06736091Joint Congestion Control and Scheduling in Wireless Networks with Network Coding

8/12/2019 06736091Joint Congestion Control and Scheduling in Wireless Networks with Network Coding

1/15018-9545 (c) 2013 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEEpermission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

is article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2014.2298404, IEEE Transactions on Vehicular Technology

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Joint Congestion Control and Scheduling inWireless Networks with Network Coding

Ronghui Hou, King-Shan Lui, and Jiandong Li

Abstract This paper studies how to perform joint conges-tion control and scheduling with network coding in wirelessnetworks. Under network coding, a node may need to buffera sent packet for decoding a packet to be received later. If sent packets are not forgotten smartly, much buffer space willbe taken up, leading to dropping of new incoming packets.This unexpected packet dropping harms the nal throughputobtained, even though an optimal scheduling has been used.To solve the problem, we introduce a new node model in-corporating transmission mode pre-assignment procedure andscheduling procedure. The introduced transmission mode pre-assignment avoids memorizing lots of sent packets to reducebuffer overhead. We develop a new scheduling policy based onour node model, and formally analyze the stability property of network system using the proposed policy. We nally evaluatethe efciency of our algorithm through simulations from theperspectives of throughput and packet loss ratio.

Index Terms Cross-layer design, network coding, conges-tion control, scheduling, wireless interference

I. I NTRODUCTIONRecently, new techniques were proposed to intelligently

utilize wireless interference to improve network throughput.Network coding exploits the wireless medium broadcastnature to improve network capacity. Generally, network coding can be classied into two different categories: intra-session and inter-session . Intra-session network coding isperformed on packets from the same session, while inter-session network coding is performed on packets acrossdifferent sessions. This work considers the COPE-style inter-session network coding. Consider a set of receivers thateach wants to receive its desired packet from a common

sender. If each receiver has all the other packets except thedesired one, the common sender can code all the packetsand transmit a single coded packet to all receivers, and eachreceiver can successfully decode the desired one. Following[1], [2], we consider network coding without opportunisticlistening, which allows network coding between two ows

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Ronghui Hou and Jiandong Li are with the State Key Lab of IntegratedService Networks, Xidian University, China; King-Shan Lui is with theDepartment of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong.

This work was supported in part by the National Natural ScienceFoundation of China (Grants Nos. 61231008 and 61101143), the importantnational science & technology specic projects 2013ZX03004007-003, theHKU small project fund (104001905), the Fundamental Research Funds forthe Central Universities K50511010006, and the 111 Project under GrantB08038.

p1 xor p 2

1 2 3

f 1

f 2

slot1

slot2

slot3

2

2

p1

p2

2p1 xor p 2

Fig. 1. An illustration for network coding.

only. Fig. 1, which is adapted from Fig. 1 of [3], illustratesthe coding opportunity at Node 2. There are two owsgoing on < 1, 2, 3> and < 3, 2, 1> , respectively. After Node

2 receives packets p1 and p2 from both 1 and 3, respectively,Node 2 can code the packets and transmit the coded packetto both 1 and 3. Since Node 1 has sent p1 before, Node1 can decode p2 from the coded packet p1 p2 . Similarly,Node 3 can decode p1 .

It is well known that intelligent scheduling policy isvery important to improve network throughput. Schedulingin wireless networks is a big challenge due to wirelessinterference. Many works study scheduling issue in wirelessnetworks [4]. Network coding further complicates the issue.In addition to determining which link should be active,each node also needs to determine which transmission mode

(traditional or coded) should be used at the current time. Forinstance, assume that the data rates of f 1 and f 2 in Fig. 1are 14 and

38 , respectively. The link capacity is one unit. In

this scenario, if Node 2 wants to code all the packets of f 2 ,packets will be backlogged. The queue becomes overowedwhile the link capacities are not fully utilized. A better wayis to code f 1 and f 2 at a rate of 14 and send the remainingpackets of f 2 in a traditional manner. On the other hand,under the stochastic trafc model, it is possible that Node 2gets several packets of f 1 before getting one packet of f 2 .Node 2 should determine whether transmitting a packet of f 1 traditionally or waiting for the future coding opportunity.Efcient scheduling policy should utilize all the possiblecoding opportunities to improve network throughput.

The scheduling policy proposed in [5] uses the queue-length at each node to determine which link should be activeat the current time slot. The problem of this scheme is that




2

each node needs to keep each packet sent by itself earlieruntil the next hop transmits the packet. This is because anode does not know whether the packet it sent previouslywill be used for coding by the next hop node until the nexthop node sends it out. For instance, in Fig. 1, after Node 1sends p1 , p1 should be kept at Node 1 until Node 2 transmits p1 . Since Node 2 transmits p2 using network coding, Node1 uses p1 to decode p2 . When the average data rates of the ows differ a lot, many packets of a ow would betransmitted in the traditional manner. Although these packetscan be forgotten right after they are sent, because the sendingnode does not know it until these packets are sent by thenext hop, the sending node has to buffer all of them for awhile. The space overhead is thus increased.

In practice, some nodes may have limited storage re-

sources. For instance, in multihop cellular networks, eachnode is a smartphone or tablet, and the storage resourcesare limited [6], [7]. The future incoming packets wouldbe dropped when the node space allocated for packet for-warding is full, which severely affects network throughputperformance. We would like to use an example to illustratethis phenomenon. Suppose the buffer size is 50 packets,which is the default value used in ns2 [8]. Consider thenetwork state that Node 1 has 30 packets to be transmittedand needs to keep another 20 sent packets used for futuredecoding. Since there is no more room in the buffer, Node1 would drop new packets coming from the upper layer

due to overow in default [7]. However, it is possible thatonly a few out of the 20 sent packets would be transmittedby Node 2 in a coded manner. If Node 1 knows whichpacket would be transmitted traditionally in advance, thenode can forget the packet immediately so as to accept morenew packets from upper layer. If the packet loss happens inthe intermediate forwarding node, the bandwidth resourcesconsumed for the packet transmission over the previoushops would be wasted. This hinders network throughput.With the declining of the memory chip prices, we may saythat routing buffers can be over-provisioned. However, largerouting buffer increases queuing delay [8], [9]. Therefore, itis desirable to forget a sent packet as soon as possible sothat a large buffer is not needed.

Motivated by this issue, this paper aims at reducing thespace overhead while providing high network throughput.We propose the transmission mode pre-assignment proce-dure telling the node which transmission mode (network coding or traditionally) the next hop will use to transmita packet immediately after the packet arrives the next hop.The next hop can then inform the previous hop to forgetpackets that are going to be transmitted traditionally. Thisinformation can be carried by the signalling messages. Sig-nalling message delivery schemes used by existing protocol[3] can be used in our mechanism.

To develop a joint scheduling and transmission modeassignment scheme, we introduce a new node model so thatwe can formulate the problem as a network utility maximiza-tion problem. We then apply the layering as optimization

decomposition technique [10] to decompose the linearprogramming optimization into several subproblems, andeach layer corresponds to a decomposable subproblem. Thetheoretical decomposition motivates us to develop practicalcross-layer optimization algorithm. In our algorithm, eachsource determines the instantaneous data rate injected intothe network based on the current network state, and then,a feasible set of links is selected to transmit at the currenttime. Both procedures adjust to each other to optimize thenetwork utility function.

I I . R ELATED W ORKS

With the rising demand of bandwidth under limitedavailable spectrum, intelligent resource allocation schemein wireless networks has received substantial attention.Scheduling, which selects a set of links to be active withoutconict, is an important issue in allocating the bandwidthresources. The scheduling problem is in general NP-hard [4],and lots of sub-optimal scheduling solutions are proposed.There have been some works studying the cross-layer issueon congestion and scheduling in wireless networks. Thework in [11] analyzes the effect of imperfect schedulingon congestion control in multi-hop wireless networks, andit shows that the cross-layer approach outperforms thelayered approach. [12] proposes the joint approach of queue-length based scheduling and congestion control in cellularnetworks, where the channel may vary according to time

or according to receivers. The work in [13] describes adistributed scheduling algorithm and a congestion controlmechanism to achieve the approximate optimal solution.Unfortunately, the authors consider the specic one-hopinterference model, which may not be applicable in a generalnetwork. The work in [14] studies the joint problem of mul-tipath routing and link-level reliability in multi-hop wirelessnetworks. The authors develop a decentralized schedulingpolicy which selects an appropriate channel code rate foreach link to cope with different degrees of data reliabilityamong the different links. The works in [15], [16], [17], [18],[19] study the control in multi-channel multi-radio wireless

networks. The works in [15], [16] present mixed-integer lin-ear programming models for the joint of congestion control,routing, and scheduling in multi-channel wireless networks.However, solving the linear programming is NP-hard, andno algorithm was proposed. [17] proposes a distributedscheduling algorithm in multi-channel wireless networks.[18] proposes a cross-layer optimization algorithm, whichrelies on the scheduling algorithm in [17] as lower-layersolutions. The work in [19] considers the same problem as[18], and it presents a new tuple-based network model tofacilitate decoupling the optimization on different layers. Allof the above works do not consider network coding.

Some works consider the scheduling problem with net-work coding with various objectives in relay-based cellularnetworks. In relay-based cellular networks, relay stationforwards downlink trafc to user and uplink trafc to basestation. Thus, many coding opportunities may exist at relay




3

station. As the transmission rate is bounded by the minimumrate among receivers, coding too many native packets togeth-er may not be benecial. [20] considers this tradeoff, andproposes a scheduling algorithm to specify which packetsshould be coded by the relay station. [21] considers thetradeoff between reducing packet delay and saving energy.To reduce energy consumption, a node should code as muchas possible. The transmission of a packet may have tobe delayed to wait for coding opportunity. Therefore, [21]proposes an opportunistic scheduling to determine whetherthe relay station should transmit (coded or non-coded)packet or wait at a certain time slot. [22] considers that therelay station applies network coding to reduce the numberof retransmissions, and proposes a scheduling algorithmto determine which packets the relay station should code.

[23] jointly considers the power control, channel allocation,and link scheduling problem, and proposes an opportunisticresource scheduling algorithm. The work in [24] studies thescheduling problem for broadcast trafc with network cod-ing in relay-based networks. We can see that different worksconcern different optimization objectives. [23] considers thesame objective as our work. However, [23] does not considerthe buffer overhead at a user node, which is particularlyimportant for cellular networks.

Many works study scheduling with network coding inmulti-hop wireless networks. The works in [25], [26], [2]analyze the theoretical throughput gain obtained by network coding in wireless networks. [27] formulates the joint con-gestion control, routing, and scheduling as a linear program-ming problem, while no algorithm was proposed to solve theproblem. [5] proposes a scheduling policy with network cod-ing. Besides network coding, the scheduling policy proposedby [28] also considers the energy consumption on each link,the packet loss probability and the transmission rate on eachlink. If we do not consider energy consumption and packetloss probability, the proposed scheduling scheme is reducedto the algorithm in [5]. [2] introduces k-tuple coding, and2-tuple coding is the same as COPE-style coding. Thescheduling policy used in [2] is the same as that in [5]when considering 2-tuple coding. [1] considers pairwise

intersession network coding (PINC), which is different fromthe COPE-style network coding model. [29] studies thetradeoff between delay and throughput with network codingin multi-hop wireless networks. Nevertheless, the bufferissue was not mentioned in the above works.

III. M ODEL AND A SSUMPTIONS

We consider a multihop wireless network with the set of nodes N . Let L be the set of links, and each link l = ( i, j ) L denotes that node j can successfully receive the data fromnode i when there is no interference. Let F denote the set of trafc ows. Following [11], [30], [31], each ow is servedby a single path, and the path is predetermined. Let s(f )and d(f ) be the source and the destination of the ow f ,respectively. If f goes through intermediate node i, denote pf (i) and sf (i) as the predecessor and successor of i on

the path carrying f , respectively. Based on the routes of thetrafc ows, we can determine all the coding opportunitiesat each node. For example, given a node i carrying two owsf 1 and f 2 , if pf 1 (i) = sf 2 (i) and pf 2 (i) = sf 1 (i), node ican code the packets of f 1 and f 2 . It is possible that nodei can also code f 1 with another ow f 3 , apart from f 2 . Inorder to clearly dene each coding opportunity, we introducethe denition of coding structure . If node i can code owsf 1 and f 2 with the next hops u and v, respectively, wehave a coding structure = {i, [u ; v], [f 1; f 2]} at nodei . denes a pair of native links, {(i, u ), (i, v )}, calledcoding link . It is possible that there are multiple codingstructures at node i. For instance, in Fig. 2, there are twocoding structures at node 2, 1 = {2, [1;3], [f 3; f 1]} and2 = {2, [1; 3], [f 3; f 2]}. 1 tells that Node 2 can code f 3and f 1 , and the next hops of f 3 and f 1 are Node 1 andNode 3, respectively. 1 and 2 specify the same next hopinformation but different trafc ows. Let (i) be the setof coding structures at node i. We write f if it is oneof the two ows in coding structure .

We assume that time is divided into slots. Following [5],let M denote the set of feasible scheduling decisions, orschedules at a certain time slot. Each element of M denes(1) the links or coding structures that are active in the timeslot, (2) the ows that are carried on the active links andcoding structures, and (3) the rates of the ows being carried.For instance, Fig. 1 shows the feasible schedules of three

time slots. Link (1, 2) carries f 1 in Slot 1, link (3, 2) carriesf 2 in Slot 2, and coding structure {2, [1; 3], [f 2, f 1]} is activein Slot 3.

We denote by r f l (M ) the rate of native link l serving f under a feasible schedule M . Denote by r i, (M ) the rateof coding structure at node i under schedule M . The link rate depends on the specic interference model [32]. In theprotocol interference model, a transmission on link (i, j ) atthe negotiated rate is successful if none of the nodes in theinterference range of j is transmitting. Thus, r f l (M ) is eithera xed rate or zero under the protocol interference model.If we consider the physical layer interference model, thedata link rate depends on the SINR at the receiver, whichis often approximated by the Shannon formula. The rateof a link may be different under the different schedule.We denote by R the feasible rate region. Each elementin R is a rate vector r(M ), containing all r f ( i,s f ( i )) (M )and r i, (M ), which is yielded by a feasible schedule M .In other words, R includes the rate vectors produced byall the possible feasible schedules in M . Without contextambiguous, we use r R to denote a feasible rate vectorwhich is determined by a feasible schedule.

Let (f ) be the input rate of the ow f F , which fallsin the region of (0, f ], and we assume that f is known inadvance [11], [18]. Dene the utility function for ow f asU f ( f ), which reects the level of satisfaction of ow f when its data rate is f . Following [11], U f () is assumed tobe strictly concave, non-decreasing and twice continuouslydifferentiable on (0, f ]. Our algorithm aims at maximizing




4

1 2 3 4

f 1

f 2

f 3

Fig. 2. An illustration for coding structure.

the network utility by jointly considering congestion control,transmission mode assignment, and scheduling.

IV. C ROSS -L AYER O PTIMIZATION

In this section, we rst describe the existing scheduling

scheme in wireless networks with network coding [2], [5].Since the existing scheduling scheme does not consider thebuffer issue, we introduce transmission mode assignmentprocedure and propose a new node model. Afterwards,the problem formulation is presented. We then develop asub-optimal cross-layer optimization algorithm. Finally, wetheoretically analyze the input rate region supported by theproposed scheduling policy.

A. Existing scheduling with network coding

A scheduling policy is dened as an algorithm thatchooses a feasible schedule M M in each time slot t [5].We denote by q f i (t) the number of packets of ow f inthe queue of node i at the beginning of time slot t. Thescheduling policy in [5] is as follows.

M (t) = arg maxM M

i f

q f i (t) q f s f ( i ) (t) r

f ( i,s f ( i )) (M ) ,

(1)The stability region of the network is the set of all

arrival rate vectors that can be supported while ensuringthat all packet queues in the network remain nite. [2],[5] show that the scheduling policy shown by (1) stabilizes

the network for all arrival rate vectors inside . Denote byM code the set of feasible schedules that considers network coding and M no code by that without network coding.We can say that M no code is a subset of M code , andsome schedules in M code may not be feasible when notconsidering network coding. Refer to Fig. 1, any two linksinterfere with each other. A feasible schedule in M codecan contain two links (2, 1) and (2, 3), while any feasibleschedule in M no code cannot.

By using (1), a node cannot know in advance whichtransmission mode the next hop will use to transmit a packetsent by itself. Considering the stochastic trafc model, itis possible that Node 2 has received lots of packets of f 1 but no packet of f 2 in Fig. 1. Let us assume thatq f 12 (t ) > q

f 11 (t) > q

f 23 (t). When q

f 22 (t ) = 0 , according to

(1), M = {(2, 3)} since q f 12 (t) is the largest. Node 2 willtransmit traditionally the Head of Line (HoL) packet of f 1

at time t . We assume that the transmission rate of each link in Fig. 1 is the same. When q f 22 (t) > 0, node 2 can code thepackets from f 1 and f 2 , and thus q

f 12 (t)r

f

(2 ,3) + q f 22 (t)r

f

(2 ,1)is the largest. In this case, the HoL packet of f 1 would betransmitted being coded with another packet of f 2 . That isto say, a node does not know which transmission modelwould be assigned for the buffered packets until they arescheduled. Thus, the node should keep each packet until thenext hop completes transmitting the packet, so as to assureeach coded packet would be decoded. In particular, when theaverage data rates of two ows differ a lot, many packets of a ow would be probably transmitted traditionally, such thatlarge unnecessary buffer is required by network coding. Thisis undesirable because the node will drop some new datapackets due to buffer overow. Consequently, we propose

the transmission mode pre-assignment procedure.

B. Node Model

In order to reduce the buffer size, this paper introducesthe procedure of transmission mode pre-assignment . Aftera node receives a packet, it decides immediately whetherthe packet should be transmitted in a coded manner ortraditionally. If the packet would be transmitted traditionally,the previous hop does not have to memorize the packet then.To achieve the above practice, we propose a node model.A node would put packets of different statuses in differentqueues, indicating they are going to be handled in different

ways. That is, for each ow f that goes through node i, imaintains1) input queue for keeping incoming packets (denoted as

X f i )Packets in this queue have not been assigned a trans-mission mode yet. Packets here will be moved to oneof the output queues after the transmission mode isdetermined.

2) output queue for packets to be sent out traditionally(denoted as W f i )Packets in this queue have been determined to betransmitted in a traditionally manner, and are waitingfor its turn to be sent out to the channel. i can informits neighbors to forget these packets.

3) output queue for packets of each coding structure where (i) (denoted as Z i, )The packets of ow f moved to this queue are tobe transmitted in coded manner. When Node i move apacket of f to Z i, , a new code packet will be formedimmediately if there is a native packet of another owf in Z i, . In other words, Z i, contains two kindsof packets. One is the coded packet, and another one isthe native packet of a ow waiting to be coded together.All the packets are waiting for its turn to be sent outto the channel.

Both output queues push trafc to physical link (i, s f (i)) .The transmission mode assignment involves deciding towhich output queue ( W f i or Z i, , f ) a packet from theinput queue ( X f i ) should be put. A wise decision should not




5

32

12

22

12

W

32

W

22

W

12, Z

22, Z

2

32,

1

32,

2

22,

32

1

12,

12

22

22

r

22,r

12,r

32

r

12

r

Fig. 3. Node model.

overwhelm any output queue while maximizing the utility.To model the relation between the queues, we represent eachqueue as a virtual node. We put a virtual link from one queueto another one if packets can be moved in that manner. Eachvirtual link is associated with a rate that tells the averageratio of the packets being moved to each output queue.

Fig. 3 shows the model of node 2 in Fig. 2. In the gure,a square box is a queue, and a virtual link is representedas a dashed arrow. Node 2 forwards three ows, and so ithas three input queues. The coding structure 1 containsf 1 and f 3 , and so there are two virtual links from X 12 toZ 2, 1 and from X 32 to Z 2, 1 , respectively. Similarly, 2contains f 2 and f 3 , and there are two virtual links from X 22to Z 2, 2 and from X 32 to Z 2, 2 , respectively. It is obviousthat the optimal transmission mode assignment should move

the same number of packets of f 1 and f 3 to Z 2, 1 .Note that all the packets of the source node of f are

transmitted traditionally, and so the proposed node model isnot applied at s(f ). In other words, there is one output queueof f at s(f ). When the upper layer injected new packets,all the packets are immediately moved to the output queueW f s ( f ) .

Let f i, denote the rate on the virtual link from X f i to

Z i, . For f and f , we should have f i, = f

i, inthe optimal solution. Let W f i denote the queue containingthe packets to be transmitted traditionally. The rate of thevirtual link from X f i to W

f i is

f i . The rate of the trafc

leaving input queue X f i is thus ( i ) ,f f i, + f i . Toassure the stability of the system, is bounded by the rateon the physical links. For instance, f i, should not be largerthan r i, ; otherwise, Z i, would be innitely large. Denote

by the feasible rate region for , which will be denedin Section VI, based on the throughput-optimal and stabilityarguments.

C. Problem Formulation

Based on the proposed node model, the problem con-cerned in this paper is formulated as (2)-(6). Our objectiveis to maximize the sum of the utility functions of the datarates for all ows. (3) makes sure the rate of incoming trafcto queue X f i is no larger than the rate that trafc leavesthe queue; otherwise, the input queue would go to innity.Similarly, (4) ensures that the rate of incoming packets of f to queue Z i, does not exceed the rate on coding structure. (5) assures that the input rate to W f i is no larger than itsoutput rate. In other words, (3), (4), and (5) guarantee thatthe queues of each node would not be innity.

The optimal solution for (2) tells the maximum datarate of each ow and the data rate on each link or eachcoding structure. We would like to use Lagrangian dualdecomposition method to solve our problem. Correspondingto constraints (3)-(6), we dene Lagrange multipliers f i,in , f i,,out ,

f i,out , and

f s ( f ) ,out respectively [33]. Later, we

will see that these multipliers reect the queue sizes. TheLagrangian is (9), and the dual of problem (2) is (10) whereG f ( ) is a function of f , V 1 ( ) is a function of i and f i, , and V 2 ( ) is a function r

f i and r i, .

min D ( ), (10)

where

D ( ) = max ,,r L( , , r, )= f F max 0




6

maximizef F

U f ( f ) (2)

subject to :

( p f ( i )) ,f

r p f ( i ) , + rf pf ( i )

( i ) ,f

f i, + f i i = s (f ), f (3)

f i, r i, i, (i), f (4)

f i rf i i = s (f ), f (5)

f r f s ( f ) f (6)r R (7) (8)

L ( , , r, ) =

f U f ( f )

+ f,i = s ( f ) f i, in ( i ) ,f f i, + f i ( p f ( i )) ,f r p f ( i ) , r f p f ( i )+ i, ( i ) ,f

f i,, out r i,

f i,

+ f,i = s ( f ) f i, out r

f i

f i

+ f f s ( f ) ,out r

f s ( f ) f

r R

(9)

f i, in (t + 1) =

f i, in (t) +

f i ( pf ( i )) ,f r p f ( i ) , (t) + r

f p f ( i ) (t) ( i )

f i, (t )

f i (t )

+

(13)

f i,, out (t + 1) = f i,, out (t ) +

f i,, out

f i, (t) r i, (t )

+(14)

f i, out (t + 1) = f i, out (t ) +

f i, out

f i (t ) r

f i (t)

+(15)

f s ( f ) ,out (t + 1) = f s ( f ) ,out (t) +

f i, out f (t) r

f s ( f ) (t )

+(16)

f (t) = arg max0




7

number of packets coming at X f i at time t. Therefore, f i, in (t + 1) calculated by (13) implies the the size of X

f i at

time t + 1 . Similarly, f i,

(t) denotes the number of packetsof ow f arriving in Z i, at time t , while r i, (t ) denotes thenumber of coded packets sent out at t . Therefore, f i,, out (t)implies the size of Z i, at time t. For the same reason, f i, out (t) reects the size of W

f i at time slot t.

There are three categories of variables in (17)-(19): the setof ow data rate, , transmission mode assignment decision, , and the transmission schedule, r. In each iterative step,the optimal solutions of these variables can be found usingthe lagrangian multipliers accordingly. In other words, (17),(18), and (19) provide the policies for congestion control,transmission mode assignment, and scheduling based on thecurrent backlog of each queue.

We now proceed to describe our algorithm. At the be-ginning of each time slot, some new packets may arrive inX f i . Each node decides the transmission mode (traditionallyor coded) for each packet in X f i such that the packets inX f i are transported to a certain output queue. Then, pf (i)can drop the packets which will be transmitted traditionallyby i. After the transmission mode assignment procedure,a certain feasible schedule is selected, and then a set of links transmit at the current time slot. The transmissionschedule at the current time slot would affect the queuesize at each node at the next time slot, and then the datarate injected into the network at the next time slot would

be adjusted. In the next time slot, the whole procedurewill be executed again. The procedures of ow control,transmission mode assignment, and transmission schedulingcooperate with each other to improve network throughputperformance. Each time slot is divided into three phases. Inthe rst phase, the source node determines the amount of new packets injected into the network. In the second phase,node i decides the transmission mode (traditional or coded)of each newly received packet. This involves moving packetfrom the input queue ( X f i ) to a certain output queue. In thethird phase, a feasible schedule is selected to allow a set of links to transmit data packets during the whole time slot.

When the context is clear, we use X f i (t ) and W f i (t) to

denote the queue sizes at time slot t . Let Z f i, (t) denote thenumber of packets for ow f contained in queue Z i, at timet . For instance, if Z i, contains m coded packets and l nativepackets of f at time t , Z f i, (t) = m + l , while Z

f

i, (t) = m ,where f . In other words, Z f i, (t ) is determined basedon the current status of output queue Z i, . As mentionedbefore, we consider lagrangian multipliers in (13)-(15) asthe queue sizes. We thus rewrite (17)-(19) as follows.

(20)-(22) describe the policies on three layers: congestioncontrol, transmission mode assignment, and scheduling. (20)species how to determine the data rate injected into the net-work in phase 1 of time slot t . Given U f ( f ), we can calcu-late an optimal f to maximize U f ( f ) f s ( f ) W f s ( f ) (t ) f .In other words, (20) denotes a ow control policy, where f s ( f ) is a factor for congestion control. U f ( f ) is normallya monotonically increasing function of f , and thus, smaller

f s ( f ) implies that more packets would be injected intonetwork. f s ( f ) should be set according to the buffer size.For instance, if each node in the network has a largerbuffer size, we can set smaller f s ( f ) to allow more packetsinjected into network. On the other hand, the larger f s ( f )is suitable for the smaller buffer size of each node. Ac-cording to (21), we should move the packet from X f i tothe output queue containing the least number of packetsfor f . In the case that Z i, and W

f i contain the same

number of packets for f , we prefer to move the packet toW f i . (22) presents the scheduling policy to determine whichlinks should transmit concurrently at time t. Based on ourtransmission mode assignment scheme, Z f i, (t) must not belarger than W f i (t). Under the stochastic trafc model, it ispossible that Z

i,(t ) contains all native packets of ow f

but no packet of another ow f . In this case, (Z f i, (t ) X f s f ( i ) (t)) r i, + ( Z

f

i, (t ) X f

s f ( i ) (t )) r i, must not be largerthan (W f i (t) X

f s f ( i ) (t)) r

f i +( W

f

i (t) X f

s f ( i ) (t)) rf i , where

r i, = min {r f i , rf

i }. This implies that our schedulingscheme would not schedule a native packet in Z i, tobe transmitted. The joint solution of transmission modeassignment and the scheduling policy intentionally assignsome native packets in Z i, waiting to be coded in the future.Moreover, the packets in Z i, must be transmitted in a codedmanner, the channel resources would be efciently utilized.The outline of our algorithm is shown in Algorithm 1.

Algorithm 1 Cross-layer optimization algorithm1: for Each time slot t do2: for each ow f going through i do3: if i = s (f ) then4: if U ( f ) W f i (t ) f 0 for any f (0, f ]

then5: set f (t ) = 06: else7: inject new packets containing f amount of

data.8: for each packet in X f i do9: move the packet to the output queue with the

smallest size10: Apply Greedy Maximal Scheduling framework to

nd a feasible schedule based on (22)

As mentioned in Section III, each vector r actuallycorresponds to a feasible schedule. (22) actually representsa scheduling policy. We rewrite (22) as

Finding the optimal solution of (23) is NP-hard [4]. Manypractical scheduling solutions have been proposed. One of the most well known sub-optimal scheduling policies isthe Greedy Maximal Scheduling (GMS) policy [4]. GMSschedules links in decreasing order of the link weightconforming to interference constraints. According to thepolicy of (23), the weight of each link should correspondto the queue size and the rate of that link. Generally, given




8

f (t) = arg max 0 0, Z i,must contain the coded packets from two ows. Therefore,we have

r f i, (t) = r i, (t). (28)

X f i (t +1) is calculated as two parts: the remaining packetsin X f i which are not transmitted at time slot t, and theamount of packets for f arriving at i at time slot t. Leteach element in be upper bounded by a positive number.For instance, we set f i (t) c( i,s f ( i )) , where ci,s f ( i ) is themaximum supported link rate between i and sf (i). Sinceeach element in r and is upper bounded by a positiveconstant, according to Lemma 4.3 in [35], we have (29).

In (29), B1 , B2 , B3 , and B4 are constant positive num-bers. As strictly falls in the stability region , there exists

also inside of , such that each element in is largerthan the corresponding element in , where is a smallpositive number. Denote by f i the rate of f carried on link (i, s f (i)) and by f i, the rate of the coded data carried inthe coding structure at node i. We can identify f i and i, corresponding to , and so we have

f s ( f ) = f + (30)

According to (21) and (22), we have (31) and (32),respectively.




9

L X (t), W (t), Z (t) =f,i = s ( f )

X f i (t)2 + W f i (t)

2 +( i )

Z f i, (t)2 +

f

W f s ( f ) (t )2

(26)

X f i (t + 1)2 X f i (t)

2 B 1 + 2 X f i (t) ( ( j ) rf j, + r

f j (t )) ( ( i )

f i, (t) +

f i (t))

W f i (t + 1)2 W f i (t)

2 B 2 + 2 W f i (t) f i (t ) r

f i (t)

Z f i, (t + 1)2 Z f i, (t)

2 B 3 + 2 Z f i, (t) f i, (t) r

f i, (t)

W f s ( f ) (t + 1)2 W f s ( f ) (t)

2 B 4 + 2 W f i (t) f (t ) rf s ( f ) (t)

(29)

i,f, ( i ) X f i (t) Z

f i, (t) i, +

i = s ( f ) ,f X

f i (t ) W

f i (t)

f i

i,f, ( i ) X f i (t) Z

f i, (t)

f i, (t) + i = s ( f ) ,f X

f i (t) W

f i (t)

f i (t)

(31)

i, i f Z f i, (t) X

f s f ( i ) (t) i, + i,f W

f i (t ) X

f s f ( i ) (t)

f i

i, i f Z f i, (t) X

f s f ( i ) (t) r i, (t) + i,f W

f i (t) X

f s f ( i ) (t) r

f i (t)

(32)

We then calculate (33). By (29), we have the inequality(a), where B is a constant positive number. Based on (28),we have equality (b). By (31) and (32), we have inequality

(c) in (33). Since X f d ( f ) (t ) = 0 for any t , where d(f ) is the

destination of f , we have equality (d).Finally, we calculate the Lyapunov drift as in (34). We

have shown that our policy satises the conditions of Lemma4.2 in [35], and therefore, our policy stabilizes the network for all arrival rate vectors that are strictly interior to thestability region.

V. S IMULATION R ESULTS

In this section, we evaluate the performance of our pro-posed algorithms via packet level simulation. We comparethe proposed algorithm with the method [2], [5] presented

in (1). [8] describes the disparity in the buffer size usedin various research platforms. The buffer keeps both thepackets waiting to be transmitted and the packets waiting fordecoding future coded packets. If the buffer at a node is full,the node will drop the new incoming packet in default [7].Another option is to drop a sent packet to accommodatethe new incoming packet. If the sent packet dropped isneeded for decoding later, more bandwidth resources willbe wasted. Therefore, dropping new incoming packets ismore appropriate. For simplicity, each link in the network has the same transmission rate 1Mbps. In our simulation, weuse the objective of maximizing network throughput, that is,U ( f ) = f . in Algorithm 1 is a factor for congestioncontrol. We apply the commonly used 2-hop interferencemodel [4] in our simulations. Each second is divided into100 time slots, and each link can transmit a packet in eachtime slot. The simulation runs 500 seconds, and the average

throughput is counted as the amount of data received by thedestinations divided by 500 seconds.

We randomly deploy 80 nodes in an area of

1000m*1000m. The transmission range is 200m. We nd12 source-destination pairs, and then deploy two ows withopposite direction on each pair. There are totally 24 owsin the network. For each pair of source-destination, theaverage data rate of one direction is twice of that of theother direction. Here the data rate means the amount of data injected from the upper layer, and the amount of datagetting into routing layer depends on the specic congestioncontrol scheme. We conduct simulations on two data arrivalmodes: poisson and uniform. We produce different instancesfor each scenario, and the results are the average on vedifferent instances. We rst apply the default ns-2 buffer sizeof 50 packets in each node. We set

= 0.1

which impliesthat the source node will not inject new data packets into thenetwork if the buffer size is larger than 10, which is calledthe congestion window size.

Fig. 4 shows the throughput and packet loss ratio withvarying the average data rate of the ows. The data arrivalfollows poisson distribution. When the data rate is small,the network can support all the injected packets, and thus,the throughput with the existing method differs only a littlewith the proposed method, as shown in Fig. 4(a). As theaverage data rate increases, some packets would be droppeddue to buffer overow. Since the existing method requiresa larger decoding buffer, the throughput decreases due topacket dropping. Although the throughput of the proposedmethod reduces too, the gap between the throughputs of the two methods becomes larger as the data rate increases.From Fig. 4(a), when the data rate changes from 0.2 to 0.25,




10

L X (t + 1) , W (t + 1) , Z (t + 1) L X (t ), W (t ), Z (t)

(a ) B + 2 f,i = s ( f ) X f i (t) ( j = p f ( i ) , ( j ) r

f j, + r

f j (t )) ( ( i )

f i, (t) +

f i (t))

+ W f i (t) f i (t) r

f i (t ) + ( i ) Z

f i, (t)

f i, (t) r

f i, (t)

+2 f W f s ( f ) (t ) f (t) r

f s ( f ) (t )

= (b) B + 2 f W f s ( t ) (t) f (t )

2 i, i f Z f i, (t ) X

f s f ( i ) (t) r i, (t) + i,f W

f i (t) X

f s f ( i ) (t) r

f i (t )

2 i,f, ( i ) X f i (t ) Z

f i, (t)

f i, (t) + i = s ( f ) ,f X

f i (t ) W

f i (t)

f i (t )

(c) B + 2 f W f s ( t ) (t) f (t )

2 i, i f Z f i, (t ) X

f s f ( i ) (t) i, +

i,f W

f i (t ) X

f s f ( i ) (t)

f i

2 i,f, ( i ) X f i (t ) Z

f i, (t) i, + i = s ( f ) ,f X

f i (t) W

f i (t )

f i

= (d ) B + 2 f W f s ( t ) (t) f (t ) 2 f W

f s ( f )

f s ( f ) + f X

f s f (s ( f )) (t) i,

B + 2 f W f s ( t ) (t) f (t ) 2 f W

f s ( f )

f s ( f )

(33)

( t) E L X (t + 1) , W (t + 1) , Z (t + 1) L X (t), W (t), Z (t ) |L X (t), W (t), Z (t )

B + 2 f W f s ( t ) (t) f 2 f W

f s ( f )

f s ( f )

= B 2 f W f s ( f ) (based on (30))

(34)

the throughput of our policy reduces a little. We apply thesame congestion control policy in the existing schedulingmechanism. With the congestion control, the total numberof packets injected into the network is almost the same.Thus, the throughput does not change a lot. This implies thatwhen the data rate is too large, congestion control wouldguarantee the stable throughput of the network. We alsoobserve that the stable throughput of the existing methodis much lower than that of our method. Fig. 4(b) shows thechange of packet loss ratio as data rate varies. Note thatpacket loss means that packets are dropped due to overow.As the data rate increases, the packet loss ratio increases,and the packet loss ratio of the existing method grows fasterthan that of our method. We observe that the packet lossratio of our proposed method does not grow a lot when thedata rate is larger than 0.2, which is because the number of packets injected into the network does not increase by usingcongestion control. Fig. 5 shows the simulation results withthe uniform data arrival distribution, and the performanceof our algorithm is similar as that with poisson data arrivalmodel.

In both Fig. 4 and Fig. 5, channel is assumed to be idealand each packet transmission is successful. We then simulatethe rayleigh fading channel and evaluate the performance of the two methods. We apply the poisson arrival model, andFig. 6 shows the simulation results. We observe the differentvariation trends for the throughput of the two algorithms in

Fig. 6(a). When the data rate is small, the network is notsaturated, the packet loss is mainly due to fading. Therefore,the throughputs and packet loss ratios of two algorithmsare almost the same. Since some packets are lost due tofading, as compared with the links without fading, bufferoverow occurs at a higher data rate. In other words, alarger data rate is required to saturate the network whenconsidering fading. This explains that the throughput of ouralgorithm with fading is lower than that without fading.Moreover, the maximum throughput of our algorithm withfading happens at a larger data rate as compared with thatwithout fading. On the other hand, the network is saturatedat a small data rate with the existing method. Therefore, thethroughput decreases as the increase of data rate, and thepacket loss at the large data rate is mainly due to bufferoverow. Fig. 6(b) veried that the packet loss ratio of ouralgorithms grows a little bit. Since throughput of our policyincreases a little bit as data rate increases, the number of packets being transmitted increases a little. Moreover, thepacket loss is mainly due to fading under this situation, andthus, the packet loss ratio grows a little. Afterwards, we letthe successful transmission ratio on each link randomly fallin [0.85, 0.99], and Fig. 7 shows the simulation results. For

the same reason, the performance change is similar as thatwith rayleigh fading channel.

Afterwards, we study the performance when the linksare of different rates. We let the transmission rate of each




11

link follow the uniform distribution [1, 10]Mbps. Since thetransmission rate is larger, we set the buffer size of eachnode to be 1000 packets, and the congestion control windowsize to be 200 packets. Fig. 8 shows the simulation results.Performance analysis in multi-rate scenario is more compli-cated than that in single-rate. When the data rate is small,the backlog may be smaller than the transmission rate, andso, bandwidth resources would not be fully utilized. On theother hand, the larger data rate may introduce more packetsdropped, which reduces network throughput. This is whythat we observe that the throughput does not have an obvioustrend. Generally, our algorithm yields higher throughput andlower packet loss ratio.

We also test the performance of our algorithm as thebuffer size and congestion control window size change.

When the number of packets in the output buffer of thesource node is larger than the congestion window size,the source node would not inject new packets from theupper layer. The data rate is set to 0.25Mbps. We setthe congestion window size to be 20 packets, and Fig. 9shows the simulation results with change of buffer size.As less packets would be dropped by using larger buffersize, the throughput increases as the buffer size increases.When the buffer size is large enough, there is almost nopacket dropped, and so the throughput of our algorithmis almost the same as that of the existing algorithm. Weobserve that the throughput of our algorithm is much largerthan that of the existing algorithm at several instances. Thisshows that buffer space plays a more signicant impacton the existing algorithm than our algorithm. We then setthe buffer size to be 100 packets, and Fig. 10 shows thesimulation results as congestion window size changes. Whenthe congestion window size is smaller, less packets would beinjected into the network, so that the network would not beheavy-loaded and less packets are dropped due to overow.Therefore, the throughput is higher and packet loss ratio islower when the congestion window size is smaller. Withthe larger congestion control window size, more packets areinjected into the network. The existing algorithm requiresmore buffer space than our algorithm, so that more packets

are dropped. We thus observe that the throughput of theexisting algorithm reduces more quickly than that of ouralgorithm.

Generally, under the limited buffer space, the proposedalgorithm can effectively reduce buffer overhead intro-duced by network coding through transmission mode pre-assignment procedure. In particular, under the heavy-loadednetwork, the proposed algorithm produces higher throughputand smaller packet loss ratio compared with the existingalgorithm.

VI. C ONCLUSION

This paper studied scheduling issue with network codingin wireless networks. Particularly, the space overhead issueintroduced by network coding was studied, since each nodenormally has a nite buffer space and packets may be

0.1 0.15 0.2 0.250.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

Average data rate (Mbps)

A v e r a g e

T h r o u g

h p u

t ( M b p s

)

Proposed methodExisting method

(a) Average throughput.

0.1 0.15 0.2 0.250

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04


P a c

k e

t l o s s r a

t i o


(b) Average packet loss ratio.

Fig. 4. Poisson arrival.

dropped due to overow. To reduce packet loss ratio and im-prove network throughput, this paper proposed a scheduling

scheme comprising transmission mode pre-assignment pro-cedure and transmission scheduling procedure. Simulationresults demonstrated that space overhead introduced by net-work coding signicantly affect network performance, andthe proposed scheduling method outperforms the existingmethod.

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0.1 0.15 0.2 0.250.7

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0.03

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14

95 100 105 110 1150.7

0.8

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t ( M b p s

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95 100 105 110 1150

0.01

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0.04

0.05

0.06

0.07

0.08

Buffer size

A v e r a g e

T h r o u g

h p u

t ( M b p s

)



Fig. 9. Impact of buffer size.

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Ronghui Hou obtained her B.Eng., M.Eng., andPh.D. degrees in Communication Engineeringfrom Northwestern Polytechnical University in2002, 2005, and 2007, respectively. She workedas a Post-Doctoral Fellow in the Departmentof Electrical and Electronic Engineering of theUniversity of Hong Kong between 2007 and 2009.Since December 2009 she has been with XidianUniversity, China, where she is currently associateprofessor at Department of TelecommunicationEngineering. Her research interests include net-

work quality of service issues, routing algorithm design, and wirelessnetworks.

15 16 17 18 19 200.8

0.9

1

1.1

1.2

1.3

1.4

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A v e r a g e

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)



15 16 17 18 19 200

0.01

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0.06

Congestion control window size

P a c

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Fig. 10. Impact of congestion control window size.

King-Shan Lui (S00-M03-SM14) received herPhD in Computer Science from the Universi-ty of Illinois at Urbana-Champaign, and she is

now an Associate Professor in the Departmentof Electrical and Electronic Engineering in theUniversity of Hong Kong. Her research interestsinclude network protocols design and analysis,wireless networks, smart grids, and Quality-of-Service issues.


15/15


15

Jiandong Li (SM05) was graduated from XidianUniversity with Bachelor, Master and Ph.D de-grees in Communications and Electronic Systemrespectively in 1982, 1985 and 1991. He hasbeen with Xidian University from 1985, wherehe is professor from 1994 and Dean of Schoolof Telecommunication Engineering from 1997,respectively. He was a visiting professor at Schoolof Electrical and Computer Engineering in Cor-nell University between Jan. 2002 and Jan. 2003.His current research interests include wireless

communications, network protocol, and algorithm design.

Documents

06736091Joint Congestion Control and Scheduling in Wireless Networks with Network Coding