1538 IEEE SENSORS JOURNAL, VOL. 17, NO. 5, MARCH 1, …thealphalab.org/papers/A QoS-oriented High-Efficiency Resource... · Medical Image Computing, ... speciﬁed in IEEE 802.15.4

1538 IEEE SENSORS JOURNAL, VOL. 17, NO. 5, MARCH 1, 2017

A QoS-Oriented High-Efficiency ResourceAllocation Scheme in WirelessMultimedia Sensor Networks

Lei Guo, Zhaolong Ning, Qingyang Song, Lu Zhang, and Abbas Jamalipour, Fellow, IEEE

Abstract— Deadline constrained packet scheduling andtransmission are important in real-time multimedia applications.This is because packets missing their deadlines would becomeuseless and are frequently dropped, which seriously degradethe quality of service (QoS). As the utilization of Internet ofThings has become mature, multimedia data transmission isa key component to promote the QoS of citizens. To fulfillthe QoS requirement in wireless sensor networks (WSNs) withmultimedia content, the combination of multiple transmissionmethods is encouraged for packet forwarding, including con-ventional network coding, analog network coding, plain routing,and direct transmission (i.e., no-relaying, NR). The diversity oftransmission method is helpful to lower packet dropping proba-bility, while complicating the packet transmitting and schedulingprocess instead. Therefore, we first introduce an exhaustivesearch method to obtain the optimal scheduling sequence andcorresponding transmission method for deadline constrainedmultimedia transmissions in WSNs. With the objective ofpromoting computing efficiency for the formulated problem, wethen propose two heuristic methods based on the Markov chainapproximation and the dynamic graph, respectively. Simulationresults illustrate that our methods can effectively reduce packetdropping probability and simulation time, so that QoS ofindividuals can be promoted.

Index Terms— QoS, packet dropping, scheduling, adaptivetransmission.

I. INTRODUCTION

THE past decades have witnessed the rapid growth ofcomputational capability and various breakthroughs in

wireless technologies. Based on these developments, a variety

Manuscript received October 16, 2016; revised December 9, 2016; acceptedDecember 23, 2016. Date of publication December 28, 2016; date of currentversion February 17, 2017. This work was supported in part by the NationalNatural Science Foundation of China under Grant 61471109, Grant 91438110,and Grant 61502075, in part by the Fundamental Research Funds for theCentral Universities under Grant N150401002 and Grant DUT15RC(3)009,in part by the China Post-Doctoral Science Foundation Project underGrant 2015M580224, in part by the Liaoning Province Doctor StartupFund under Grant 201501166, and in part by the State Key Labora-tory for Novel Software Technology within the Nanjing University underGrant KFKT2015B12. The associate editor coordinating the review ofthis paper and approving it for publication was Prof. Giancarlo Fortino.(Corresponding authors: Zhaolong Ning; Qingyang Song.)

L. Guo, Q. Song, and L. Zhang are with the Key Laboratory ofMedical Image Computing, Northeastern University, Ministry Education,Shenyang 110819, China, and are also with the School of Computer Scienceand Engineering, Northeastern University, Shenyang 110819, China (e-mail:[email protected]).

Z. Ning is with the School of Software, Dalian University of Technology,Dalian 116024, China, and is also with the State Key Laboratory for NovelSoftware Technology, Nanjing University, Nanjing 210093, China (e-mail:[email protected]).

A. Jamalipour is with the School of Electrical and Information Engineering,University of Sydney, Sydney, NSW 2006, Australia.

Digital Object Identifier 10.1109/JSEN.2016.2645709

of services with strict delay requirements have emergedin commercial wireless networks, such as live-streamingmultimedia applications in mobile cellular systems, real-timesensing and control in wireless sensor networks (WSNs) andso on [1]. In these applications, packets have strict deadlineconstraints and must arrive at their destinations before theirdeadlines. Otherwise, they become invalid and are generallydropped, which degrade the quality of service (QoS).Therefore, how to meet the strict delay requirements in wire-less networks has drawn increasing attention nowadays [2].

Traditional WSNs mainly concerned scalar sensor networksfor physical phenomena measurement, for example the tem-perature, pressure, humidity, or location of objects, whose datastreams can be transmitted through low-bandwidth and delay-tolerant networks. In recent years, the research hotspot hastransferred to the networks that enable delivery of multimediacontent, such as audio and video streams and images, as wellas scalar data, which is defined as wireless multimedia sensornetworks (WMSNs) [3]. Since Internet of things (IoTs) withrich multimedia content have become an emerging paradigmfor the further expansion of ubiquitous computing in modernwireless communications to provide connectivity and mobility,WMSNs are gaining wide interest of researchers in recentyears [4], [5]. On one hand, the overall system throughputis desired to be increased by taking advantage of multi-userdiversity. On the other hand, fairness and QoS guaranteesrequire to be maintained for individual users, especially underthe circumstance of multimedia applications with strict delaydemands [6].

In order to decrease packet transmission delay in WMSNs,some effort has been made on different aspects, such as QoSbased routing mechanisms [7], deadline concerned queuingstrategies in relays [8], efficient access methods in MediaAccess Control (MAC) layer [9], and cross-layer optimizationalgorithms that not only consider the relaying method innetwork layer, but also the transmission rate in physical layersystematically [10]. Although some QoS features have beenspecified in IEEE 802.15.4 standard for WSNs, the open issueof end-to-end delay still remains. A cooperative MAC protocolfor real-time data transmission was investigated in [11], whichconcentrated on the beacon-enabled mode in star networktopology and can be viewed as a kind of supplement ofIEEE 802.15.4 standard. A multi-user setup for users withdelay QoS constraints has been studied in [12], and theresource allocation policy has also been derived for sum videoquality maximization.

1558-1748 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

GUO et al.: QoS-ORIENTED HIGH-EFFICIENCY RESOURCE ALLOCATION SCHEME IN WIRELESS MULTIMEDIA SENSOR NETWORKS 1539

Apart from the above work, network coding has attractedmuch interest as an orthogonal solution to reduce the transmis-sion delay in wireless networks. It is widely acknowledged thatconventional non-physical-layer network coding (CNC) cangreatly improve the network throughput when packet deadlineconstraints are not considered [13]. CNC takes the advantageof the broadcast nature of wireless channel. It can reducetransmission time by permitting a relay to encode at least twopackets, which are received separately from different sourcenodes, into one packet and broadcast it to destinations for thedecoding of the intended packets. Hence, CNC is also oneof the promising solutions tackling the packet transmissionproblem with deadline constraints in cooperative communi-cations. However, the decoding delay in CNC may be highif the destination nodes cannot receive sufficient packets fordecoding [14]. Therefore, CNC should be carefully employedin deadline constrained packet transmissions. Compared withCNC, analog network coding (ANC), as a type of physical-layer network coding (PNC), can further reduce transmissiontime by allowing two signals to be transmitted simultaneouslyfrom their source nodes and superpose at the relay [15].Nevertheless, ANC has more stringent restrictions on channelconditions and network topologies. Therefore, it is encouragedto integrate different transmission methods to fulfill theiradvantages.

For one thing, due to the diversity of transmission ratesand methods when supporting real-time services in cooperativeWMSNs, it is very challenging to design the packet schedulingand transmission schemes with low computational complexity.For another, it is also a great opportunity to decrease theend-to-end delay if we choose the most efficient transmissionmethod with an appropriate transmission sequence. Therefore,it is necessary to develop a QoS-oriented high-efficiencyscheduling and transmission scheme to minimize the packetdropping probability in multi-rate WMSNs. The contributionsof our work are as follows:• In order to deal with real-time transmissions in multi-

rate WMSNs, we propose an adaptive integration schemefor different transmission methods, including CNC, ANC,PR and NR. By formulating the forwarding method intoan optimization problem, we can select the optimal trans-mission methods and sequences of packets via exhaustivesearch.

• Due to the high computational complexity of the for-mulated optimization problem (O(N N )), we present aMarkov chain based approximation approach to get thenear-optimal solution by formulating optimization prob-lem into the form of maximum weighted configurationproblem.

• For the sake of reducing computational complexityfurther, we introduce the approach based on dynamicgraph, and solve the problem by constructing a graph toobtain the near-optimal solution, in which we choose theappropriate packet(s) for each transmission. The compu-tational complexity of the dynamic graph based approachis O(N4), which is polynomial.

The rest of this paper is organized as follows. In Section II,some related works are introduced. Section III formulates the

optimization problem by jointly combining different transmis-sion methods. In Section IV, we present three schemes toresolve the deadline-aware packet scheduling and transmissionproblem. Simulation results are shown in Section V, andSection VI concludes our work.

II. RELATED WORKS

Although some studies have been conducted for providingQoS to each individual in WSNs, space still exist for transmis-sion efficiency improvement, which motivates us to combinevarious kinds of forwarding methods in an adaptive method.As the research in WMSNs has gained high momentumthrough the combination of IoTs, the study of emerging codingmethods and their adaptive combination are recommended forinvestigation.

CNC was first designed to improve the network throughputand most related works focused on throughput maximization.Recently, some effort has been made to meet deadline con-straints of packet transmission through the utilization of CNCand PNC. Alvandi et al. [16] proposed a systematic method toanalyze the end-to-end delay performance in wireless networksand proved that CNC can reduce the packet delay. Li et al. [17]proposed another analytical method based on networkcalculus, and a generalized processor sharing schedulingscheme was studied to improve the network delay perfor-mance. However, these works mainly focused on the averagepacket delay and ignored the per-packet delay constraint,where the latter can be critical for packets of real-timeapplications in WMSNs.

Some work has been conducted for packets with strictdeadline constraints [18]–[23]. Generally speaking, most ofthe works concentrated on optimizing coding block size com-putation to decrease decoding delay. Larger block size meansmore packets are coded together in one transmission, whichcauses longer decoding delay at the same time. A monotonicitybased backward induction algorithm was developed in [18]to calculate the optimal block size in polynomial time.Zhan and Xu [19] studied the scheduling problem to minimizethe number of dropped packets, and an encoding algorithm wasinvestigated based on CNC. However, they assumed a fixedtransmission rate and ignored the possibility of using multi-rate transmission in wireless networks. An efficient algorithmwas proposed to determine the coding strategy and transmis-sion rate of each transmission in [20]. Unfortunately, the aboveapproaches are limited to single-hop broadcast channel, andthey may not work well in a multi-hop network.

In order to cope with the packet transmission delay in multi-hop wireless networks, Mao et al. [21] and Seferoglu andMarkopoulou [22] have designed some packet queue manage-ment schemes to reduce the queuing delay. Mao et al. [21]compared their queue management scheme based on a min-imum cost flow formulation with maximum weight packetfirst [22] and urgent packet first schemes, and proved the supe-riority of their scheme. In [23], an efficient relay placementalgorithm was proposed to find the optimal relay positions fordelay minimization in general relay-assisted wireless multicastnetworks when employing PNC protocol.


Although CNC and PNC have their special advantages indifferent network situations, their combination is not wellstudied especially for the delay sensitive networks. It can bebeneficial to allow different transmission schemes (includingCNC, PNC, PR, and NR) to be chosen on the same wirelesscommunication system according to the observed channelstate. This enlightens us to consider multiple transmissionschemes, and design an adaptive transmission method selec-tion scheme. In [24], an adaptive relaying method selectionscheme was developed for multi-rate wireless networks, butthe goal was to optimize the throughput without consideringdeadline constraints of packets. When aiming at meeting thedeadlines of packets, solutions become quite different andmuch more complex [25].

In this paper, we integrate transmission method selectionwith packet scheduling to deal with the deadline constrainedtransmission in cooperative WMSNs. Our scheme is orthog-onal to the methods listed above, and can be viewed asa supplement of the existing methods for delay sensitivenetworks. Some preliminary ideas have been presented in [26],this paper differs from the previous work in that: (1) Since itis time consuming to obtain the optimum result, especiallywhen the number of packets is large, this paper presentsa Markov chain based approximation approach to get thenear-optimal solution by formulating the optimization probleminto the form of maximum weighted configuration problem;(2) An improved dynamic graph based method is leveraged toobtain the near-optimal solution by selecting the appropriatepacket(s) for each transmission. Compared with our proposedheuristic method in [26], the computational complexity isdecreased from O(N5) to O(N4), so that the computationalefficiency is promoted; (3) Extensive simulation experimentsare conducted to examine the obtained performance broughtby the studied methods. It is also important to mention thatin this paper, packet transmissions within two-hop topologiesare considered, and the proposed methods can be extendedto general multi-hop networks, for example using a properlydesigned MAC scheme. More details can be found in ourrecent published work in [27].

III. SYSTEM MODEL

A network topology containing one relay and N pairs ofnodes is considered in our work, where each pair of nodesincludes a source and destination nodes.

The size of packets each source node requires to transmitto its destination node is assumed to be the same. Eachpacket can be either relayed or directly transmitted, and has adeadline requirement, so that the packet would be dropped ifthe deadline requirement is not satisfied.

Fig. 1 shows an example of the network topology, whereN = 3, i.e. there are three pairs of source and destinationnodes (i.e., S = {s1, s2, s3} and D = {d1, d2, d3}), and onerelay node r . Each source node maintains an output queuecontaining the packets it will transmit. P = {p1, p2, . . . , pn}is the set of all packets in the network to be transmitted.Source node s1 sends the packets p1, p5, . . . in the queueto destination node d1, and the rest pairs of nodes performlikewise as Fig. 1 shows. For the sake of fairness, we assume

Fig. 1. Network topology and one possible scheme in a scheduling round.

that only the first packet in each source node’s output queueis scheduled and transmitted each time slot. We call theperiod during which each source node finishes one packettransmission as a Scheduling Round. During one schedulinground, the packets are transmitted either individually (by NRor PR), or cooperatively with other packets (by CNC or ANC).The process that an individually-transmitted packet is sent (orseveral cooperatively-transmitted packets are sent) from sourcenode(s) to destination node(s) is called One Transmission.One Time Slot is defined as the time for packet transmissionwithin one-hop. Take PR as an example, the packet is firsttransmitted from source node to relay, then from relay todestination node, thus the transmission takes two time slots.Due to the complexity of wireless environment, the capacityof each link is different and varies from time to time.

Packets delivered in the network have their deadlines, whichare represented by D = {D1, D2, . . . Dn}. At the beginningof a scheduling round, the first packet of each output queueis dequeued. The transmission of the packet begins when ascheduling round starts and ends when the packet arrives atthe destination node. If the process is not complete beforethe deadline (i.e. the packet misses the deadline), this packetbecomes invalid and is dropped by the destination node. Wedefine the Packet Dropping Probability as the ratio of thenumber of packets missing their deadlines to the total numberof packets that need to be transmitted.

How to transmit and schedule the packets in such ascenario? The table in Fig. 1 shows a feasible scheme forpacket transmission (p1, p2 and p3) in one scheduling round.p1 and p2 are transmitted cooperatively at first with themethod of ANC, then p3 is forwarded by plain routing.It takes two transmissions and four time slots. Obviously,


there are many feasible transmission and scheduling schemes,which may lead to different packet dropping probabilities.Our objective is to find a best scheme adaptively to minimizethe number of packets missing their deadlines according todifferent network scenarios.

IV. ADAPTIVE PACKET SCHEDULING

AND TRANSMISSION SCHEMES

For the sake of solving the mentioned packet scheduling andtransmission problem, we present three solutions. In the firstsubsection, we present the optimization problem mentionedin Section III more concretely, with an objective functionand its corresponding constraints. Then, the optimal solutionis achieved by exhaustive search based on this formulation.Due to its high computational complexity as the number ofpackets increases, two heuristic methods (i.e. Markov approx-imation approach and dynamic graph approach) are proposedto achieve near-optimal solutions with low computationalcomplexity.

A. Exhaustive Search

In order to obtain the optimum transmission and schedulingscheme, an ordered set partition C = {C1, C2, . . . , CK } isleveraged, where 1 ≤ K ≤ N , to represent subsets of N pack-ets that will be sequentially transmitted during a schedulinground. The packets transmitted by invoking a certain method(ANC, CNC, PR, or NR) are included in each subset. Threeproperties should be satisfied in the partition, namely: 1) Nosubset is empty; 2) C1∩C2∩ . . .∩CK = φ; 3) C1∪C2∪ . . .∪CK = P . For one subset Ck , k ∈ {1, 2, . . . , K }, the requiredtransmission time for each possible method can be calculatedaccording to the formulas in [24], and the transmission time ofall the subsets is expressed by T = {TC1, TC2, . . . , TCK }. Withthe objective of minimizing the packet dropping probability,the set partition C with the optimal transmission sequence andcorresponding transmission methods should be selected.

We then introduce two groups of binary variables: xn,k andzn,k , where n ∈ {1, 2, . . . , N} and k ∈ {1, 2, . . . , K }. Denotexn,k = 1 as the packet pn assigned to subset Ck , otherwisexn,k = 0. If packet pn belongs to subset Ck and misses itsdeadline Dn , we define zn,k = 1, and zn,k = 0 otherwise.Then, the optimization problem can be formulated as:

minK∑

k=1

N∑

n=1

zn,k (1)

s.t.K∑

k=1

xn,k = 1 (2)

xn,k ·k∑

i=1

TCi ≤ Dn + η · zn,k (3)

xn,k ·k∑

i=1

TCi > Dn − η(1− zn,k). (4)

With a specific value of K , the the number of packets thatmiss their deadlines should be minimized as illustrated in theobjective function (1). Each packet is transmitted once during

one scheduling round, which is constrained in (2). For thesake of guaranteeing zn,k = 1 when packet pn belongs tosubset Ck and missing its deadline Dn , a constant value ηis denoted in constraints (3) and (4). The transmission timeof each subset TCi (1 ≤ i ≤ k) can be gained based on thefollowing equation:

TCi =

⎧⎪⎨

⎪⎩

T C NCCi

‖Ci‖ > 2

min{T C NCCi

, T ANCCi} ‖Ci‖ = 2

min{T P RCi

, T N RCi} ‖Ci‖ = 1,

(5)

where ‖Ci‖ stands for the size of subset Ci . For the subsetswith more than two packets, CNC is the only choice. For thesubsets with two packets, both ANC and CNC can be selected.Packets in single-packet subsets can be forwarded via eitherNR or PR.

To solve this optimization problem, a straight-forwardmethod is through exhaustive search. In this method, allpartitions of packet set P (the number of partitions is equalto a Bell number [28]) require to be obtained at first. Thenumber of subsets in a partition ranges from 1 to N , andthe optimal transmission method of each subset is the onewith the least time consumption. Furthermore, all the possibletransmission sequences of the subsets are checked through foreach partition, to calculate the number of dropped packets.Finally, the ordered partition with the minimum packet drop-ping probability is chosen as the optimal packet schedulingand transmission solution. The complexity of the exhaustivesearch based method is O(N N ).

B. Markov Approximation Approach

In the exhaustive search based approach, we solve theoptimization problem by finding all the possible schedulingand transmission schemes and choosing the best one. However,this method is time consuming that it is very hard to obtain theoptimum result especially when the number of packets is large.To make the optimization problem solvable within requiredtime, in this section, we provide another way, i.e., a Markovapproximation approach to get the near-optimal solution of theproblem.

Markov approximation has been used to solve the MaximumWeighted Configuration problem [29], [30], such as designingthe CSMA mechanism to achieve the optimal throughput,selecting path in wireline networks, or solving the chan-nel assignment problem in wireless LANs. Many practicaland important problems can be formulated in the form ofMaximum Weighted Configuration problem, and so is ouroptimization problem in this paper.

Consider the optimization problem described in Section IIIwith a configuration set F . A configuration F(F ∈ F)is an N × N array. The element fmn = 1 in the arraymeans the packet n is transmitted on the mth transmission,otherwise fmn = 0. A feasible configuration should satisfy∑N

m=1 fmn = 1(1 ≤ m, n ≤ N). The transmission method ofeach transmission is related to the number of packets in thetransmission. From above we can see that, a configuration Fis a feasible packet scheduling and transmission scheme.


Apparently the network has different performance on packetdropping probability when operating under different configu-rations. We use U(F)(F ∈ F) to denote the number of packetsmeeting their deadlines in a scheduling round, according to theoptimization problem we defined in part IV-A, we have:

U(F) = N −K∑

k=1

N∑

n=1

zn,k , (6)

where N is the number of packets need to be transmitted ina scheduling round and zn,k satisfies (2), (3), (4) and (5).In fact, U(F) is another way to present the optimizationproblem. To minimize the packet dropping probability isactually to maximize the number of packets sent successfully,when the total number of packets is fixed.

Hence, the optimization problem in part IV-A can be

maxF∈F

U(F). (7)

It can be transformed into the following problem:

maxp>0

∑

F∈FpFU(F) (8)

s.t.∑

F∈FpF = 1, (9)

where pF is the probability that the configuration F is in use.Consider U(F) in (8) as the "weight" of a configuration F, theproblem can be taken as a Maximum Weighted Configurationproblem.

Next, we make a Markov approximation to solve theproblem in (8).

1) Log-Sum-Exp Approximation: Markov approximationfirst uses a convex log-sum-exp function to approximate theoriginal max function as

Aaprox(U) = 1

βlog(

∑

F∈Fexp(βU(F))), (10)

Aaprox(U) ≈ maxF∈F

U(F), (11)

in which U � [U(F), F ∈ F ] and β is a positive constant.It is proved in [31] that the approximation holds with aupper-bound approximation gap of 1

β log |F |. The conjugateof Aaprox(U) is A∗aprox(U). Because Aaprox(U) is a convexand closed function, the conjugate function of A∗aprox(U)is Aaprox(U) [31], i.e., A∗∗aprox(U) = Aaprox(U), whereA∗∗aprox(U) is

maxp>0

∑

F∈FpFU(F)− 1

β

∑

F∈FpF log pF (12)

s.t.∑

F∈FpF = 1. (13)

In other words, the optimal solution of the problem in (12)is the same as (10) and close to the optimal solution to (8) withan additional entropy term 1

β

∑F∈F pF log pF. By solving the

Karush-Kuhn-Tucker (KKT) conditions of problem (12), wecan get the optimal probabilities of different configurations

p∗F(U) = exp(βU(F))∑F′∈F exp(βU(F′))

∀F ∈ F , (14)

which is the approximate solution of problem (8) and ouroriginal problem (7).

2) Designing Markov Chain: We now get the optimalsolution as (14). Unfortunately, although the number of con-figurations is limited, it is usually very large, which makes thecomputing of (14) difficult. To solve this problem, we designa Markov chain, whose state space is F ∈ F , and stationarydistribution is p∗F(U). Thus the optimal probabilities of config-urations stay at the stationary distribution after enough timesof state transition and the network’s performance in packetdropping probability approaches the best, approximately.1

For any product form p∗F(U) probability distributionin (14), we can construct at least one continuous-time time-reversible ergodic Markov chains whose stationary distributionis p∗F(U) [29]. To construct this continuous-time time-reversible ergodic Markov chain, we need to obey the fol-lowing two rules [29]:• Rule 1: the Markov chain is irreducible, any two states

can reach each other;Here, to simplify the process of sate transition, we define

two states are adjacent and can reach each other if and only ifthere is one packet changing its sequence in the array, i.e., onlyone column vector in the array varies. To be more specific, theconstraint of two states being adjacent can be written as

θ(F, F′) = 1. (15)

θ(F, F′′) means the number of elements changing their placesin F′ compared with F. In the following example,

F =⎡

⎣0 1 01 0 00 0 1

⎤

⎦ F′ =⎡

⎣1 1 00 0 00 0 1

⎤

⎦ F′′ =⎡

⎣1 0 00 1 00 0 1

⎤

⎦,

(16)

θ(F, F′) = 1, so F and F′ are adjacent states, while F andF′′ are not, because in F′′ the sequence of both packet p1 andp2 are changed compared with F, making θ(F, F′′) = 2. Forstate F compared with itself, we have θ(F, F) = 0. A state willonly convert to its adjacent state and itself, i.e., θ(F, F) ≤ 1.The purpose to set more strict restrictions on sate transition isto decrease computational complexity of the transition rate ineach transition, while at the same time insuring the ergodicityof the Markov chain.• Rule 2: the nonnegative transition rate qF,F′ between two

states should meet the detailed balanced equation:

p∗F(U)qF,F′ = p∗F′(U)qF′,F ∀F, F′ ∈ F . (17)

By substitute pF and p∗F with equation (14), we have:

exp(βU(F))qF,F′ = exp(βU(F′))qF′,F. (18)

1The theoretical basis is the the Markov chain convergence theorem whichguarantees that the distribution of an irreducible and aperiodic Markov chainconverges to the stationary distribution π as n →∞, no matter which statethe chain starts in. Nevertheless we have no idea about how large n needs to betaken before the Markov chain converges. Generally speaking, it is possible toextract an upper bound of n (for example by using a coupling argument), butthe result is often astronomical magnitude, which have little practical use [29].In fact, the Markov chain converges much faster but to obtain the proof turnsout to be quite difficulty. In this paper, instead of theoretical analysis, weobtain the practical needed state transitions by observing the performance ofMarkov chain during the state transition process, as in the section V shows.


Algorithm 1 : Process of Markov Chain ApproximationApproach

1: Set the initial state Fin = diag(1, 1, · · · , 1), settranstime = 1, and the needed state transfer time is S

2: F = Fin

3: while transtime = S do4: for all θ(F, F′) ≤ 1 do5: Compute the transition rate qF,F′6: end for7: F∗ = Fad

8: transtime = transtime + 19: end while

10: return F∗

As we mentioned above, only adjacent states are reachablefrom each other. The transition rate between the non-adjacentstates is zero as:

qF,F′ = 0 ∀ θ(F, F′) > 1. (19)

Obviously, qF,F′ = 0 meets the detailed balancedequation (18).

When designing the transition rate between adjacent states,we desire the current state to transfer to a better state inwhich more packets meet their deadlines. So the transition ratemust be positively correlated to the difference of the numbersof packets meeting their deadlines under two configurations.At the same time, the transition rate should satisfy the detailedbalanced equation (18). The sum of the transition rates thatcurrent state F transfers to all its adjacent states F′ or itselfshould make

∑θ(F,F′)≤1 qF,F′ = 1. Thus, a feasible designing

of transition rate for all θ(F, F′) ≤ 1 can be as (20), but notlimited to it:

qF,F′ =exp( 1

2β(U(F′)−U(F)))∑

θ(F,F′)≤1 exp( 12β(U(F′)−U(F)))

. (20)

Particularly, the rate that state F stays at itself, i.e., whenθ(F, F′) = 0 is:

qF,F = 1∑

θ(F,F′)≤1 exp( 12β(U(F′)−U(F)))

. (21)

It is easy to see that this transition rate meets the detailedbalanced equation, and encourages the system to transfer toa better configuration. The process of Markov chain approxi-mation approach is shown in Algorithm 1.

C. Dynamic Graph Approach

Markov approximation approach can obtain the schemesthat are very close to the optimum results, when the numberof state transitions is large enough. As the amount of thestates, i.e., the possible scheduling and transmission schemes,increases rapidly with the number of packets, we can demon-strate that the corresponding complexity is still very high.Therefore, we proceed seeking a method with less compu-tational complexity. In this section, we introduce the dynamicgraph based approach and solve the problem by constructing

a graph for the selection of appropriate packet(s) of eachtransmission.

Following the optimal solutions obtained through exhaustivesearch under various channel conditions, the following factscan be observed:• Observation 1: Among all the optimal ordered set

partitions, the chance that more than two packets arecooperatively transmitted via CNC is rare.• Observation 2: In PNC-based optimal ordered set par-

titions, once a packet in one subset misses its deadline, thepacket(s) in its subsequent subset(s) will also miss its/theirdeadline(s), if any.

Then, based on the above observations, three rules on packetscheduling and transmission are defined by us:• Rule 3: The number of packets within one subset is no

more than two.• Rule 4: All the packet(s) in any scheduled subset should

be transmitted successfully.• Rule 5: The transmission of one subset may cause some

other packets miss their deadlines. Therefore, in this paper,the efficiency of one-subset transmission is regarded as thedifference between the number of packets in the subset andthe number of dropped packets caused by this transmission.The subset with the highest transmission efficiency should bescheduled with the highest priority.

With the objective of employing these rules to guide packetscheduling and transmission, a dynamic graph G(V , E, W ) isconstructed, where V is a set of vertices indicating packetsthat are waiting for transmission before their deadlines, E isa set of edges expressing possible subsets, and W is a setof weights of edges. If ANC or CNC is possible to beconducted with any two packets, an edge exists betweentheir corresponding vertices. Therefore, for edge ei, j ∈ E ,if i = j , the corresponding packet represented by νi ∈ V isfrom a single-packet subset to be forwarded by PR or NR;If i = j , the corresponding two packets are within a subset tobe transmitted by ANC or CNC. Based on Rule 3, the weightof edge ei, j corresponds to the transmission efficiency of thesubset including packets represented by νi and ν j , as follows:

ωi, j = Ui, j − Ai, j , (22)

where Ui, j is the number of packets in the subset, and Ai, j

is the number of the packets to be dropped if the subsetassociated to ei, j is scheduled in the next transmission round.The edge with the maximum weight in the graph is alwaysselected and the corresponding subset in the next transmissionwould be scheduled. If there exist two or more than two edgeswith the maximum weight, the subset with the earliest deadlinewould be scheduled primarily. If there happens to be morethan one edge with both the maximum weight and the earliestdeadline, the subset with the shortest transmission time hashigher scheduling priority.

The graph would be updated if one subset of packet(s)is transmitted during each time slot. The vertices and edgesassociate with both the transmitted packets and the droppedpackets because the constraints of their deadlines are deleted.Furthermore, if the remaining time is not long enough forcompleting their transmissions before some waiting packets’


Fig. 2. Example of graph updating process in heuristic strategy for 6 packets. (a) Initial minimum transmission time of all the possible subsets. (b) Initialgraph before the first one-subset transmission. (c) First updated minimum transmission time of all the possible subsets. (d) First updated graph before thesecond one-subset transmission.

deadlines, the packets would be removed from the queueand the associated vertices and edges are deleted correspond-ingly no matter which transmission method is employed. Theweights of the residual edges are recomputed according to thetime left for each packet.

Fig. 2 illustrates the graph updating process, where 6 pack-ets intend to be scheduled during one scheduling round,and their deadlines are D = {D1, D2, . . . , D6}, respectively.The minimum transmission time of all the possible subsetswould be calculated at first, i.e. Ti, j = min{T P R

pi, T N R

pi}

when i = j , and Ti, j = min{T ANCpi ,p j

, T C NCpi ,p j} when i = j ,

i, j ∈ {1, 2, . . . , 6}. As shown in Fig. 2(a), the under-lined numbers indicate that their corresponding transmissionsare infeasible, and the ones without underlines are feasible.If Ti, j > (Ti,i + Tj, j ) (i = j ), the corresponding transmissionof two packets separately by PR or NR consumes less timethan forwarding them cooperatively via ANC or CNC, thetransmission associated with Ti, j is infeasible. Let t denotethe accumulative transmission time, which is set to 0 initially.If t+Ti, j > min{Di , D j } (i and j may be the same), the pack-ets in the subset would miss their deadlines no matter whichtransmission method is leveraged. These values of Ti, j are alsoillustrated with underlines in Fig. 2(a). An initial graph basedon feasible transmissions would be constructed after neglectingthe infeasible transmissions demonstrated with underlines inFig. 2(a). The constructed graph is shown in Fig. 2(b), andthe weight of each edge is computed based on equation (22).It can be seen that e1,1 and e3,5 have the same maximumweight 0, while D1 < min{D3, D5}. Therefore, a single-packetsubset associated to e1,1 is scheduled for transmission, t isupdated by setting T1,1 = 0.0973 simultaneously, and thevalue T1,1 is underlined in Fig. 2(c). After this round, thepacket transmissions in the subsets associated to e6,6 and e3,5become infeasible due to t + T6,6 > D6, t + T3,5 > D5.Therefore, the values T6,6 and T3,5 are also underlined inFig. 2(c). After that, we remove ν1, ν6, e1,1, e6,6 and e3,5 fromthe initial graph, and recalculate the weights of residual edges,which is demonstrated in Fig. 2(d). Then, the subset withthe maximum transmission efficiency ω5,5 is scheduled basedon the new constructed graph. The updating and schedulingprocess are repeated until no vertex exists. The whole processof the graph based near-optimal method is demonstrated inAlgorithm 2.

Algorithm 2 : Process of Dynamic Graph Approach1: Construct a complete graph G(V , E, W ), the V ={ν1, ν2, . . . , νN } corresponds to a set of packets P ={p1, p2, . . . , pN }

2: Define an empty partition C3: Define a variable t = 0 to record current cumulative

transmission time4: Calculate minimum transmission time of all the possible

subsets: Ti, j , i ≤ j , i, j ∈ {1, 2, . . . , N}5: Delete those edges having Ti, j > (Ti,i + Tj, j ) when i = j6: while V = φ do7: for all νi ∈ V do8: Delete vertex νi if (t + Ti,i ) > Di

9: end for10: for all ei, j ∈ E do11: Delete edge ei, j if (t + Ti, j ) > min{Di , D j }12: end for13: for all ei, j ∈ E do14: ωi, j ← Ui, j − Ai, j

15: end for16: Choose the edge with maximum transmission efficiency,

denoted by ωi∗, j∗ , from W17: t ← t + Ti∗, j∗18: Add the subset associated to ei∗, j∗ into C19: Delete vertices νi∗ and ν j∗ and the edges that connect to

these two nodes20: W ← φ21: end while22: return C

The efficiency maximization of one-subset transmission isthe main focus of our heuristic strategy, where all the possiblesingle-packet and two-packet subsets are considered duringeach transmission to make the best scheduling choice. Thecomplexity of this heuristic strategy is O(N4), thus it ispolynomial.

V. SIMULATION RESULTS

We evaluate the performance of the two proposed adaptivepacket scheduling and transmission schemes via simulations.We assume that one relay node is placed in the center of aregion which covers 500× 500 m2 square, and 50 end nodes


Fig. 3. Packet dropping probability vs. number of state transition times.

are distributed in the region uniformly. The network scenariocan be viewed as a community or school building deployingWSNs. The source nodes and their corresponding destinationnodes are randomly selected, and packets are generated bythe source nodes. We consider a Rician flat-fading channelwith Rician factor γ = 5 dB. The noise power density is−174 dBm/Hz, the bandwidth is set to 1 MHz, and the noisefigure is 6 dB. The deadlines of the packets is set to threeclasses (100ms, 400ms and 1s) which meet the ITU-T QoSstandard for IP-based networks [32].

First we study how the number of state transition timesaffects the performance of markov approximation approach,the results are shown in Fig. 3. The number of packets in onescheduling round is fixed to 6, and the maximum transmissionpower is 5dBm. We run the dynamic graph approach on1000 different topologies, and record the average packet drop-ping probability. Then we run Markov approximation approachon the same 1000 topologies but with different times of statetransition. It is clear that as the number of state transition timesgrows, the performance of Markov approximation approachbecomes better. Not surprisingly, as the number of state tran-sition times increases, the Markov chain converges, the statesstay at the stationary distribution. In fact, when the number ofpackets is 6, 100 state transition are good enough comparedwith the dynamic graph approach, and more transitions bringtiny improvement.

However, this is not always the case when the number ofpackets increases, as shown in Fig. 4. When the number ofpackets ranges from 6 to 21, 100 transitions seem not so goodas the number of packet grows. The performance of 1000 tran-sitions is more acceptable. Considering the result in Fig. 3, wecan conjecture that the performance of 10000 times of transi-tion will be better. Observing the three Markov approximationapproach curves of different numbers of transitions, we canalso draw a conclusion that the more the number of packetis, the slower the Markov chain converges, the more the statetransitions are required to reach its stationary distribution.

Since the simulation time of the optimal scheme (i.e.,exhaustive search method) increases exponentially with the

Fig. 4. Dropped packet number vs. packet number.

Fig. 5. Packet dropping probability vs. packet number.

number of packets N , it takes much time to get the resultswhen N is over 7. We compare the performance of the twoheuristic schemes with the optimal scheme in the scenariowhere the number of packets is no more than 6. Consideringthe fact that the Markov approximation approach performsgood enough when the number of state transitions is 100 andthe number of packets is 6, we fix the times of state transitionto 100 in the following two simulations.

We compare the average packet dropping probability of thetwo proposed heuristic strategies with several other schemes,which include the optimal scheme, optimal scheme withoutANC, and optimal scheme without network coding (includingboth ANC and CNC) in Figs. 5 and 6. We first considerscenarios with different numbers of packets in each schedulinground in Fig. 5. We run 1000 times with 1000 differentrandom seeds, which corresponding to 1000 different networktopologies. The maximum transmission power is set to 5 dBm.We can observe that the performance of the two heuristicschemes is close to the optimal scheme. The results alsoconfirm that network coding has great advantage on reducingpacket dropping probability, especially ANC.


Fig. 6. Average packet dropping probability vs. max. transmission power.

In Fig. 6, we fix the number of packets to 6, and vary themaximum transmission power from 0 dBm to 15 dBm. Theresults show that the two heuristic methods perform well underdifferent maximum transmission powers. We also find thatfive schemes have similar performance when the transmissionpower is high. This is because when the transmission poweris large enough, packets can be successfully delivered via NR,the advantage of network coding is overshadowed.

Then, we compare the number of dropped packets oftwo heuristic methods in a fixed topology with time varyingchannels. We run 20 scheduling rounds, in each schedulinground N packets from different source nodes with randomdeadlines are scheduled. In each scheduling round the channelconditions vary a little (random changes on multipath phaseand amplitude with upper bound of 10% based on the con-ditions in the last scheduling round). To ensure that the twomethods conduct about the same times of calculation, we setthe number of state transitions to N2 in the Markov approxi-mation approach in each scheduling round, considering the thecomplexity of two strategy is O(N4) and O(N2) respectively.We also consider three scenarios with different numbers ofpackets transmitted in a scheduling round. The number ofdropped packets in two methods are shown in Fig. 7. We cansee that when the number of packets is 5, two methods performthe same. When the packets grows, the Markov approximationapproach becomes worse than the dynamic graph approachbecause of its slow convergence. The simulation results indi-cate that the Markov approximation approach doesn’t workwell under time varying channel conditions when the numberof packets is large.

The numbers of execution times of CNC and ANC indifferent transmission schemes are compared in Figs. 8 and 9,where the number of packets varies in the former and themaximum transmission power changes in the latter. It canbe observed in Fig. 8 that as the number of packets fortransmission increases, the numbers of execution times ofCNC and ANC in different schemes grow also. We note thatfor the optimal method without ANC, the execution time ofCNC is more than that in the optimal method. This is obvious

Fig. 7. Dropped packet number vs. scheduling round.



since ANC can reduce transmission slot further comparingwith CNC, so that some opportunity can be leveraged forANC transmission in the optimal method. Because the number



of CNC-coded packets is limited to 2 under dynamic graphmodel, the gap of execution times between ANC and CNCdiffers greatly, and this situation aggravates as the numberof transmission packet increases. The reason behind is thatpacket number larger than three would be divided into differentgroups, which is another reason that causes the performancesgap between sub-optimal and the optimal methods.

The relationship between execution times of CNC togetherwith ANC and node maximum transmission power is illus-trated in Fig. 9, where the packet number is set to 6.It is interesting to find that as the increase of the maximumtransmission power, the execution time of CNC increasesconstantly, while the execution time of ANC enhances atfirst and then decreases. This is because when the maximumtransmission power is leveraged for transmission, comparedwith ANC, the optimal transmission scheme prefers employingCNC to encode more than three packets during one transmis-sion slot for time saving. For the reduction of ANC executiontimes in dynamic graph based scheme, the reason is thismethod is more inclined to adopt NR for packet transmission.

The simulation time of Markov chain based and graphbased schemes is shown in Fig. 10. We notice that the gapof simulation time between these two methods is broadlyapparent, and this gap enlarges as the number of packetsincreases. This is because on one hand, the number of statetransfer increases sharply in Markov chain based approxima-tion method. On the other hand, since the dynamic graphbased scheme only schedules the packet to the destination nodewithin the deadline during each update of the graph, the actualcomputational complexity is far from O(N4).

To sum up, the Markov chain based approximation approachis not so complex. With enough state transitions, it can alwaysget a better perform than the dynamic graph based approachif the channel conditions are static or change very slowly.Dynamic graph based approach doesn’t need iterations, and itis a better choice under the fast changing channel conditions.

We have also conducted some preliminary experimentalresearch on the practical deployment of the WMSN, and nowthe network contains 10 wireless nodes equipped with FieldProgrammable Gate Array (FPGA). The theoretical value of

CNC can be reached, and the corresponding value of PNC canbe effectively approached. It is noted that under the currentcircumstance, network size cannot be large in the realisticnetwork circumstance. The reasons are from two aspects. First,the synchronization of PNC-based transmission is difficult forimplementation. Second, the hardware cost is rather high byequipping with FPGA.

VI. CONCLUSIONS

Since the volume and characteristics of multimedia datahave distinct characters compared with the traditional gen-erated data in WSNs, the corresponding features desire tobe investigated. In this paper, we have focused on packetscheduling and transmission with deadline constraints in multi-rate WMSNs by jointly combining ANC, CNC, PR, and NR.We first formulate this problem to an optimized method,by which we could select the optimal transmission methodvia exhaustive search. Since the computational complexityof the formulated optimization problem is high, a Markovchain based approximation approach has been presented bytransferring the optimization problem to the form of themaximum weighted configuration problem. With the objectiveof reducing computational complexity further, the dynamicgraph based method has been proposed to solve the formu-lated problem through graph construction. Simulation resultsdemonstrate that the adaptive packet scheduling and transmis-sion methods can reduce average packet dropping probabilityand simulation time, by which the QoS indexes of individualscan be improved. Besides, the proposed heuristic strategiescan approach the optimal network performance effectivelywith low computational complexity, which can be utilized fordifferent network scenarios effectively.

For the future work, we plan to overcome the implemen-tation problems from two aspects. In order to synchronizetransmissions in PNC, one possible solution is to move thescheduling of PNC-based transmission from time domainto frequency domain. Another aspect is to design coarsesynchronization strategy and consider the effect of networkperformance brought by the node buffer.

REFERENCES

[1] Z. Ning, L. Liu, F. Xia, B. Jedari, I. Lee, and W. Zhang,“CAIS: A copy adjustable incentive scheme in community-basedsocially-aware networking,” IEEE Trans. Veh. Technol., 2017,doi: 10.1109/tvt.2016.2593051. [Online]. Available: http://ieeexplore.ieee.org/document/7516598

[2] I. Al-Anbagi, M. Erol-Kantarci, and H. T. Mouftah, “Delay-awaremedium access schemes for WSN-based partial discharge measurement,”IEEE Trans. Instrum. Meas., vol. 63, no. 12, pp. 3045–3057, Dec. 2014.

[3] G. Mali and S. Misra, “TRAST: Trust-based distributed topologymanagement for wireless multimedia sensor networks,” IEEE Trans.Comput., vol. 65, no. 6, pp. 1978–1991, Jun. 2016.

[4] H. Shen and G. Bai, “Routing in wireless multimedia sensor networks:A survey and challenges ahead,” J. Netw. Comput. Appl., vol. 71,pp. 30–49, Aug. 2016.

[5] G. Fortino and P. Trunfio, Internet of Things Based on Smart Objects:Technology, Middleware and Applications. Cham, Switzerland: Springer,2014.

[6] H. Chen, H. Chan, C. Chan, and V. Leung, “QoS-based cross-layerscheduling for wireless multimedia transmissions with adaptive modula-tion and coding,” IEEE Trans. Commun., vol. 61, no. 11, pp. 4526–4538,Nov. 2013.


[7] Y. Xiao, K. Thulasiraman, X. Fang, D. Yang, and G. Xue, “Computinga most probable delay constrained path: NP-hardness and approximationschemes,” IEEE Trans. Comput., vol. 61, no. 5, pp. 738–744, May 2012.

[8] Z. Mao, C. E. Koksal, and N. B. Shroff, “Online packet scheduling withhard deadlines in multihop communication networks,” in Proc. IEEEINFOCOM, Apr. 2013, pp. 2463–2471.

[9] Z. Ning, F. Xia, X. Hu, Z. Chen, and M. Obaidat, “Social-orientedadaptive transmission in opportunistic Internet of smartphones,” IEEETrans. Ind. Informat., 2017, doi: 10.1109/tii.2016.2635081. [Online].Available: http://ieeexplore.ieee.org/document/7763832/

[10] Z. Ning, Q. Song, L. Guo, Z. Chen, and A. Jamalipour, “Integration ofscheduling and network coding in multi-rate wireless mesh networks:Optimization models and algorithms,” Ad Hoc Netw., vol. 36, no. 1,pp. 386–397, 2016.

[11] J. Kim, J. Barrado, and D. Jeon, “An energy-efficient transmissionscheme for real-time data in wireless sensor networks,” Sensors, vol. 15,no. 5, pp. 11628–11652, 2015.

[12] A. Khalek, C. Caramanis, and R. Heath, “Delay-constrained videotransmission: Quality-driven resource allocation and scheduling,” IEEEJ. Sel. Topics Signal Process., vol. 9, no. 1, pp. 60–75, Jan. 2015.

[13] X. Li, C.-C. Wang, and X. Lin, “On the capacity of immediately-decodable coding schemes for wireless stored-video broadcast with harddeadline constraints,” IEEE J. Sel. Areas Commun., vol. 29, no. 5,pp. 1094–1105, May 2011.

[14] W.-L. Yeow, A. T. Hoang, and C.-K. Tham, “Minimizing delay formulticast-streaming in wireless networks with network coding,” in Proc.IEEE INFOCOM, Apr. 2009, pp. 190–198.

[15] S. Katti, S. Gollakota, and D. Katabi, “Embracing wireless interference:Analog network coding,” ACM SIGCOMM Comput. Commun. Rev.,vol. 37, pp. 397–408, Aug. 2007.

[16] M. Alvandi, M. Mehmet-Ali, and J. Hayes, “Delay optimization in multi-hop wireless networks with network coding,” in Proc. IEEE WirelessCommun. Netw. Conf. (WCNC), Apr. 2013, pp. 1381–1386.

[17] H. Li, X. Liu, W. He, J. Li, and W. Dou, “End-to-end delay analysis inwireless network coding: A network calculus-based approach,” in Proc.31st Int. Conf. Distrib. Comput. Syst. (ICDCS), Jun. 2011, pp. 47–56.

[18] L. Yang, Y. Sagduyu, J. Zhang, and J. Li, “Deadline-aware schedulingwith adaptive network coding for real-time traffic,” in Proc. IEEE/ACMTrans. Netw., vol. 23, no. 5, pp. 1430–1443, Oct. 2015.

[19] C. Zhan and Y. Xu, “Broadcast scheduling based on network codingin time critical wireless networks,” in Proc. IEEE Int. Symp. Netw.Coding (NetCod), Jun. 2010, pp. 1–6.

[20] X. Wang, C. Yuen, and Y. Xu, “Joint rate selection and wireless networkcoding for time critical applications,” in Proc. IEEE Wireless Commun.Netw. Conf. (WCNC), Apr. 2012, pp. 1964–1969.

[21] Y. Mao, C. Dong, H. Dai, X. Zhu, and G. Chen, “Optimal schedulingwith pairwise coding under heterogeneous delay constraints,” in Proc.IEEE Int. Conf. Commun. (ICC), Jun. 2014, pp. 385–390.

[22] H. Seferoglu and A. Markopoulou, “Opportunistic network coding forvideo streaming over wireless,” in Proc. Packet Video, Nov. 2007,pp. 191–200.

[23] Q. T. Vien, H. X. Nguyen, B. Barn, and X. N. Tran, “On the perspec-tive transformation for efficient relay placement in wireless multicastnetworks,” IEEE Commun. Lett., vol. 19, no. 2, pp. 275–278, Feb. 2015.

[24] F. Wang, S. Wang, Q. Song, and L. Guo, “Adaptive relaying methodselection for multi-rate wireless networks with network coding,” IEEECommun. Lett., vol. 16, no. 12, pp. 2004–2007, Dec. 2012.

[25] A. Youssif, A. Ghalwash, and A. El-Kader, “Acwsn: An adaptive crosslayer framework for video transmission over wireless sensor networks,”Wireless Netw., vol. 21, no. 8, pp. 2693–2710, 2015.

[26] L. Zhang, Y. Yu, F. Huang, Q. Song, L. Guo, and S. Wang, “Deadline-aware adaptive packet scheduling and transmission in cooperative wire-less networks,” in Proc. IEEE PIMRC, Sep. 2014, pp. 1980–1984.

[27] Q. Song, L. Guo, F. Wang, S. Wang, and A. Jamalipour, “MAC-centriccross-layer collaboration: A case study on physical-layer network cod-ing,” IEEE Wireless Commun., vol. 21, no. 6, pp. 160–166, Dec. 2014.

[28] G.-C. Rota, “The number of partitions of a set,” Amer. Math. Monthly,vol. 71, no. 5, pp. 498–504, 1964.

[29] M. Chen, S. C. Liew, Z. Shao, and C. Kai, “Markov approximation forcombinatorial network optimization,” IEEE Trans. Inf. Theory, vol. 59,no. 10, pp. 6301–6327, Oct. 2013.

[30] C.-K. Chau, M. Chen, and S. C. Liew, “Capacity of large-scaleCSMA wireless networks,” IEEE/ACM Trans. Netw., vol. 19, no. 3,pp. 893–906, Jun. 2011.

[31] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.:Cambridge Univ. Press, 2004.

[32] N. Seitz, “ITU-T QoS standards for IP-based networks,” IEEE Commun.Mag., vol. 41, no. 6, pp. 82–89, Jun. 2003.

Lei Guo, photograph and biography not available at the time of publication.

Zhaolong Ning, photograph and biography not available at the time ofpublication.

Qingyang Song, photograph and biography not available at the time ofpublication.

Lu Zhang, photograph and biography not available at the time of publication.

Abbas Jamalipour, photograph and biography not available at the time ofpublication.

Documents

1538 IEEE SENSORS JOURNAL, VOL. 17, NO. 5, MARCH 1, …thealphalab.org/papers/A QoS-oriented High-Efficiency Resource... · Medical Image Computing, ... speciﬁed in IEEE 802.15.4