Lin Zhang
Copyright copy 2014 Shucong Jia et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Long-term evolution advanced (LTE-A) systems will offer better service to users by applying advanced physical layer transmissiontechniques and utilizingwider bandwidth To further improve service quality lowpower nodes are overlaidwithin amacro networkcreating what is referred to as a heterogeneous network However load imbalance among cells often decreases the network resourceutilization ratio and consequently reduces the user experience level Load balancing (LB) is an indispensable function in LTE-Aself-organized network (SON) to efficiently accommodate the imbalance in traffic In this paper we firstly evaluate the negativeimpact of unbalanced load among cells through Markovian model Secondly we formulate LB as an optimization problem whichis solved using network flow approach Furthermore a novel algorithm named optimal solution-based LB (OSLB) is proposedTheproposed OSLB algorithm is shown to be effective in providing up to 20 gain in load distribution index (LDI) by a system-levelsimulation
1 Introduction
Nowadays smart phone and tablet users are growing rapidlyThe remarkable explosion of mobile internet traffic requireswireless communication systems to support higher datarate Various kinds of transmission techniques in wirelesspropagation environment were applied to meet the growingdemand such as the high-order multiple input multiple out-put (MIMO) [1] and the heterogeneous network where somelower power nodes are overlaid within a macro networkLong-term evolution advanced (LTE-A) which was stan-dardized by the 3rd generation partnership project (3GPP)[2] is a promising wireless communication system to providehigh date rate and spectral efficiency The bandwidth of LTE-A can be up to 100MHz by using carrier aggregation tech-nology which guarantees effective bandwidth allocation to auser through concurrent utilization of radio resources acrossmultiple carriers and efficient carrier scheduling schemes [3]To improve the service quality of cell edge users some lowpower nodes can be deployed at the edge of a cell creatingwhat is referred to as a heterogeneous network Besidesthe transmission techniques mentioned above some othertechniques (eg coordinated multipoint transmission and
reception) are applied to improve the performance of LTE-Asystem However there are still some challenges in deployinga real LTE-A system For example in LTE-A the trafficrequest of some cells may be far higher than an acceptablelevel named as ldquohotspotsrdquo while some of the other cells mayhave extra resources to serve more users which would resultin load unbalance and user dissatisfaction As the topology ofthe LTE-A heterogeneous network is more complex networkplanning and optimization bring a heavy burden to LTE-A network operators Self-optimizing network (SON) is asolution to relieve the burden by selecting and adjustingthe key parameters in the LTE-A system automatically [4]Load balancing (LB) which hands off some users of a heavypayload cell to neighboring comparatively less loaded cellshas been widely discussed to increase the network resourceutilization
2 Related Work
There are a great deal of articles which analyze the loadbalancing problem of cellular networks To equalize loadamong cells power control algorithms were proposed in [5]which have reduced (or risen) the transmission power to
Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 934101 10 pageshttpdxdoiorg1011552014934101
2 International Journal of Antennas and Propagation
contract (or expand) the coverage of heavy (or low) payloadcells By controlling beam coverage patterns of ldquocommonsignalsrdquo sizes and shapes of cells can be automaticallyadjusted to balance cell load [6] In [7] the cell-specificoffset was adjusted automatically based on payloads of thesource cell and the neighboring cells A two-layermobility LBalgorithmwas discussed in [8] where the overloaded cell canchoose a target cell by considering the situation of its two layersurrounding cells Authors in [9] selected the appropriate LBmethod from handover parameter control and cell coveragecontrol according to the situation To cope with the potentialping-pong load transfer and low convergence issues authorsin [10] proposed a game-theoretic solution to the SONLB In [11] a multidomain LB framework was proposedwhich focuses on reducing the radio resource cost andmitigating the cochannel interference across domains in theheterogeneous network In [12] authors proposed an antcolony self-optimizing method for LB In the method firstthe load of all cells is estimated then some users are selectedto be handed over to the neighbor cells according to thestimulation intensity of all users in the cell But none of theabove researches analyzes either the optimal target cell for aheavily loaded cell or the optimal number of users that shouldbe transferred between two cells
There are a lot of articles which analyze wireless networkthrough aMarkovian model In [13] the blocking probabilityof different types of service in a network is calculated Theauthors of [14] performed a stochastic performance analysisof a finite-state Markovian channel shared by multiple usersand derived delay and backlog upper bounds based on theanalytical principle behind stochastic network calculus
In this paper we firstly evaluate the negative impact ofload imbalance among cells through a Markovian modelSecondly we present a mathematical model for LB andintroduce the network flow approach to derive the optimalsolution Finally we present a novel LB algorithm basedon the optimal solution Compared with the previous LBalgorithms our method can not only lighten the load of thebusy cells but also avoid handover to much traffic to a lowpayload target cell and change the target cell into a busy cell
The rest of this paper proceeds as follows the scenario ofa LTE-A heterogeneous network is described in Section 3 InSection 4 we evaluate the negative impact of load imbalanceamong cells through a Markovian model In Section 5 weformulate LB as an optimization problem analyze loadbalancing based on the network flow approach and introducea novel LB algorithm in an LTE-A heterogeneous networkIn Section 6 a system-level simulation model is presentedand the simulation results are analyzed The paper draws aconclusion in Section 7
3 The Scenario
The scenario we considered is a heterogeneous network com-posed of macrocells and picocells whose coverage is providedby macrobase stations (Macro eNBs) and picobase stations(pico eNBs) respectively [16] as shown in Figure 1 Thecombination of one macrocell and some picocells overlaid
PicoeNB
PicoeNB
PicoeNB
PicoeNB
MacroeNB
MacroeNBMaUE
MaUE
MaUE
MaUE
PiUE
PiUE
Figure 1 The heterogeneous network
within themacrocell can be named as cellTheusers served bya macro eNB are referred to as macrousers (MaUEs) and theusers served by a pico eNB are referred as picousers (PiUEs)The system bandwidth of each cell is equal and the frequencyspectrums of each cell are divided among macrocell and thepicocells to avoid interference between a MaUE and a PiUE
4 Impact of Load Imbalance
In this section we evaluate the negative impact of loadimbalance among cells through a Markovian model Tosimplify the analysis we consider the load imbalance betweentwo cells (cell 1 and cell 2) The arrival of user is assumedas a Poisson process and the arrival rate of user in cell 119894 isassumed as 120582
119894 We assume that users are equally distributed
across three locations macrocell center macrocell edge andpicocell We assume that the arrival rate of center users ofcell 1 is 120582
11 the arrival rate of edge users of cell 1 is 120582
12 and
the arrival rate of picousers of cell 1 is 12058213 Parameters 120582
21
12058222 and 120582
23are the same meanings for cell 2 We assume
that the service time of users follows negative exponentialdistribution The service rate of all users in cell 119894 is assumedas 120583119894 The signal to interference and noise ratio of cell center
users is larger than that of cell edge users so the transmissionrate of one physical resource block (PRB) for a cell edge useris smaller than that of a cell center user [17] Therefore weassume that the number of physical resource blocks (PRBs)needed by a center user is one the number of PRBs neededby an edge user is four and the number of PRBs needed bya picouser is two The total number of PRBs of each cell isassumed to be 100 Then the PRBs occupied by users in cell119894 can be evaluated by a three-dimensional Markovian modelas shown in Figure 2
The state (119888 119889 119890) denotes that the number of PRBsoccupied by cell center users of cell 119894 is 119888 the number of PRBsoccupied by cell edge users of cell 119894 is 119889 and the number ofPRBs occupied by picousers of cell 119894 is 119890The number of PRBsoccupied by total users of cell 119894 is 119888 + 119889 + 119890 which can notbe larger than the total number of PRBs of each cell that is100 If the free PRB number in a cell is no smaller than thenumber of PRBs required by a user the cell will allocate thePRBs to the user Otherwise the requirement from the userwill be rejected The probability that 119899 PRBs are used by all
International Journal of Antennas and Propagation 3
c d 0
c d e minus 2
0 d e c minus 1 d e c + 1 d ec d e
c 0 e
c d minus 4 e
c d e + 2
c d + 4 e
120582i1 120582i1
120582i2
120582i2
120582i3
120582i3
120583i
120583i
120583i
120583i
120583i
120583i
middot middot middot middot middot middotmiddot middot middot
middot middot middot middot middot middot
middot middot middot
Figure 2 The three-dimensional Markovian model for the PRB occupation of cell 119894
users can be respected by the stationary distribution 119902(119899) in[13] 119902(119899) is determined by the recursive formula as follows
119902 (119899) =
119878
sum
119904=1
119886119904sdot 119887119904
119899sdot 119902 (119899 minus 119887
119904) 119899 = 0 1 119873 (1)
where 119902(119899) = 0 for 119899 lt 0 and sum119873119899=1119902(119899) = 1 119878 is the number
of service types that is the dimension of the model In ourcase there are three service types the service of macrocellcenter user the service ofmacrocell edge user and the serviceof picocell user 119886
119904= 120582119904120583119904is the type 119904 offered load 119887
119904is the
number of PRBs required by type 119904119873 is the total number ofPRBs of an LTE cell
The blocking probability 119875119887119904
of type 119904 user can be calcu-lated as
119875119887119904
=
119873
sum
119899=119873minus119887119904+1
119902 (119899) 119904 = 1 2 119878 (2)
Using formulas (1) and (2) we can calculate the blockingprobability of users in case of different traffic densities andload distributions
For example we consider two load distribution scenariosbetween two cells In the first scenario we assume that thetotal arrival rate of users in cell 1 is three times larger thanthe arrival rate of users in cell 2 In the second scenario weassume that the total arrival rate of users in cell 1 is equal tothe total arrival rate of users in cell 2 Besides we assumethat the arrival rate of total users that is users in cell 1with the addition of users in cell 2 is equal in the two loaddistribution scenarios Moreover the resource requirementand the service ratio are assumed to be the same in the twoload distribution scenarios and the total number of PRBsof each cell is 100 Some detail parameters are presented in
0 4 8 12 16 20
Bloc
king
pro
babi
lity
Arrival ratio of total users (1s)
Balanced load distribution scenarioUnbalanced load distribution scenario
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
Figure 3 The blocking probability of users in two load distributionscenarios versus the arrival rate of total users
Table 1 Using formulas (1) and (2) we calculate the blockingprobability of user in two load distribution scenarios as thearrival rate of total users 120582total increasing from 1 to 20 asshown in Figure 3
From Figure 3 we can see that although the total trafficis the same in the two load distribution scenarios theblocking probability of users in case of unbalanced loaddistribution is larger than the blocking probability of usersin case of balanced load distribution So we need using LBto hands off some users of heavily loaded cell to neighboringcomparatively less loaded cells for the purpose of improvingnetwork performance
4 International Journal of Antennas and Propagation
Table 1 The Markovian model parameters
Scenario User type 120582 120583 119887119904
The center user of cell 1 025lowast120582total 02 1
Unbalanced load distribution scenario
The edge user of cell 1 025lowast120582total 02 4The picouser of cell 1 025lowast120582total 02 2
The center user of cell 2 0083lowast120582total 02 1The edge user of cell 2 0083lowast120582total 02 4The picouser of cell 2 0083lowast120582total 02 2
Balanced load distribution scenarioThe center user of cell 1 or 2 0167lowast120582total 02 1The edge user of cell 1 or 2 0167lowast120582total 02 4The picouser of cell 1 or 2 0167lowast120582total 02 2
5 LB Based on Network Flow Approach
As described in Section 4 load imbalance between twoadjacent cells will affect the resource utilization of the twocells If there aremore cells in a system the problem of how tobalance the load among cells is more complex In this sectionwe formulate the LB problem as an optimization problem andsolve the problem using network flow approach
51 LB Problem Formulation and Analysis We consider anetwork consisting of 119899 cells and several users Among the 119899cells the number of physical resource blocks (PRBs) neededby a cell 119896 to support the traffic of users in the cell 119896 is denotedby119873119896 Due to traffic distribution imbalance119873
119896varies in size
We assume a scenario like Figure 4 where cells A and C haveone user and cells B and D have three users In Figure 4 weassume each user needs the same number of PRBs to keepthe analysis simple Two LB schemes are shown in Figure 4In scheme 1 a user in cell B is switched to cell C After the LBthe numbers of users in four cells are 1 2 2 and 3 respectivelyIn scheme 2 a user in cell B is switched to cell A and a userin cell D is switched to cell C After the LB the number ofusers in each cell is 2 It is obvious that scheme 2 is betterthan scheme 1
From the example we think that LB should be analyzedamong multiple cells rather than just between two cells Ifthere are 119899 cells we need to switch user among cells to make119873119896approaching119873 = (1119899)sum
119899
119896=1119873119896119873 is the average number
of PRBs needed by a cell However switching among cellshas some signaling overhead and the switched userrsquos signalquality may decrease Therefore in LB we should minimizethe number of handovers Then the problem is equivalent toan optimization problem that can be written as
(1198751) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
(3)
where 119875119894119895
is the number of PRBs occupied by businesswhich switched from cell 119894 to cell 119895 It should be noticed
that there may be no solution to the constraint equationof (3) if 119875
119894119895are integers so we assume that 119875
119894119895are real
numbers in this subsection and round off 119875119894119895in the novel LB
algorithm subsection We analyze the optimization problemin the following cases of Figure 5
511 Case 1Three Cells in a Row To balance the load of threecells in a row we firstly need calculate the average load of onecell 119873 Secondly we start to balance the load from the cellin the left side (denoted as cell 1) If the load of cell 1 is largerthan119873 we transfer services which occupy119873
1minus119873 PRBs from
cell 1 to the middle cell (denoted as cell 2) If the load of cell 1is smaller than119873 we transfer services which occupy119873minus119873
1
PRBs from cell 2 to cell 1 At last we balance the load betweencell 2 and the cell in the right side (denoted as cell 3) If theload of cell 1 and cell 2 is larger than 2 lowast 119873 then we transferservices which occupy119873
1+ 1198732minus 2 lowast 119873 from cell 2 to cell 3
If the load of cell 1 and cell 2 is smaller than 2 lowast 119873 then wetransfer services which occupy 2 lowast 119873 minus 119873
1minus 1198732from cell 3
to cell 2 At last the solution of (3) is described as follows
119875119894119895=
max((4 minus 119895)119873 minus3
sum
119909=119895
119873119909 0) 119894 isin 1 2 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1
(4)
As a consequence of the objective function in (3) either119875119894119895or 119875119895119894is zero and those two parameters are nonnegative
so we define other parameters 1198751015840119894119895which can be negative
1198751015840
119894119895=
119875119894119895
(119875119894119895gt 0)
minus119875119895119894
(119875119894119895= 0)
(5)
Property (1198751015840119894119895= minus1198751015840
119895119894) Combining formulas (4) and (5) the
simultaneous equation of LB model is as follows
1198731minus 1198751015840
12= 119873 (6)
1198732minus 1198751015840
23+ 1198751015840
12= 119873 (7)
1198733+ 1198751015840
23= 119873 (8)
International Journal of Antennas and Propagation 5
Cell A Cell B
Scheme 1
Cell C Cell D
(a)
Scheme 2
(b)
Figure 4 A LB scenario and two corresponding schemes
Case 1 Three cells in a row
Case 3 n cellsCase 2 n cells in a row
middot middot middot middot middot middotmiddot middot middot
N1N1
N1
N2 N2
N2
N3
N3 N4 N5
N6Nn
Figure 5 Network layout cases
Formula (6) means that after transferring some servicefrom cell 1 to cell 2 if 1198751015840
12ge 0 (or from cell 2 to cell 1 if
1198751015840
12lt 0) cell 1 has an average load level Formulas (7) and
(8) are the same meanings to cell 2 and cell 3 We sum up (6)(7) and (8) and obtain119873
1+1198732+1198733= 3119873which is an identity
There are two unknown numbers in the above simultaneousequation and the number of linearly independent equationsis two that is (6) and (8) are linearly independent So thesolution (4) is the optimal solution because of the uniquenessof the solution
512 Case 2 119899 Cells in a Row In this case using the samemethod in case 1 we can calculate the solution of (3) whichis described as
119875119894119895=
max((119899 minus 119895 + 1)119873 minus119899
sum
119909=119895
119873119909 0)
119894 isin 1 2 119899 minus 1 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0)
119894 isin 2 3 119899 119895 = 119894 minus 1
(9)
Similarly to case 1 we can demonstrate the solution (9) isthe optimal solution
4
5 1 2
6
3 1
5 4 3
6
2
middot middot middot middot middot middot middot middot middot middot middot middot
Figure 6 Two methods to mark 119899 cells with numbers
513 Case 3 119899 Cells When there are 119899 cells we can markthem in accordancewith the sequence in Figure 6 If only cellswith adjacent sequence numbers can switch users then case3 is equal to case 2 So (9) is a solution to case 3 But it is notthe optimal solution In the remainder of this paper we usenetwork flow approach to obtain the optimal solution of theoptimization problem
52 LB Base on Network Flow Approach In this sectionfirstly we describe the optimization problem by graph theoryIn graph theory network flow has been rapidly expandingsince the work of Ford and Fulkerson [18] on flow in 1962The broad applicability in different systems of network flowoptimization has brought great interest in it A network flowis a directed graph composed of nodes and edges Each edgereceives a flowwhich cannot exceed the edgersquos capacityNodesare classified as three types source middle and sink
In imbalance traffic distribution scenario some heavilyloaded cells have more than 119873 PRBs occupied Thereforesome users need to switch to adjacent low payload cells Weterm those heavy payload cells as the source nodes whilethose low payload cells are termed as the sink nodes ingraph theory The target is to transfer occupied PRBs in sinknodes exceeding119873 to the sink nodes Handoff from a cell toanother (119894 rarr 119895) is viewed as an arc The arc is bidirectional
6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7 Seven nodes representing 7 cells
because handoff between two cells is bidirectional as shownin Figure 7
The number of PRBs occupied by the users switchedbetween two cells 119875
119894119895is compared as the amount of flow on
the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873
119894 where 0 lt 120596 lt 1 120596 is
used to indicate that only a part of users at the edge of a cellcan be switched to adjacent cell Then the LB is equivalent tothe following optimization problem
(1198752) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
119875119894119895⩽ 120596 sdot 119873
119894
(10)
Now the optimization problem is a transportation net-work flow problem including multiple source multiple sinknodes Each source node needs to transfer out services whichoccupy 119873
119896minus 119873 PRBs and consequently each sink node
needs to take over those services We need to assign flowdistribution in each arc of the graph In the flow distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873
119894minus 119873 so that the source
node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) the difference of theamount of flow from other nodes to the sink node and theamount of flow from the sink node to other nodes is equal to119873 minus 119873
119895so that the sink node will have119873 PRBs occupied by
users after the handover processAmultiple source nodes and sinknodes problem is harder
than a single source node and sink node problem By usinga virtual source node and a virtual sink node the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8 Arcs between the virtual source node and source nodes(sink nodes and the virtual sink node)
is transformed into a single source node and single sinknode transportation network flow problem In order to makethe above two problems equivalent a unidirectional arc isassumed from the virtual source node to each source nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 minus the number of PRBs occupied in each low payloadcell as shown in Figure 8 If an arc between the virtual sourcenode and a source node is saturated then the source nodewillhave 119873 PRBs occupied by users after the handover processbecause the flow in the arc between the virtual source nodeand a source node is equal to the amount of flow fromthe source node to other nodes minus the amount of flowfrom other nodes (except the virtual source node) to thesource node Similarly If an arc between a sink node and thevirtual sink node is saturated then the sink node will have119873PRBs occupied by users after the handover process Now themultiple source nodes and sink nodes problem is equal to thesingle source node and single sink node problem
If we give a flow distribution of which the amount of flowout of the virtual source node is the amount of PRBs occupiedby users in all source node subtract 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 PRBs occupied after the handover process and theflow distribution is a solution to the optimization problem(10) Judging the existence of the solution to (10) is equal tojudging if there is a flow distribution where arcs between thevirtual source node and all source nodes are saturated Sowe need to calculate the maximum flow between the virtualsource node and the virtual sink node If the maximumflow is equal to the sum of capacities of arcs between thevirtual source node and all source nodes (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)solution to (10) exists We can calculate network maximum
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
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DistributedSensor Networks
International Journal of
2 International Journal of Antennas and Propagation
contract (or expand) the coverage of heavy (or low) payloadcells By controlling beam coverage patterns of ldquocommonsignalsrdquo sizes and shapes of cells can be automaticallyadjusted to balance cell load [6] In [7] the cell-specificoffset was adjusted automatically based on payloads of thesource cell and the neighboring cells A two-layermobility LBalgorithmwas discussed in [8] where the overloaded cell canchoose a target cell by considering the situation of its two layersurrounding cells Authors in [9] selected the appropriate LBmethod from handover parameter control and cell coveragecontrol according to the situation To cope with the potentialping-pong load transfer and low convergence issues authorsin [10] proposed a game-theoretic solution to the SONLB In [11] a multidomain LB framework was proposedwhich focuses on reducing the radio resource cost andmitigating the cochannel interference across domains in theheterogeneous network In [12] authors proposed an antcolony self-optimizing method for LB In the method firstthe load of all cells is estimated then some users are selectedto be handed over to the neighbor cells according to thestimulation intensity of all users in the cell But none of theabove researches analyzes either the optimal target cell for aheavily loaded cell or the optimal number of users that shouldbe transferred between two cells
There are a lot of articles which analyze wireless networkthrough aMarkovian model In [13] the blocking probabilityof different types of service in a network is calculated Theauthors of [14] performed a stochastic performance analysisof a finite-state Markovian channel shared by multiple usersand derived delay and backlog upper bounds based on theanalytical principle behind stochastic network calculus
In this paper we firstly evaluate the negative impact ofload imbalance among cells through a Markovian modelSecondly we present a mathematical model for LB andintroduce the network flow approach to derive the optimalsolution Finally we present a novel LB algorithm basedon the optimal solution Compared with the previous LBalgorithms our method can not only lighten the load of thebusy cells but also avoid handover to much traffic to a lowpayload target cell and change the target cell into a busy cell
The rest of this paper proceeds as follows the scenario ofa LTE-A heterogeneous network is described in Section 3 InSection 4 we evaluate the negative impact of load imbalanceamong cells through a Markovian model In Section 5 weformulate LB as an optimization problem analyze loadbalancing based on the network flow approach and introducea novel LB algorithm in an LTE-A heterogeneous networkIn Section 6 a system-level simulation model is presentedand the simulation results are analyzed The paper draws aconclusion in Section 7
3 The Scenario
The scenario we considered is a heterogeneous network com-posed of macrocells and picocells whose coverage is providedby macrobase stations (Macro eNBs) and picobase stations(pico eNBs) respectively [16] as shown in Figure 1 Thecombination of one macrocell and some picocells overlaid
PicoeNB
PicoeNB
PicoeNB
PicoeNB
MacroeNB
MacroeNBMaUE
MaUE
MaUE
MaUE
PiUE
PiUE
Figure 1 The heterogeneous network
within themacrocell can be named as cellTheusers served bya macro eNB are referred to as macrousers (MaUEs) and theusers served by a pico eNB are referred as picousers (PiUEs)The system bandwidth of each cell is equal and the frequencyspectrums of each cell are divided among macrocell and thepicocells to avoid interference between a MaUE and a PiUE
4 Impact of Load Imbalance
In this section we evaluate the negative impact of loadimbalance among cells through a Markovian model Tosimplify the analysis we consider the load imbalance betweentwo cells (cell 1 and cell 2) The arrival of user is assumedas a Poisson process and the arrival rate of user in cell 119894 isassumed as 120582
119894 We assume that users are equally distributed
across three locations macrocell center macrocell edge andpicocell We assume that the arrival rate of center users ofcell 1 is 120582
11 the arrival rate of edge users of cell 1 is 120582
12 and
the arrival rate of picousers of cell 1 is 12058213 Parameters 120582
21
12058222 and 120582
23are the same meanings for cell 2 We assume
that the service time of users follows negative exponentialdistribution The service rate of all users in cell 119894 is assumedas 120583119894 The signal to interference and noise ratio of cell center
users is larger than that of cell edge users so the transmissionrate of one physical resource block (PRB) for a cell edge useris smaller than that of a cell center user [17] Therefore weassume that the number of physical resource blocks (PRBs)needed by a center user is one the number of PRBs neededby an edge user is four and the number of PRBs needed bya picouser is two The total number of PRBs of each cell isassumed to be 100 Then the PRBs occupied by users in cell119894 can be evaluated by a three-dimensional Markovian modelas shown in Figure 2
The state (119888 119889 119890) denotes that the number of PRBsoccupied by cell center users of cell 119894 is 119888 the number of PRBsoccupied by cell edge users of cell 119894 is 119889 and the number ofPRBs occupied by picousers of cell 119894 is 119890The number of PRBsoccupied by total users of cell 119894 is 119888 + 119889 + 119890 which can notbe larger than the total number of PRBs of each cell that is100 If the free PRB number in a cell is no smaller than thenumber of PRBs required by a user the cell will allocate thePRBs to the user Otherwise the requirement from the userwill be rejected The probability that 119899 PRBs are used by all
International Journal of Antennas and Propagation 3
c d 0
c d e minus 2
0 d e c minus 1 d e c + 1 d ec d e
c 0 e
c d minus 4 e
c d e + 2
c d + 4 e
120582i1 120582i1
120582i2
120582i2
120582i3
120582i3
120583i
120583i
120583i
120583i
120583i
120583i
middot middot middot middot middot middotmiddot middot middot
middot middot middot middot middot middot
middot middot middot
Figure 2 The three-dimensional Markovian model for the PRB occupation of cell 119894
users can be respected by the stationary distribution 119902(119899) in[13] 119902(119899) is determined by the recursive formula as follows
119902 (119899) =
119878
sum
119904=1
119886119904sdot 119887119904
119899sdot 119902 (119899 minus 119887
119904) 119899 = 0 1 119873 (1)
where 119902(119899) = 0 for 119899 lt 0 and sum119873119899=1119902(119899) = 1 119878 is the number
of service types that is the dimension of the model In ourcase there are three service types the service of macrocellcenter user the service ofmacrocell edge user and the serviceof picocell user 119886
119904= 120582119904120583119904is the type 119904 offered load 119887
119904is the
number of PRBs required by type 119904119873 is the total number ofPRBs of an LTE cell
The blocking probability 119875119887119904
of type 119904 user can be calcu-lated as
119875119887119904
=
119873
sum
119899=119873minus119887119904+1
119902 (119899) 119904 = 1 2 119878 (2)
Using formulas (1) and (2) we can calculate the blockingprobability of users in case of different traffic densities andload distributions
For example we consider two load distribution scenariosbetween two cells In the first scenario we assume that thetotal arrival rate of users in cell 1 is three times larger thanthe arrival rate of users in cell 2 In the second scenario weassume that the total arrival rate of users in cell 1 is equal tothe total arrival rate of users in cell 2 Besides we assumethat the arrival rate of total users that is users in cell 1with the addition of users in cell 2 is equal in the two loaddistribution scenarios Moreover the resource requirementand the service ratio are assumed to be the same in the twoload distribution scenarios and the total number of PRBsof each cell is 100 Some detail parameters are presented in
0 4 8 12 16 20
Bloc
king
pro
babi
lity
Arrival ratio of total users (1s)
Balanced load distribution scenarioUnbalanced load distribution scenario
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
Figure 3 The blocking probability of users in two load distributionscenarios versus the arrival rate of total users
Table 1 Using formulas (1) and (2) we calculate the blockingprobability of user in two load distribution scenarios as thearrival rate of total users 120582total increasing from 1 to 20 asshown in Figure 3
From Figure 3 we can see that although the total trafficis the same in the two load distribution scenarios theblocking probability of users in case of unbalanced loaddistribution is larger than the blocking probability of usersin case of balanced load distribution So we need using LBto hands off some users of heavily loaded cell to neighboringcomparatively less loaded cells for the purpose of improvingnetwork performance
4 International Journal of Antennas and Propagation
Table 1 The Markovian model parameters
Scenario User type 120582 120583 119887119904
The center user of cell 1 025lowast120582total 02 1
Unbalanced load distribution scenario
The edge user of cell 1 025lowast120582total 02 4The picouser of cell 1 025lowast120582total 02 2
The center user of cell 2 0083lowast120582total 02 1The edge user of cell 2 0083lowast120582total 02 4The picouser of cell 2 0083lowast120582total 02 2
Balanced load distribution scenarioThe center user of cell 1 or 2 0167lowast120582total 02 1The edge user of cell 1 or 2 0167lowast120582total 02 4The picouser of cell 1 or 2 0167lowast120582total 02 2
5 LB Based on Network Flow Approach
As described in Section 4 load imbalance between twoadjacent cells will affect the resource utilization of the twocells If there aremore cells in a system the problem of how tobalance the load among cells is more complex In this sectionwe formulate the LB problem as an optimization problem andsolve the problem using network flow approach
51 LB Problem Formulation and Analysis We consider anetwork consisting of 119899 cells and several users Among the 119899cells the number of physical resource blocks (PRBs) neededby a cell 119896 to support the traffic of users in the cell 119896 is denotedby119873119896 Due to traffic distribution imbalance119873
119896varies in size
We assume a scenario like Figure 4 where cells A and C haveone user and cells B and D have three users In Figure 4 weassume each user needs the same number of PRBs to keepthe analysis simple Two LB schemes are shown in Figure 4In scheme 1 a user in cell B is switched to cell C After the LBthe numbers of users in four cells are 1 2 2 and 3 respectivelyIn scheme 2 a user in cell B is switched to cell A and a userin cell D is switched to cell C After the LB the number ofusers in each cell is 2 It is obvious that scheme 2 is betterthan scheme 1
From the example we think that LB should be analyzedamong multiple cells rather than just between two cells Ifthere are 119899 cells we need to switch user among cells to make119873119896approaching119873 = (1119899)sum
119899
119896=1119873119896119873 is the average number
of PRBs needed by a cell However switching among cellshas some signaling overhead and the switched userrsquos signalquality may decrease Therefore in LB we should minimizethe number of handovers Then the problem is equivalent toan optimization problem that can be written as
(1198751) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
(3)
where 119875119894119895
is the number of PRBs occupied by businesswhich switched from cell 119894 to cell 119895 It should be noticed
that there may be no solution to the constraint equationof (3) if 119875
119894119895are integers so we assume that 119875
119894119895are real
numbers in this subsection and round off 119875119894119895in the novel LB
algorithm subsection We analyze the optimization problemin the following cases of Figure 5
511 Case 1Three Cells in a Row To balance the load of threecells in a row we firstly need calculate the average load of onecell 119873 Secondly we start to balance the load from the cellin the left side (denoted as cell 1) If the load of cell 1 is largerthan119873 we transfer services which occupy119873
1minus119873 PRBs from
cell 1 to the middle cell (denoted as cell 2) If the load of cell 1is smaller than119873 we transfer services which occupy119873minus119873
1
PRBs from cell 2 to cell 1 At last we balance the load betweencell 2 and the cell in the right side (denoted as cell 3) If theload of cell 1 and cell 2 is larger than 2 lowast 119873 then we transferservices which occupy119873
1+ 1198732minus 2 lowast 119873 from cell 2 to cell 3
If the load of cell 1 and cell 2 is smaller than 2 lowast 119873 then wetransfer services which occupy 2 lowast 119873 minus 119873
1minus 1198732from cell 3
to cell 2 At last the solution of (3) is described as follows
119875119894119895=
max((4 minus 119895)119873 minus3
sum
119909=119895
119873119909 0) 119894 isin 1 2 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1
(4)
As a consequence of the objective function in (3) either119875119894119895or 119875119895119894is zero and those two parameters are nonnegative
so we define other parameters 1198751015840119894119895which can be negative
1198751015840
119894119895=
119875119894119895
(119875119894119895gt 0)
minus119875119895119894
(119875119894119895= 0)
(5)
Property (1198751015840119894119895= minus1198751015840
119895119894) Combining formulas (4) and (5) the
simultaneous equation of LB model is as follows
1198731minus 1198751015840
12= 119873 (6)
1198732minus 1198751015840
23+ 1198751015840
12= 119873 (7)
1198733+ 1198751015840
23= 119873 (8)
International Journal of Antennas and Propagation 5
Cell A Cell B
Scheme 1
Cell C Cell D
(a)
Scheme 2
(b)
Figure 4 A LB scenario and two corresponding schemes
Case 1 Three cells in a row
Case 3 n cellsCase 2 n cells in a row
middot middot middot middot middot middotmiddot middot middot
N1N1
N1
N2 N2
N2
N3
N3 N4 N5
N6Nn
Figure 5 Network layout cases
Formula (6) means that after transferring some servicefrom cell 1 to cell 2 if 1198751015840
12ge 0 (or from cell 2 to cell 1 if
1198751015840
12lt 0) cell 1 has an average load level Formulas (7) and
(8) are the same meanings to cell 2 and cell 3 We sum up (6)(7) and (8) and obtain119873
1+1198732+1198733= 3119873which is an identity
There are two unknown numbers in the above simultaneousequation and the number of linearly independent equationsis two that is (6) and (8) are linearly independent So thesolution (4) is the optimal solution because of the uniquenessof the solution
512 Case 2 119899 Cells in a Row In this case using the samemethod in case 1 we can calculate the solution of (3) whichis described as
119875119894119895=
max((119899 minus 119895 + 1)119873 minus119899
sum
119909=119895
119873119909 0)
119894 isin 1 2 119899 minus 1 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0)
119894 isin 2 3 119899 119895 = 119894 minus 1
(9)
Similarly to case 1 we can demonstrate the solution (9) isthe optimal solution
4
5 1 2
6
3 1
5 4 3
6
2
middot middot middot middot middot middot middot middot middot middot middot middot
Figure 6 Two methods to mark 119899 cells with numbers
513 Case 3 119899 Cells When there are 119899 cells we can markthem in accordancewith the sequence in Figure 6 If only cellswith adjacent sequence numbers can switch users then case3 is equal to case 2 So (9) is a solution to case 3 But it is notthe optimal solution In the remainder of this paper we usenetwork flow approach to obtain the optimal solution of theoptimization problem
52 LB Base on Network Flow Approach In this sectionfirstly we describe the optimization problem by graph theoryIn graph theory network flow has been rapidly expandingsince the work of Ford and Fulkerson [18] on flow in 1962The broad applicability in different systems of network flowoptimization has brought great interest in it A network flowis a directed graph composed of nodes and edges Each edgereceives a flowwhich cannot exceed the edgersquos capacityNodesare classified as three types source middle and sink
In imbalance traffic distribution scenario some heavilyloaded cells have more than 119873 PRBs occupied Thereforesome users need to switch to adjacent low payload cells Weterm those heavy payload cells as the source nodes whilethose low payload cells are termed as the sink nodes ingraph theory The target is to transfer occupied PRBs in sinknodes exceeding119873 to the sink nodes Handoff from a cell toanother (119894 rarr 119895) is viewed as an arc The arc is bidirectional
6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7 Seven nodes representing 7 cells
because handoff between two cells is bidirectional as shownin Figure 7
The number of PRBs occupied by the users switchedbetween two cells 119875
119894119895is compared as the amount of flow on
the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873
119894 where 0 lt 120596 lt 1 120596 is
used to indicate that only a part of users at the edge of a cellcan be switched to adjacent cell Then the LB is equivalent tothe following optimization problem
(1198752) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
119875119894119895⩽ 120596 sdot 119873
119894
(10)
Now the optimization problem is a transportation net-work flow problem including multiple source multiple sinknodes Each source node needs to transfer out services whichoccupy 119873
119896minus 119873 PRBs and consequently each sink node
needs to take over those services We need to assign flowdistribution in each arc of the graph In the flow distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873
119894minus 119873 so that the source
node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) the difference of theamount of flow from other nodes to the sink node and theamount of flow from the sink node to other nodes is equal to119873 minus 119873
119895so that the sink node will have119873 PRBs occupied by
users after the handover processAmultiple source nodes and sinknodes problem is harder
than a single source node and sink node problem By usinga virtual source node and a virtual sink node the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8 Arcs between the virtual source node and source nodes(sink nodes and the virtual sink node)
is transformed into a single source node and single sinknode transportation network flow problem In order to makethe above two problems equivalent a unidirectional arc isassumed from the virtual source node to each source nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 minus the number of PRBs occupied in each low payloadcell as shown in Figure 8 If an arc between the virtual sourcenode and a source node is saturated then the source nodewillhave 119873 PRBs occupied by users after the handover processbecause the flow in the arc between the virtual source nodeand a source node is equal to the amount of flow fromthe source node to other nodes minus the amount of flowfrom other nodes (except the virtual source node) to thesource node Similarly If an arc between a sink node and thevirtual sink node is saturated then the sink node will have119873PRBs occupied by users after the handover process Now themultiple source nodes and sink nodes problem is equal to thesingle source node and single sink node problem
If we give a flow distribution of which the amount of flowout of the virtual source node is the amount of PRBs occupiedby users in all source node subtract 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 PRBs occupied after the handover process and theflow distribution is a solution to the optimization problem(10) Judging the existence of the solution to (10) is equal tojudging if there is a flow distribution where arcs between thevirtual source node and all source nodes are saturated Sowe need to calculate the maximum flow between the virtualsource node and the virtual sink node If the maximumflow is equal to the sum of capacities of arcs between thevirtual source node and all source nodes (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)solution to (10) exists We can calculate network maximum
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
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Active and Passive Electronic Components
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
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Electrical and Computer Engineering
Journal of
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
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DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 3
c d 0
c d e minus 2
0 d e c minus 1 d e c + 1 d ec d e
c 0 e
c d minus 4 e
c d e + 2
c d + 4 e
120582i1 120582i1
120582i2
120582i2
120582i3
120582i3
120583i
120583i
120583i
120583i
120583i
120583i
middot middot middot middot middot middotmiddot middot middot
middot middot middot middot middot middot
middot middot middot
Figure 2 The three-dimensional Markovian model for the PRB occupation of cell 119894
users can be respected by the stationary distribution 119902(119899) in[13] 119902(119899) is determined by the recursive formula as follows
119902 (119899) =
119878
sum
119904=1
119886119904sdot 119887119904
119899sdot 119902 (119899 minus 119887
119904) 119899 = 0 1 119873 (1)
where 119902(119899) = 0 for 119899 lt 0 and sum119873119899=1119902(119899) = 1 119878 is the number
of service types that is the dimension of the model In ourcase there are three service types the service of macrocellcenter user the service ofmacrocell edge user and the serviceof picocell user 119886
119904= 120582119904120583119904is the type 119904 offered load 119887
119904is the
number of PRBs required by type 119904119873 is the total number ofPRBs of an LTE cell
The blocking probability 119875119887119904
of type 119904 user can be calcu-lated as
119875119887119904
=
119873
sum
119899=119873minus119887119904+1
119902 (119899) 119904 = 1 2 119878 (2)
Using formulas (1) and (2) we can calculate the blockingprobability of users in case of different traffic densities andload distributions
For example we consider two load distribution scenariosbetween two cells In the first scenario we assume that thetotal arrival rate of users in cell 1 is three times larger thanthe arrival rate of users in cell 2 In the second scenario weassume that the total arrival rate of users in cell 1 is equal tothe total arrival rate of users in cell 2 Besides we assumethat the arrival rate of total users that is users in cell 1with the addition of users in cell 2 is equal in the two loaddistribution scenarios Moreover the resource requirementand the service ratio are assumed to be the same in the twoload distribution scenarios and the total number of PRBsof each cell is 100 Some detail parameters are presented in
0 4 8 12 16 20
Bloc
king
pro
babi
lity
Arrival ratio of total users (1s)
Balanced load distribution scenarioUnbalanced load distribution scenario
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
Figure 3 The blocking probability of users in two load distributionscenarios versus the arrival rate of total users
Table 1 Using formulas (1) and (2) we calculate the blockingprobability of user in two load distribution scenarios as thearrival rate of total users 120582total increasing from 1 to 20 asshown in Figure 3
From Figure 3 we can see that although the total trafficis the same in the two load distribution scenarios theblocking probability of users in case of unbalanced loaddistribution is larger than the blocking probability of usersin case of balanced load distribution So we need using LBto hands off some users of heavily loaded cell to neighboringcomparatively less loaded cells for the purpose of improvingnetwork performance
4 International Journal of Antennas and Propagation
Table 1 The Markovian model parameters
Scenario User type 120582 120583 119887119904
The center user of cell 1 025lowast120582total 02 1
Unbalanced load distribution scenario
The edge user of cell 1 025lowast120582total 02 4The picouser of cell 1 025lowast120582total 02 2
The center user of cell 2 0083lowast120582total 02 1The edge user of cell 2 0083lowast120582total 02 4The picouser of cell 2 0083lowast120582total 02 2
Balanced load distribution scenarioThe center user of cell 1 or 2 0167lowast120582total 02 1The edge user of cell 1 or 2 0167lowast120582total 02 4The picouser of cell 1 or 2 0167lowast120582total 02 2
5 LB Based on Network Flow Approach
As described in Section 4 load imbalance between twoadjacent cells will affect the resource utilization of the twocells If there aremore cells in a system the problem of how tobalance the load among cells is more complex In this sectionwe formulate the LB problem as an optimization problem andsolve the problem using network flow approach
51 LB Problem Formulation and Analysis We consider anetwork consisting of 119899 cells and several users Among the 119899cells the number of physical resource blocks (PRBs) neededby a cell 119896 to support the traffic of users in the cell 119896 is denotedby119873119896 Due to traffic distribution imbalance119873
119896varies in size
We assume a scenario like Figure 4 where cells A and C haveone user and cells B and D have three users In Figure 4 weassume each user needs the same number of PRBs to keepthe analysis simple Two LB schemes are shown in Figure 4In scheme 1 a user in cell B is switched to cell C After the LBthe numbers of users in four cells are 1 2 2 and 3 respectivelyIn scheme 2 a user in cell B is switched to cell A and a userin cell D is switched to cell C After the LB the number ofusers in each cell is 2 It is obvious that scheme 2 is betterthan scheme 1
From the example we think that LB should be analyzedamong multiple cells rather than just between two cells Ifthere are 119899 cells we need to switch user among cells to make119873119896approaching119873 = (1119899)sum
119899
119896=1119873119896119873 is the average number
of PRBs needed by a cell However switching among cellshas some signaling overhead and the switched userrsquos signalquality may decrease Therefore in LB we should minimizethe number of handovers Then the problem is equivalent toan optimization problem that can be written as
(1198751) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
(3)
where 119875119894119895
is the number of PRBs occupied by businesswhich switched from cell 119894 to cell 119895 It should be noticed
that there may be no solution to the constraint equationof (3) if 119875
119894119895are integers so we assume that 119875
119894119895are real
numbers in this subsection and round off 119875119894119895in the novel LB
algorithm subsection We analyze the optimization problemin the following cases of Figure 5
511 Case 1Three Cells in a Row To balance the load of threecells in a row we firstly need calculate the average load of onecell 119873 Secondly we start to balance the load from the cellin the left side (denoted as cell 1) If the load of cell 1 is largerthan119873 we transfer services which occupy119873
1minus119873 PRBs from
cell 1 to the middle cell (denoted as cell 2) If the load of cell 1is smaller than119873 we transfer services which occupy119873minus119873
1
PRBs from cell 2 to cell 1 At last we balance the load betweencell 2 and the cell in the right side (denoted as cell 3) If theload of cell 1 and cell 2 is larger than 2 lowast 119873 then we transferservices which occupy119873
1+ 1198732minus 2 lowast 119873 from cell 2 to cell 3
If the load of cell 1 and cell 2 is smaller than 2 lowast 119873 then wetransfer services which occupy 2 lowast 119873 minus 119873
1minus 1198732from cell 3
to cell 2 At last the solution of (3) is described as follows
119875119894119895=
max((4 minus 119895)119873 minus3
sum
119909=119895
119873119909 0) 119894 isin 1 2 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1
(4)
As a consequence of the objective function in (3) either119875119894119895or 119875119895119894is zero and those two parameters are nonnegative
so we define other parameters 1198751015840119894119895which can be negative
1198751015840
119894119895=
119875119894119895
(119875119894119895gt 0)
minus119875119895119894
(119875119894119895= 0)
(5)
Property (1198751015840119894119895= minus1198751015840
119895119894) Combining formulas (4) and (5) the
simultaneous equation of LB model is as follows
1198731minus 1198751015840
12= 119873 (6)
1198732minus 1198751015840
23+ 1198751015840
12= 119873 (7)
1198733+ 1198751015840
23= 119873 (8)
International Journal of Antennas and Propagation 5
Cell A Cell B
Scheme 1
Cell C Cell D
(a)
Scheme 2
(b)
Figure 4 A LB scenario and two corresponding schemes
Case 1 Three cells in a row
Case 3 n cellsCase 2 n cells in a row
middot middot middot middot middot middotmiddot middot middot
N1N1
N1
N2 N2
N2
N3
N3 N4 N5
N6Nn
Figure 5 Network layout cases
Formula (6) means that after transferring some servicefrom cell 1 to cell 2 if 1198751015840
12ge 0 (or from cell 2 to cell 1 if
1198751015840
12lt 0) cell 1 has an average load level Formulas (7) and
(8) are the same meanings to cell 2 and cell 3 We sum up (6)(7) and (8) and obtain119873
1+1198732+1198733= 3119873which is an identity
There are two unknown numbers in the above simultaneousequation and the number of linearly independent equationsis two that is (6) and (8) are linearly independent So thesolution (4) is the optimal solution because of the uniquenessof the solution
512 Case 2 119899 Cells in a Row In this case using the samemethod in case 1 we can calculate the solution of (3) whichis described as
119875119894119895=
max((119899 minus 119895 + 1)119873 minus119899
sum
119909=119895
119873119909 0)
119894 isin 1 2 119899 minus 1 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0)
119894 isin 2 3 119899 119895 = 119894 minus 1
(9)
Similarly to case 1 we can demonstrate the solution (9) isthe optimal solution
4
5 1 2
6
3 1
5 4 3
6
2
middot middot middot middot middot middot middot middot middot middot middot middot
Figure 6 Two methods to mark 119899 cells with numbers
513 Case 3 119899 Cells When there are 119899 cells we can markthem in accordancewith the sequence in Figure 6 If only cellswith adjacent sequence numbers can switch users then case3 is equal to case 2 So (9) is a solution to case 3 But it is notthe optimal solution In the remainder of this paper we usenetwork flow approach to obtain the optimal solution of theoptimization problem
52 LB Base on Network Flow Approach In this sectionfirstly we describe the optimization problem by graph theoryIn graph theory network flow has been rapidly expandingsince the work of Ford and Fulkerson [18] on flow in 1962The broad applicability in different systems of network flowoptimization has brought great interest in it A network flowis a directed graph composed of nodes and edges Each edgereceives a flowwhich cannot exceed the edgersquos capacityNodesare classified as three types source middle and sink
In imbalance traffic distribution scenario some heavilyloaded cells have more than 119873 PRBs occupied Thereforesome users need to switch to adjacent low payload cells Weterm those heavy payload cells as the source nodes whilethose low payload cells are termed as the sink nodes ingraph theory The target is to transfer occupied PRBs in sinknodes exceeding119873 to the sink nodes Handoff from a cell toanother (119894 rarr 119895) is viewed as an arc The arc is bidirectional
6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7 Seven nodes representing 7 cells
because handoff between two cells is bidirectional as shownin Figure 7
The number of PRBs occupied by the users switchedbetween two cells 119875
119894119895is compared as the amount of flow on
the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873
119894 where 0 lt 120596 lt 1 120596 is
used to indicate that only a part of users at the edge of a cellcan be switched to adjacent cell Then the LB is equivalent tothe following optimization problem
(1198752) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
119875119894119895⩽ 120596 sdot 119873
119894
(10)
Now the optimization problem is a transportation net-work flow problem including multiple source multiple sinknodes Each source node needs to transfer out services whichoccupy 119873
119896minus 119873 PRBs and consequently each sink node
needs to take over those services We need to assign flowdistribution in each arc of the graph In the flow distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873
119894minus 119873 so that the source
node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) the difference of theamount of flow from other nodes to the sink node and theamount of flow from the sink node to other nodes is equal to119873 minus 119873
119895so that the sink node will have119873 PRBs occupied by
users after the handover processAmultiple source nodes and sinknodes problem is harder
than a single source node and sink node problem By usinga virtual source node and a virtual sink node the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8 Arcs between the virtual source node and source nodes(sink nodes and the virtual sink node)
is transformed into a single source node and single sinknode transportation network flow problem In order to makethe above two problems equivalent a unidirectional arc isassumed from the virtual source node to each source nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 minus the number of PRBs occupied in each low payloadcell as shown in Figure 8 If an arc between the virtual sourcenode and a source node is saturated then the source nodewillhave 119873 PRBs occupied by users after the handover processbecause the flow in the arc between the virtual source nodeand a source node is equal to the amount of flow fromthe source node to other nodes minus the amount of flowfrom other nodes (except the virtual source node) to thesource node Similarly If an arc between a sink node and thevirtual sink node is saturated then the sink node will have119873PRBs occupied by users after the handover process Now themultiple source nodes and sink nodes problem is equal to thesingle source node and single sink node problem
If we give a flow distribution of which the amount of flowout of the virtual source node is the amount of PRBs occupiedby users in all source node subtract 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 PRBs occupied after the handover process and theflow distribution is a solution to the optimization problem(10) Judging the existence of the solution to (10) is equal tojudging if there is a flow distribution where arcs between thevirtual source node and all source nodes are saturated Sowe need to calculate the maximum flow between the virtualsource node and the virtual sink node If the maximumflow is equal to the sum of capacities of arcs between thevirtual source node and all source nodes (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)solution to (10) exists We can calculate network maximum
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
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Active and Passive Electronic Components
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
4 International Journal of Antennas and Propagation
Table 1 The Markovian model parameters
Scenario User type 120582 120583 119887119904
The center user of cell 1 025lowast120582total 02 1
Unbalanced load distribution scenario
The edge user of cell 1 025lowast120582total 02 4The picouser of cell 1 025lowast120582total 02 2
The center user of cell 2 0083lowast120582total 02 1The edge user of cell 2 0083lowast120582total 02 4The picouser of cell 2 0083lowast120582total 02 2
Balanced load distribution scenarioThe center user of cell 1 or 2 0167lowast120582total 02 1The edge user of cell 1 or 2 0167lowast120582total 02 4The picouser of cell 1 or 2 0167lowast120582total 02 2
5 LB Based on Network Flow Approach
As described in Section 4 load imbalance between twoadjacent cells will affect the resource utilization of the twocells If there aremore cells in a system the problem of how tobalance the load among cells is more complex In this sectionwe formulate the LB problem as an optimization problem andsolve the problem using network flow approach
51 LB Problem Formulation and Analysis We consider anetwork consisting of 119899 cells and several users Among the 119899cells the number of physical resource blocks (PRBs) neededby a cell 119896 to support the traffic of users in the cell 119896 is denotedby119873119896 Due to traffic distribution imbalance119873
119896varies in size
We assume a scenario like Figure 4 where cells A and C haveone user and cells B and D have three users In Figure 4 weassume each user needs the same number of PRBs to keepthe analysis simple Two LB schemes are shown in Figure 4In scheme 1 a user in cell B is switched to cell C After the LBthe numbers of users in four cells are 1 2 2 and 3 respectivelyIn scheme 2 a user in cell B is switched to cell A and a userin cell D is switched to cell C After the LB the number ofusers in each cell is 2 It is obvious that scheme 2 is betterthan scheme 1
From the example we think that LB should be analyzedamong multiple cells rather than just between two cells Ifthere are 119899 cells we need to switch user among cells to make119873119896approaching119873 = (1119899)sum
119899
119896=1119873119896119873 is the average number
of PRBs needed by a cell However switching among cellshas some signaling overhead and the switched userrsquos signalquality may decrease Therefore in LB we should minimizethe number of handovers Then the problem is equivalent toan optimization problem that can be written as
(1198751) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
(3)
where 119875119894119895
is the number of PRBs occupied by businesswhich switched from cell 119894 to cell 119895 It should be noticed
that there may be no solution to the constraint equationof (3) if 119875
119894119895are integers so we assume that 119875
119894119895are real
numbers in this subsection and round off 119875119894119895in the novel LB
algorithm subsection We analyze the optimization problemin the following cases of Figure 5
511 Case 1Three Cells in a Row To balance the load of threecells in a row we firstly need calculate the average load of onecell 119873 Secondly we start to balance the load from the cellin the left side (denoted as cell 1) If the load of cell 1 is largerthan119873 we transfer services which occupy119873
1minus119873 PRBs from
cell 1 to the middle cell (denoted as cell 2) If the load of cell 1is smaller than119873 we transfer services which occupy119873minus119873
1
PRBs from cell 2 to cell 1 At last we balance the load betweencell 2 and the cell in the right side (denoted as cell 3) If theload of cell 1 and cell 2 is larger than 2 lowast 119873 then we transferservices which occupy119873
1+ 1198732minus 2 lowast 119873 from cell 2 to cell 3
If the load of cell 1 and cell 2 is smaller than 2 lowast 119873 then wetransfer services which occupy 2 lowast 119873 minus 119873
1minus 1198732from cell 3
to cell 2 At last the solution of (3) is described as follows
119875119894119895=
max((4 minus 119895)119873 minus3
sum
119909=119895
119873119909 0) 119894 isin 1 2 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1
(4)
As a consequence of the objective function in (3) either119875119894119895or 119875119895119894is zero and those two parameters are nonnegative
so we define other parameters 1198751015840119894119895which can be negative
1198751015840
119894119895=
119875119894119895
(119875119894119895gt 0)
minus119875119895119894
(119875119894119895= 0)
(5)
Property (1198751015840119894119895= minus1198751015840
119895119894) Combining formulas (4) and (5) the
simultaneous equation of LB model is as follows
1198731minus 1198751015840
12= 119873 (6)
1198732minus 1198751015840
23+ 1198751015840
12= 119873 (7)
1198733+ 1198751015840
23= 119873 (8)
International Journal of Antennas and Propagation 5
Cell A Cell B
Scheme 1
Cell C Cell D
(a)
Scheme 2
(b)
Figure 4 A LB scenario and two corresponding schemes
Case 1 Three cells in a row
Case 3 n cellsCase 2 n cells in a row
middot middot middot middot middot middotmiddot middot middot
N1N1
N1
N2 N2
N2
N3
N3 N4 N5
N6Nn
Figure 5 Network layout cases
Formula (6) means that after transferring some servicefrom cell 1 to cell 2 if 1198751015840
12ge 0 (or from cell 2 to cell 1 if
1198751015840
12lt 0) cell 1 has an average load level Formulas (7) and
(8) are the same meanings to cell 2 and cell 3 We sum up (6)(7) and (8) and obtain119873
1+1198732+1198733= 3119873which is an identity
There are two unknown numbers in the above simultaneousequation and the number of linearly independent equationsis two that is (6) and (8) are linearly independent So thesolution (4) is the optimal solution because of the uniquenessof the solution
512 Case 2 119899 Cells in a Row In this case using the samemethod in case 1 we can calculate the solution of (3) whichis described as
119875119894119895=
max((119899 minus 119895 + 1)119873 minus119899
sum
119909=119895
119873119909 0)
119894 isin 1 2 119899 minus 1 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0)
119894 isin 2 3 119899 119895 = 119894 minus 1
(9)
Similarly to case 1 we can demonstrate the solution (9) isthe optimal solution
4
5 1 2
6
3 1
5 4 3
6
2
middot middot middot middot middot middot middot middot middot middot middot middot
Figure 6 Two methods to mark 119899 cells with numbers
513 Case 3 119899 Cells When there are 119899 cells we can markthem in accordancewith the sequence in Figure 6 If only cellswith adjacent sequence numbers can switch users then case3 is equal to case 2 So (9) is a solution to case 3 But it is notthe optimal solution In the remainder of this paper we usenetwork flow approach to obtain the optimal solution of theoptimization problem
52 LB Base on Network Flow Approach In this sectionfirstly we describe the optimization problem by graph theoryIn graph theory network flow has been rapidly expandingsince the work of Ford and Fulkerson [18] on flow in 1962The broad applicability in different systems of network flowoptimization has brought great interest in it A network flowis a directed graph composed of nodes and edges Each edgereceives a flowwhich cannot exceed the edgersquos capacityNodesare classified as three types source middle and sink
In imbalance traffic distribution scenario some heavilyloaded cells have more than 119873 PRBs occupied Thereforesome users need to switch to adjacent low payload cells Weterm those heavy payload cells as the source nodes whilethose low payload cells are termed as the sink nodes ingraph theory The target is to transfer occupied PRBs in sinknodes exceeding119873 to the sink nodes Handoff from a cell toanother (119894 rarr 119895) is viewed as an arc The arc is bidirectional
6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7 Seven nodes representing 7 cells
because handoff between two cells is bidirectional as shownin Figure 7
The number of PRBs occupied by the users switchedbetween two cells 119875
119894119895is compared as the amount of flow on
the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873
119894 where 0 lt 120596 lt 1 120596 is
used to indicate that only a part of users at the edge of a cellcan be switched to adjacent cell Then the LB is equivalent tothe following optimization problem
(1198752) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
119875119894119895⩽ 120596 sdot 119873
119894
(10)
Now the optimization problem is a transportation net-work flow problem including multiple source multiple sinknodes Each source node needs to transfer out services whichoccupy 119873
119896minus 119873 PRBs and consequently each sink node
needs to take over those services We need to assign flowdistribution in each arc of the graph In the flow distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873
119894minus 119873 so that the source
node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) the difference of theamount of flow from other nodes to the sink node and theamount of flow from the sink node to other nodes is equal to119873 minus 119873
119895so that the sink node will have119873 PRBs occupied by
users after the handover processAmultiple source nodes and sinknodes problem is harder
than a single source node and sink node problem By usinga virtual source node and a virtual sink node the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8 Arcs between the virtual source node and source nodes(sink nodes and the virtual sink node)
is transformed into a single source node and single sinknode transportation network flow problem In order to makethe above two problems equivalent a unidirectional arc isassumed from the virtual source node to each source nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 minus the number of PRBs occupied in each low payloadcell as shown in Figure 8 If an arc between the virtual sourcenode and a source node is saturated then the source nodewillhave 119873 PRBs occupied by users after the handover processbecause the flow in the arc between the virtual source nodeand a source node is equal to the amount of flow fromthe source node to other nodes minus the amount of flowfrom other nodes (except the virtual source node) to thesource node Similarly If an arc between a sink node and thevirtual sink node is saturated then the sink node will have119873PRBs occupied by users after the handover process Now themultiple source nodes and sink nodes problem is equal to thesingle source node and single sink node problem
If we give a flow distribution of which the amount of flowout of the virtual source node is the amount of PRBs occupiedby users in all source node subtract 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 PRBs occupied after the handover process and theflow distribution is a solution to the optimization problem(10) Judging the existence of the solution to (10) is equal tojudging if there is a flow distribution where arcs between thevirtual source node and all source nodes are saturated Sowe need to calculate the maximum flow between the virtualsource node and the virtual sink node If the maximumflow is equal to the sum of capacities of arcs between thevirtual source node and all source nodes (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)solution to (10) exists We can calculate network maximum
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
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Active and Passive Electronic Components
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RotatingMachinery
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 5
Cell A Cell B
Scheme 1
Cell C Cell D
(a)
Scheme 2
(b)
Figure 4 A LB scenario and two corresponding schemes
Case 1 Three cells in a row
Case 3 n cellsCase 2 n cells in a row
middot middot middot middot middot middotmiddot middot middot
N1N1
N1
N2 N2
N2
N3
N3 N4 N5
N6Nn
Figure 5 Network layout cases
Formula (6) means that after transferring some servicefrom cell 1 to cell 2 if 1198751015840
12ge 0 (or from cell 2 to cell 1 if
1198751015840
12lt 0) cell 1 has an average load level Formulas (7) and
(8) are the same meanings to cell 2 and cell 3 We sum up (6)(7) and (8) and obtain119873
1+1198732+1198733= 3119873which is an identity
There are two unknown numbers in the above simultaneousequation and the number of linearly independent equationsis two that is (6) and (8) are linearly independent So thesolution (4) is the optimal solution because of the uniquenessof the solution
512 Case 2 119899 Cells in a Row In this case using the samemethod in case 1 we can calculate the solution of (3) whichis described as
119875119894119895=
max((119899 minus 119895 + 1)119873 minus119899
sum
119909=119895
119873119909 0)
119894 isin 1 2 119899 minus 1 119895 = 119894 + 1
max(119895119873 minus119895
sum
119909=1
119873119909 0)
119894 isin 2 3 119899 119895 = 119894 minus 1
(9)
Similarly to case 1 we can demonstrate the solution (9) isthe optimal solution
4
5 1 2
6
3 1
5 4 3
6
2
middot middot middot middot middot middot middot middot middot middot middot middot
Figure 6 Two methods to mark 119899 cells with numbers
513 Case 3 119899 Cells When there are 119899 cells we can markthem in accordancewith the sequence in Figure 6 If only cellswith adjacent sequence numbers can switch users then case3 is equal to case 2 So (9) is a solution to case 3 But it is notthe optimal solution In the remainder of this paper we usenetwork flow approach to obtain the optimal solution of theoptimization problem
52 LB Base on Network Flow Approach In this sectionfirstly we describe the optimization problem by graph theoryIn graph theory network flow has been rapidly expandingsince the work of Ford and Fulkerson [18] on flow in 1962The broad applicability in different systems of network flowoptimization has brought great interest in it A network flowis a directed graph composed of nodes and edges Each edgereceives a flowwhich cannot exceed the edgersquos capacityNodesare classified as three types source middle and sink
In imbalance traffic distribution scenario some heavilyloaded cells have more than 119873 PRBs occupied Thereforesome users need to switch to adjacent low payload cells Weterm those heavy payload cells as the source nodes whilethose low payload cells are termed as the sink nodes ingraph theory The target is to transfer occupied PRBs in sinknodes exceeding119873 to the sink nodes Handoff from a cell toanother (119894 rarr 119895) is viewed as an arc The arc is bidirectional
6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7 Seven nodes representing 7 cells
because handoff between two cells is bidirectional as shownin Figure 7
The number of PRBs occupied by the users switchedbetween two cells 119875
119894119895is compared as the amount of flow on
the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873
119894 where 0 lt 120596 lt 1 120596 is
used to indicate that only a part of users at the edge of a cellcan be switched to adjacent cell Then the LB is equivalent tothe following optimization problem
(1198752) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
119875119894119895⩽ 120596 sdot 119873
119894
(10)
Now the optimization problem is a transportation net-work flow problem including multiple source multiple sinknodes Each source node needs to transfer out services whichoccupy 119873
119896minus 119873 PRBs and consequently each sink node
needs to take over those services We need to assign flowdistribution in each arc of the graph In the flow distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873
119894minus 119873 so that the source
node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) the difference of theamount of flow from other nodes to the sink node and theamount of flow from the sink node to other nodes is equal to119873 minus 119873
119895so that the sink node will have119873 PRBs occupied by
users after the handover processAmultiple source nodes and sinknodes problem is harder
than a single source node and sink node problem By usinga virtual source node and a virtual sink node the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8 Arcs between the virtual source node and source nodes(sink nodes and the virtual sink node)
is transformed into a single source node and single sinknode transportation network flow problem In order to makethe above two problems equivalent a unidirectional arc isassumed from the virtual source node to each source nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 minus the number of PRBs occupied in each low payloadcell as shown in Figure 8 If an arc between the virtual sourcenode and a source node is saturated then the source nodewillhave 119873 PRBs occupied by users after the handover processbecause the flow in the arc between the virtual source nodeand a source node is equal to the amount of flow fromthe source node to other nodes minus the amount of flowfrom other nodes (except the virtual source node) to thesource node Similarly If an arc between a sink node and thevirtual sink node is saturated then the sink node will have119873PRBs occupied by users after the handover process Now themultiple source nodes and sink nodes problem is equal to thesingle source node and single sink node problem
If we give a flow distribution of which the amount of flowout of the virtual source node is the amount of PRBs occupiedby users in all source node subtract 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 PRBs occupied after the handover process and theflow distribution is a solution to the optimization problem(10) Judging the existence of the solution to (10) is equal tojudging if there is a flow distribution where arcs between thevirtual source node and all source nodes are saturated Sowe need to calculate the maximum flow between the virtualsource node and the virtual sink node If the maximumflow is equal to the sum of capacities of arcs between thevirtual source node and all source nodes (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)solution to (10) exists We can calculate network maximum
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7 Seven nodes representing 7 cells
because handoff between two cells is bidirectional as shownin Figure 7
The number of PRBs occupied by the users switchedbetween two cells 119875
119894119895is compared as the amount of flow on
the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873
119894 where 0 lt 120596 lt 1 120596 is
used to indicate that only a part of users at the edge of a cellcan be switched to adjacent cell Then the LB is equivalent tothe following optimization problem
(1198752) min (
119899
sum
119894=1
sum
119895 = 119894
119875119894119895) (1 le 119895 le 119899)
st 119873119894minus sum
119895 = 119894
119875119894119895+ sum
119895 = 119894
119875119895119894= 119873
(1 le 119894 le 119899 1 le 119895 le 119899)
119875119894119895⩽ 120596 sdot 119873
119894
(10)
Now the optimization problem is a transportation net-work flow problem including multiple source multiple sinknodes Each source node needs to transfer out services whichoccupy 119873
119896minus 119873 PRBs and consequently each sink node
needs to take over those services We need to assign flowdistribution in each arc of the graph In the flow distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873
119894minus 119873 so that the source
node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) the difference of theamount of flow from other nodes to the sink node and theamount of flow from the sink node to other nodes is equal to119873 minus 119873
119895so that the sink node will have119873 PRBs occupied by
users after the handover processAmultiple source nodes and sinknodes problem is harder
than a single source node and sink node problem By usinga virtual source node and a virtual sink node the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8 Arcs between the virtual source node and source nodes(sink nodes and the virtual sink node)
is transformed into a single source node and single sinknode transportation network flow problem In order to makethe above two problems equivalent a unidirectional arc isassumed from the virtual source node to each source nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 minus the number of PRBs occupied in each low payloadcell as shown in Figure 8 If an arc between the virtual sourcenode and a source node is saturated then the source nodewillhave 119873 PRBs occupied by users after the handover processbecause the flow in the arc between the virtual source nodeand a source node is equal to the amount of flow fromthe source node to other nodes minus the amount of flowfrom other nodes (except the virtual source node) to thesource node Similarly If an arc between a sink node and thevirtual sink node is saturated then the sink node will have119873PRBs occupied by users after the handover process Now themultiple source nodes and sink nodes problem is equal to thesingle source node and single sink node problem
If we give a flow distribution of which the amount of flowout of the virtual source node is the amount of PRBs occupiedby users in all source node subtract 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 PRBs occupied after the handover process and theflow distribution is a solution to the optimization problem(10) Judging the existence of the solution to (10) is equal tojudging if there is a flow distribution where arcs between thevirtual source node and all source nodes are saturated Sowe need to calculate the maximum flow between the virtualsource node and the virtual sink node If the maximumflow is equal to the sum of capacities of arcs between thevirtual source node and all source nodes (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)solution to (10) exists We can calculate network maximum
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node byusing algorithm of Ford and Fulkerson [18] which is to findaugmented paths by using the idea of finding independentpaths and at least one arc will reach saturated state Thecomputation complexity of calculating the maximum flow byusing independent paths method is 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie a largepart of users are located at cell edge and can be switched toadjacent cell) the maximum flow will be calculated as equalto the amount of PRBs occupied by users in all source nodesubtract 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 is close to 1 to ensure the solution to (10) will existand to keep analysis simple In future work we will analysesome scenario where solution to (10) does not exist Aftermaking sure the solution to (10) exists we need to find a flowdistribution which needs the least sum of flow between eachtwo adjacent nodes (ie the least sum of handover betweeneach two adjacent cells) To keep analysis simple we assumethat the cost for switching per PRB unit traffic is equal forall cells and users Now finding a flow distribution whichneeds the least sum of flow between each two adjacent nodesis a minimum cost flow problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 is the number of arcs It is not complicatedto calculate the maximum flow and the minimum cost flowbecause they all can be solved by polynomial algorithm Sowe can use the optimal solution solved by Orlin algorithm toguide load balance
53 A Novel LB Algorithm In this section a novel LBalgorithm is presented based on the optimal solution Thenovel LB algorithm is called optimal solution-based LB(OSLB) Firstly the optimal solution to the numbers of PRBsoccupied by communication service transfer between cells forload balancing will be figured out by the following procedure
(1) Each cell calculates the PRBs needed by each user inthe cell through channel measurements and countsthe total PRBs needed which is denoted as119873
119894
(2) Each cell transmits the 119873119894to its ambient two layer
cells so that each cell knows its own 119873119894and its
ambient two layer cellsrsquo119873119894Then by theOrlinmethod
[19] 119875119894119895can be calculated
(3) Using (5) 1198751015840119894119895
can be calculated Then each celltransmits the 1198751015840
119894119895to its ambient one layer cells
(4) All cells average their own 1198751015840119894119895and the minus1198751015840
119895119894received
from their ambient cells and the averaged values aredefined as 11987510158401015840
119894119895 which are the final amount of PRBs
occupied by the users that should be transferred Atlast 11987510158401015840
119894119895are rounded down if they are not integers
Secondly we pick out cell 119894 which has 11987510158401015840119894119895
greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863
119899= RSRP
119899119895minus RSRP
119899119894 RSRP
119899119894is reference
signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB
119899 PRB119899vary among
users because the modulation and coding mode is differentamong users with the base station
Lastly handover for load balancing in the above men-tioned cell 119894 will be implemented According to [20] ahandover event is initiated when user detects that a neighborcell offers a better signal quality than its current serving cellThis condition is referred to as measurement event A3 whichhas been formulated as
119872119904+Oc119904119905+Hyst lt 119872
119905 (11)
where 119872119904and 119872
119905are the signal strength or quality values
for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc
119904119905is the specific offset for RSRP between
cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small
it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 So the coverage of different cells is adjustableby changing the specific offset Oc among cells In our LBalgorithm LB is performed by automatically adjusting Oc
119904119905
based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited
value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc
119904119905| We define that 1198631015840
119899= 119863119899minus
HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872
119898=1PRB119898
is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell
If the process comes to an end with sum119872119898=1
PRB119898lt 11987510158401015840
119894119895
by the reason of minus119863119899lt Ocmax that is to say there are not
enough users at the edge of the heavily loaded cell and thetarget low payload cell then the load imbalance problem isnot completely solved In this case we search picocells at theedge of the heavy payload cell and switch those picocells andthe users served by those picocells to the adjacent low payloadcell to balance load
6 Simulation and Performance Analysis
In this section system-level simulation for the LTE-A cellularnetwork is carried out to evaluate the performance of theproposed algorithm There are 2 reference scenarios no LBand the load-based MLB method as presented in [7] Thesimulation platform contains 37 regular hexagonal cells andthe cell radius is 577m Some detail simulation parametersare presented in Table 2 In order to avoid boundary effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn each cell there are two to four picocells located randomlyat the cell edge User numbers of 22 normal cells are 10 Usernumbers of other 15 busy cells are varying from 10 to 40 Itis assumed that the traffic type of users is constant bit rate(CBR) The constant target date rate for each user is 1MbpsDetailed simulation assumptions and parameters are given inTable 1
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 International Journal of Antennas and Propagation
Start
End
M = 1 Oc = zero
minusDn lt Oc
minusDn lt Oc
max
OcmaxOc
Mth user notin cell i
Mth user isin cell j
Oc = Dn M = M + 1
sumM
m=1PRBm le P998400998400
ij
=
N
Y
Y
N
N
Y
Figure 9 The load balancing flow chart
Table 2 Simulation parameters
Parameters AssumptionsCarrier frequency 19GHzBandwidth 40MHzCell radius 577mAntenna type OmnidirectionalMacrocell transmitter power 46 dBmPicocell transmitter power 3 dBmChannel model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation distance 10mNoise Thermal noiseNoise power spectral density minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows
LDI =(sum119899
119894=1119873119894)2
|119899| sum119899
119894=1(119873119894)2 (12)
060
065
070
075
080
085
090
095
100
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10 The load distribution index versus the number of usersin a heavily loaded cell
This index measures the degree of similarity of loadamong cellsThemore closer the payload values are the closerthe index is to 1 When the call arrival rate of busy cells isincreased the load among cells is imbalanced So this valueis decreasing in the three lines of Figure 11 But the OSLBscheme achieves the highest load distribution index amongthree scenarios so OSLB outperforms references in terms ofLB result When user numbers of heavy-payload cells are 10PRBs needed of cells may vary because PRBs needed by usersare different (some users in cell edge need more PRBs thanusers in cell centre) So the LDIs of MLB and NO LB are not1 when all cells have 10 users The LDI of OSLB is very closeto 1 when all cells have 10 users
The average resource occupied ratio of heavily loadedcells versus the user number of a heavily loaded cell is givenin Figure 11The less resource occupied ratio of heavily loadedcells is directly proportional to the lower service failure ratioof heavy payload cells So this parameter should be as closeas possible to the line with inverted triangle which means theaverage resource occupied ratio of all cells Compared withthe NOLB scenario busy cells in OSLB have smaller resourceoccupied ratio So in OSLB the service failure ratio of busycells is less than the NO LB one since proper boundary usersare switched to neighboring idle cells and more resources arereserved to remaining and new coming users The resourceoccupied ratio of heavily loaded cell in the MLB scenario issimilar to the OSLB one which means that the two methodshave similar effect on lightening the load of the busy cell
As depicted in Figure 12 it is obvious that the proposedscheme outperforms the compared schemes in terms of theresource occupied ratio of a particular lowpayload cell whichaccepts most users switched from heavily loaded cells andhas the largest PRBs occupied after handover process amongall old low payload cells If the resource occupied ratios ofsome low payload cells after LB are high new busy cells are
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
()
Figure 11 The average resource occupied ratio of heavily loadedcells versus the number of users in a heavily loaded cell
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
()
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12 The resource occupied ratio of a particular low payloadcell versus the number of users in a heavily loaded cell
brought in So the ratio in Figure 12 should be low and shouldbe as close as possible to the line with inverted triangle whichmeans the average resource occupied ratio of all cells WhenLB is not used this value does not vary and remains near40 When MLB method in [7] is used this value increasesand is larger than average resource occupied ratio of heavilyloaded cells in the same scenario which signifies that newheavily loaded cells are brought in When OSLB is used thisvalue increases but is smaller than average resource occupiedratio of heavily loaded cells in the same scenario and is a littlebigger than the average resource occupied ratio of all cells
which signifies that new heavily loaded cells are not broughtin
7 Conclusion
In this paper LB is optimized by carefully designing anovel algorithm named OSLB Different from the previousliteratures the network flow approach is used to derive theoptimal solution which plays a large part in OSLB TheOSLB algorithm is evaluated and compared by system-levelsimulation Results show that the load distribution indexand the resource occupation ratio of cells are significantlyimproved In this paper we assume that each PRB of a cellcan only be allocated to macrocell users or picousers thatis those two kinds of users can not work on the same PRBsimultaneously In the future we will investigate the scenariowhere a macrocell user and a picouser can share the samePRB which is more realistic and more efficient
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work has been partially sponsored by EU FP7 IRSESMobileCloud Project (Grant no 612212) the 111 Project(no B08004) the major project of Ministry of Industryand Informationization of China (2013ZX03001026) and theFundamental Research Funds for the Central Universities
References
[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013
[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011
[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014
[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013
[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003
[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010
[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 International Journal of Antennas and Propagation
[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011
[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012
[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013
[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012
[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012
[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981
[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013
[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003
[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011
[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013
[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962
[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988
[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008
[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of