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[4] A. D. S. Jayalath and C. Tellambura, “SLM and PTS peak-power reduc-tion of OFDM signals without side information,” IEEE Trans. WirelessCommun., vol. 4, no. 5, pp. 2006–2013, Sep. 2005.

[5] O. Muta and Y. Akaiwa, “Weighting factor estimation method for peakpower reduction based on adaptive flipping of parity bits in Turbo-codedOFDM systems,” IEEE Trans. Veh. Technol., vol. 57, no. 6, pp. 3551–3562, Nov. 2008.

[6] O. Muta and Y. Akaiwa, “Peak power reduction method based on structureof parity-check matrix for LDPC coded OFDM transmission,” in Proc.IEEE Veh. Technol. Conf., Apr. 2007, pp. 2841–2845.

[7] Y. C. Tsai and Y. L. Ueng, “Multiple-candidate separation for PTS-basedOFDM systems by Turbo decoding,” in Proc. IEEE Veh. Technol. Conf.,May 2010, pp. 1–5.

[8] R. G. Gallager, “Low density parity check codes,” IRE Trans. Inf. Theory,vol. IT-8, no. 1, pp. 21–28, Jan. 1962.

[9] T. Richardson and R. Urbanke, “The capacity of low-density parity checkcodes under message-passing decoding,” IEEE Trans. Inf. Theory, vol. 47,no. 2, pp. 599–618, Feb. 2001.

[10] T. J. Richardson, A. Shokrollahi, and R. Urbanke, “Design of capacityapproaching irregular low-density parity-check codes,” IEEE Trans. Inf.Theory, vol. 47, no. 2, pp. 619–637, Feb. 2001.

[11] M. Luby, M. Mitzenmacher, A. Shokrollahi, and D. Spielman, “Improvedlow-density parity-check codes using irregular graphs,” IEEE Trans. Inf.Theory, vol. 47, no. 2, pp. 585–598, Feb. 2001.

[12] X. Y. Hu, E. Eleftheriou, and D. M. Arnold, “Regular and irregular pro-gressive edge-growth Tanner graphs,” IEEE Trans. Inf. Theory, vol. 51,no. 1, pp. 386–398, Jan. 2005.

Performance Analysis of Hybrid Wireless NetworksUnder Bursty and Correlated Traffic

Yulei Wu, Geyong Min, and Laurence T. Yang

Abstract—Wireless local area networks (WLANs) have risen in popular-ity for in-car networking systems that are designed to make driving safer.Wireless mesh networks (WMNs) are widely deployed to expand the cover-age of high-speed WLANs and to support last-mile connectivity for mobileusers anytime and anywhere at low cost. Many recent measurement studieshave shown that the traffic arrival process in wireless networks exhibitsthe bursty and correlated nature. A new analytical model is developed inthis paper as a cost-effective performance tool to investigate the quality-of-service (QoS) of the WMN that interconnects multiple WLANs in thepresence of bursty and correlated traffic. After validating its accuracyvia extensive simulation experiments, the analytical model is then used toinvestigate the performance of the hybrid wireless networks.

Index Terms—Analytical modeling, bursty and correlated traffic, inte-grated wireless networks, Internet, wireless mesh networks (WMNs).

Manuscript received March 30, 2012; revised July 15, 2012; acceptedAugust 26, 2012. Date of publication September 19, 2012; date of currentversion January 14, 2013. This work was supported in part by the Na-tional Program on Key Basic Research Project (973 Program) under Grant2012CB315803 and in part by the “Strategic Priority Research Program” ofthe Chinese Academy of Sciences under Grant XDA01020304. The review ofthis paper was coordinated by Prof. A. Boukerche.

Y. Wu is with the China Science and Technology Network, ComputerNetwork Information Center, Chinese Academy of Sciences, Beijing 100190,China (e-mail: wuyulei@cstnet.cn).

G. Min is with the Department of Computing, School of Computing, Infor-matics and Media, University of Bradford, Bradford BD7 1DP, U.K. (e-mail:g.min@brad.ac.uk).

L. T. Yang is with the School of Computer Science and Technology,Huazhong University of Science and Technology, Wuhan 430074, China, andalso with the Department of Computer Science, St. Francis Xavier University,Antigonish, NS B2G 2W5, Canada (e-mail: ltyang@stfx.ca).

Digital Object Identifier 10.1109/TVT.2012.2219890

I. INTRODUCTION

The ever-growing number of vehicles on roads creates numeroustraffic-related problems for our society. Wireless local area networks(WLANs) have risen in popularity as European automakers have madeprogress on in-car networking systems that are designed to enhancedriving safety. Wireless mesh networks (WMNs) are widely used toexpand the coverage of high-speed WLANs and are developed tooffer rapid development and easy reconfiguration of wireless broad-band communications, as well as to support last-mile connectivityfor mobile users anytime and anywhere at low cost [1], [10], [18].Mesh routers (MRs) facilitated with the gateway functionality can beconnected to the Internet and are often called gateways.

Performance studies on WLANs and WMNs have been widelyreported in the literature [2], [3], [11], [12], [14]. For example, Bianchi[2] developed an original analytical model to calculate the throughputof WLANs subject to the IEEE 802.11 distributed coordination func-tion (DCF) medium-access control (MAC) protocol. This model canbe applied to both packet transmission schemes, i.e., the basic DCFmechanism and the request-to-send/clear-to-send mechanism. Liu andLin [12] investigated the burst transmission and the acknowledgementaggregation in the IEEE 802.11e WLANs under unsaturated trafficloads and error-prone channel conditions. Mahani et al. [14] presentedan analytical model to investigate the performance of a MAC schemein WMNs. Their work considered the hidden terminals and the co-existing of control and data traffic at different frequency channels. In[11], a test bed to investigate a quality-of-service (QoS) scheme basedon rate-adaptive admission control methods for multimedia multicastcommunications in WMNs is employed. Furthermore, many state-of-the-art algorithms, protocols, and performance studies of wirelessnetworks have been reported in [3]. For example, a set of admissioncontrol and resource reservation schemes was presented for QoSprovisioning in wireless networks, and the evolution in the design ofthe IEEE 802.11 DCF MAC protocol was illustrated.

The analytical models for the hybrid WLANs and WMNs, particu-larly with respect to the packet delay, loss probability, and throughputanalysis, are rarely found in the current literature. Recently, Niyato andHossain [17] have presented a bandwidth management and admissioncontrol framework for the integrated WLANs and multihop infras-tructure mesh networks. However, the QoS prediction of such hybridwireless networks was not carried out. To fill in this gap, an analyticalmodel was proposed in [16] to investigate the delay and throughput inthe integrated WLANs and Internet-access mesh networks. However,the model was based on the assumption that the packets generatedby the wireless user terminals (UTs) follow the nonbursty Poissonprocess.

Multimedia applications over mobile wireless networks are becom-ing more and more popular [13]. Many recent measurement studieshave revealed that the traffic arrival process in wireless networksexhibits bursty and correlated nature, which has a considerable impacton the network performance. In this paper, a new analytical model isdeveloped as a cost-effective performance tool to investigate the QoSmetrics, including the packet delay, loss probability, and throughputof the WMNs that interconnect multiple WLANs in the presence ofbursty and correlated traffic. The WMN acts as the multihop backhaulnetwork with the gateway being connected to the Internet [16]. EachMR is connected to one access point (AP) that manages a specificWLAN containing multiple UTs. Each network entity (i.e., UT, AP,and MR) is equipped with one finite-capacity buffer. Packets in theWMN are transmitted in a multihop manner toward or from thegateway. The developed model adopts the Markov-modulated Poissonprocess (MMPP) to capture the bursty and correlated nature of the

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450 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 1, JANUARY 2013

network traffic. The effectiveness and accuracy of the analytical modelare validated through extensive simulation experiments. The analyticalmodel is then used to evaluate the performance of the hybrid wirelessnetworks under bursty and correlated traffic.

The rest of this paper is organized as follows: Section II presentshow to model the bursty and correlated traffic. Section III derives theanalytical model to investigate the packet delay, loss probability, andthroughput in the hybrid wireless networks. The accuracy of the modelis validated in Section IV. Section V carries out performance analysis.Finally, Section VI concludes this study.

II. BURSTY AND CORRELATED TRAFFIC

The MMPP is a doubly stochastic process with the arrival ratevarying according to a multistate ergodic continuous-time Markovchain [6], [9], [13]. It is capable of modeling the bursty and correlatednature of the packet arrival process due to the following attractiveproperties.

1) The MMPP can capture the time-varying arrival rate and theimportant correlations among interarrival times.

2) The MPPP is closed under the splitting and superposition oper-ations and, thus, can be used to model the traffic splitting andmerging behaviors in hybrid wireless networks.

3) The well-developed queuing theory of the MMPP makes itfeasible to model communication networks with the MMPParrival process.

A two-state MMPPs with subscript s is adopted to model thetraffic generated by the UTs. MMPPs is characterized by the in-finitesimal generator Qs of the underlying Markov chain and the ratematrix Λs as

Qs =

[−ϕs1 ϕs1

ϕs2 −ϕs2

]and Λs =

[λs1 00 λs2

](1)

where ϕs1 is the transition rate from state 1 to 2, and ϕs2 is the rate outof state 2 to 1. λs1 and λs2 are the traffic rates when the Markov chainis in states 1 and 2, respectively. The mean arrival rate λs of MMPPs

is given by

λs =ϕs1 × λs2 + ϕs2 × λs1

ϕs1 + ϕs2

. (2)

The squared coefficient of variation (SCV) of the interarrival time,i.e., C2

s , and the one-step correlation coefficient, i.e., r1s , are oftenused to represent the burstiness of packet arrivals and the correlationbetween interarrival times [13]. C2

s and r1s can be given by

C2s =1+

2 × ϕs1 × ϕs2 × (λs1 − λs2)2

(ϕs1+ϕs2)2×(λs1×λs2+λs1×ϕs2 + λs2 × ϕs1)(3)

r1s =λs1 × λs2 × (λs1 − λs2)

2 × ϕs1 × ϕs2

C2s×(ϕs1+ϕs2)2×(λs1×λs2+λs1×ϕs2+λs2×ϕs1)2

. (4)

III. ANALYTICAL MODEL

This section presents the analytical model to investigate the end-to-end packet delay, loss probability, and throughput of the hybridwireless network in the presence of bursty and correlated traffic. Weconsider an n× n grid topology where MRs are uniformly distributed[19], with the gateway being deployed at the network center [1]. Thepackets generated by the UTs follow an MMPPs with infinitesimalgenerator Qs and rate matrix Λs, as given by (1). In this paper, wefocus on the upstream traffic with the shortest path routing scheme[1], i.e., the generated packets are forwarded to the gateway via MRs

in a multihop fashion through the shortest path, which causes thetraffic to be nonuniformly distributed across the network channels. Tomodel this type of traffic pattern, we need to determine the number ofMRs that are located at i hops away from the gateway and, thus, arereferred to as i-hop MRs, where 1 ≤ i ≤ hmax, and hmax denotes themaximum possible hop-count distance from the MR to the gateway.When n is odd, the number of i-hop MRs, i.e., Ni, can be writtenas Ni = 8 × i; when n is even, Ni = 8 × i if i ≤ min(x, y), andNi = 2 × n− 1 otherwise [16], where x and y represent the row andcolumn orders of MRs in the grid topology, respectively.

To determine the packet delay and throughput at UTs, APs, andMRs, the queuing theory of the MMPP/M/1/K system with finitebuffer size K is used. Following the order in which the traffic flowcrosses the hybrid networks, we will derive the performance measuresat UTs, APs, and MRs step by step and then obtain the expressions ofthe end-to-end packet delay, loss probability, and throughput.

A. Packet Delay and Throughput at UTs

Given the finite buffer size Ks of the MMPPs/M/1/Ks queuingsystem for modeling the UTs, the arriving packets are dropped whenthe queue becomes full. Let Pbs denote the probability that an arrivingpacket finds the MMPPs/M/1/Ks queue full [Pbs will be givenin (13)]. The effective traffic entering the queuing system of a UTis a fraction (1 − Pbs) of the traffic generated by the UT. As thesplitting of an MMPP is again a new MMPP, let MMPPe

s represent theeffective traffic entering the queuing system. MMPPe

s can be obtainedby splitting MMPPs with the probability (1 − Pbs). Based on theprinciple of splitting of an MMPP [6], the infinitesimal generator Qe

s

and rate matrix Λes of MMPPe

s can be given by

Qes =Qs =

[−ϕs1 ϕs1

ϕs2 −ϕs2

](5)

Λes=(1 − Pbs)Λs

=

[(1 − Pbs)× λs1 0

0 (1 − Pbs)× λs2

]. (6)

The throughput at the UT is equivalent to the effective mean arrivalrate λ

e

s of MMPPes. λ

e

s can be obtained by virtue of (2) as

λes =

ϕes1 × λe

s2 + ϕes2 × λe

s1

ϕes1 + ϕe

s2

(7)

where ϕes1, ϕe

s2, λes1, and λe

s2 are the parameters of MMPPes and can

be given by Qes and Λe

s.In what follows, we will determine the packet delay at the UT. Let

Pv,j , 0 ≤ v ≤ Ks and j = 1, 2, represent the probability that there arev packets in the queue and the underlying Markov chain of MMPPs,characterizing the traffic arriving at the queue, is at state j. Pv,j can beobtained by a bivariate Markov chain. State (v, j) corresponds to thecase that there are v packets in the queue and the MMPPs is at statej. The transition rate out of state (v, j) to (v + 1, j) is λsj , where λsj

is the packet arrival rate at the queue and can be obtained from Λs.The rate from state (v + 1, j) to (v, j) is the service rate μs. Let Ps

denote the successful channel-access probability for the UT. μs can beexpressed as μs ≈ ln(1 − Ps)

−1/t�, where t� denotes the amount ofairtime required to transmit one packet in WLANs [16]. The transitionrate out of state (v, 1) to (v, 2) is ϕs1, whereas the rate from state(v, 2) to (v, 1) is ϕs2, where ϕs1 and ϕs2 can be given by Qs.

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The transition rate matrix G of the bivariate Markov chain can bereadily obtained. The steady-state probability vector P = (Pv,j) =(P0,P1, . . . ,PKs), where Pv = (Pv,1, Pv,2), 0 ≤ v ≤ Ks, satisfiesthe following equations:

P×G = 0 and P× e = 1. (8)

Solving these equations yields the steady-state vector as

P = u× (I−Φ+ e× u)−1 (9)

where Φ = I+G/min{G(i, i)}, e is a unit column vector, and u isan arbitrary row vector of Φ.

Let Pv , 0 ≤ v ≤ Ks denote the probability that there are v packetsin the queue of the UT. Pv is given by

Pv =

2∑j=1

Pv,j . (10)

The delay Ds experienced by a packet to cross a UT is equivalent toits waiting time in the queuing system. According to Little’s law [8],Ds can be written as

Ds =

∑Ks

v=0v × Pv

λes

(11)

where λe

s is given by (7).To determine Pbs in (6), let us first calculate the probability P ′

v ,0 ≤ v ≤ Ks that there are v packets in an MMPPs/M/1/Ks queueobserved by an arriving packet. P ′

v can be given by [15]

P ′v =

(Ks∑v=0

Pv ×Λs × e

)−1

Pv ×Λs × e. (12)

Therefore, the probability Pbs that an arriving packet finds the finitebuffer full can be written as

Pbs = P ′Ks

. (13)

B. Packet Delay and Throughput at APs

Packets departing from the UTs enter the queue of its associ-ated AP. We adopt the output process, denoted by MMPPo

s, of theMMPPe

s/M/1 queuing system, where MMPPes represents the effective

traffic entering the queuing system at the UT to approximately modelits output process. This approximation is validated by comparing theanalytical performance results with those obtained through simulation(please note that this approximation of the output process is not usedin the simulation experiments). MMPPo

s can be obtained by matchingthe moments of the interdeparture time of the packets. Following themethod used in [5] to derive the output process from an MMPP/M/1queue, the infinitesimal generator Qo

s and rate matrix Λos of MMPPo

s

can be determined.The traffic arriving at the queue in the AP can be obtained by

applying the flow conservation law [8]. Since there are N UTs ina WLAN, the traffic arriving at the queue of the AP is the super-position of N traffic flows, each of which is modeled by MMPPo

s.As the superposition of multiple MMPPs gives rise to MMPP again,let MMPPa denote the traffic arriving at the queue of the AP. Theinfinitesimal generator Qa and rate matrix Λa of MMPPa can be

obtained by matching the following four statistical characteristicsof N MMPPo

s: 1) mean; 2) variance; 3) third central moment; and4) integral of the covariance function of the arrival rate [9]. Theeffective traffic entering the queue of AP, which is denoted by MMPPe

a,can be determined using the similar way of deriving MMPPe

s thatwas presented in Section III-A. The throughput at the AP is the meanarrival rate λ

e

a of MMPPea and can be obtained using (2). To determine

the packet delay at the AP, the queue in the AP is modeled as anMMPPa/M/1/Ka queuing system, where the service rate is μa andcan be determined based on the successful channel-access probabilityPa for the AP. According to (8)–(11), we can determine the packetdelay Da at the AP. Following the derivation of the output processfrom the queuing system in the UT, which is presented in Section III-A,we can obtain the output process MMPPo

a from the AP.

C. Packet Delay and Throughput at MRs

Packets leaving the AP will enter the queue of its associated MRor get lost when the buffer of the MR is full. Let MMPPri , MMPPe

ri,

and MMPPori

denote the traffic arriving at, entering into, and departingfrom the queue of MRs located at i hops away from the gateway,where 1 ≤ i ≤ hmax. Since MRs located at the rim of the network(i.e., hmax-hop MRs) do not relay packets from MRs that are locatedfarther away, the packets arriving at the queue of an MR locatedat the network rim come from those departing from its associatedAP only, i.e., MMPPo

a. According to (5) and (6), we can obtain theparameter matrices of MMPPe

rhmax. Following the method presented

in Section III-A, we can readily obtain the output process from theMRs located at the network rim, i.e., MMPPo

rhmax.

The traffic arriving at the queue of MRs located at i, (1 ≤ i ≤hmax − 1) hops away from the gateway is the superposition of thetraffic departing from MRs located at (i+ 1) hops away and the trafficcoming from the associated AP. Since there are Ni+1 MRs located at(i+ 1) hops away from the gateway, the traffic leaving these MRs,denoted by MMPPTotal_o

ri+1, is the superposition of Ni+1 traffic flows

modeled by MMPPori+1

, where MMPPori+1

can be obtained followingthe derivation of MMPPo

rhmax. As the traffic departing from the MRs

located at (i+ 1) hops away from the gateway is evenly distributed onthe MRs located at i hops away, the traffic arriving at an MR at i hopsaway from the gateway, which is denoted by MMPP′

ri, is the splitting

of the traffic flow MMPPTotal_ori+1

with the splitting probability 1/Ni.Based on (5) and (6), we can obtain the infinitesimal generator Q′

ri

and rate matrix Λ′ri

of MMPP′ri

.The traffic arriving at the queue of an MR located at i hops,

1 ≤ i ≤ hmax − 1, away from the gateway is the superposition of oneMMPP′

riand one MMPPo

a. According to the method of determinationof MMPPa, characterizing the traffic arriving at the AP, the infinites-imal generator Qri and rate matrix Λri of MMPPri can be obtained.The parameter matrices of MMPPe

riand MMPPo

rican be determined

by following the derivation of MMPPerhmax

and MMPPorhmax

, respec-tively. The throughput at the MRs located at i hops away from thegateway is equivalent to the mean arrival rate λ

e

riof MMPPe

riand

can be determined based on (2). The delay experienced by a packet tocross an MR located at i hops away from the gateway, i.e., Dri , can beidentified using (8)–(11).

D. Delay, Loss, and Throughput Analysis in the HybridWireless Networks

The end-to-end delay Ds→gi (1 ≤ i ≤ hmax) experienced by a

packet generated by a UT in the WLAN that is associated with anMR located at i hops away from the gateway is equal to the sum of thepacket transmission time and the delay experienced at the source UT,

452 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 1, JANUARY 2013

its associated AP, and all intermediate MRs. Therefore, the end-to-enddelay can be written as

Ds→gi = i× tm + 2 × t� +Ds +Da +

i∑j=1

Drj (14)

where tm and t� denote the amounts of airtime required to transmitone packet in the WMN and the WLAN, respectively; and Ds, Da,and Drj represent the delays experienced by a packet to cross the UT,the AP, and the MR located at j hops away from the gateway. Theend-to-end throughput T s→g

i (1 ≤ i ≤ hmax) is defined as the averagenumber of packets generated by a UT in the coverage of an MR locatedat i hops away from the gateway that are successfully received by thegateway in a time unit. Thus, T s→g

i is given by

T s→gi = λs × (1 − Pbs)× (1 − Pba)×

∏i

j=1(1 − Pbrj ) (15)

where Pba and Pbrj are the blocking probabilities at the AP and theMRs located at j hops away from the gateway, respectively, and canbe determined based on (12) and (13).

In what follows, we will derive the aggregate network throughput,loss probability, and average end-to-end delay experienced by thepackets as the performance metrics of the hybrid wireless networks.The aggregate network throughput Tagg is defined as the total numberof packets received by the gateway and can be given by

Tagg =

hmax∑i=1

N ×Ni × T s→gi . (16)

The total number of packets generated by all UTs can be expressedas Ttotal =

∑hmax

i=1N ×Ni × λs. Therefore, the loss probability for

the hybrid wireless networks is

Lnet = 1 − Tagg

Ttotal

= 1 −∑hmax

i=1Ni × T s→g

i

λs ×∑hmax

i=1Ni

. (17)

The aggregate end-to-end delay Dagg is the total delay experiencedby all the packets that are successfully received by the gateway, i.e.,Dagg =

∑hmax

i=1N ×Ni × T s→g

i ×Ds→gi . The average end-to-end

delay De2e experienced by the packets in the hybrid wireless networkscan be obtained by averaging the delay of packets that are successfullyreceived by the gateway. Therefore, De2e can be written as

De2e =Dagg

Tagg

=

∑hmax

i=1Ni × T s→g

i ×Ds→gi∑hmax

i=1Ni × T s→g

i

. (18)

IV. VALIDATION OF THE MODEL

The effectiveness and accuracy of the developed analytical modelare validated via a discrete-event simulator based on the OMNeT++simulation framework. The packets generated by the UTs are modeledby MMPPs with infinitesimal generator Qs and rate matrix Λs.Extensive simulation experiments have been performed to achievethis purpose. However, for specific illustration purposes, we presentthe results of the following typical cases: the number of MRs in theWMN (C = 81) and the number of UTs in a WLAN (N = 8 and15, respectively). Many commercial companies have deployed real-life high-performance WMNs. For example, Teletronics International,Inc., provided the solutions of WMNs in hotels, private yacht industry,U.S. government and public service agencies, etc., using their devised

facilities, called EZMESH™ units, including backhaul routers andAPs. Following the representative parameter settings, the channelcapacities in the WLAN and the WMN are set to be 11 and 54 Mb/s,respectively. Furthermore, two different packet sizes, i.e., 8000 and10 000 bits, are considered because they are typical settings for real-world applications (e.g., IEEE 802.11 environments) and have beenwidely adopted in related studies [4], [7], [20]. As a result, the lengthof a time slot is set to be the amount of airtime required to transmitone packet, i.e., t� = 7.27e− 4s and 9.09e− 4s in the WLAN andtm = 1.48e− 4s and 1.85e− 4s in the WMN. The buffer size is setto be 32 packets in the UTs, 48 packets in the APs, and 64 packets inthe MRs due to the increase in traffic loads at UTs, APs, and MRs.The successful channel-access probabilities Ps, Pa, and Pri (1 ≤ i ≤hmax) for UTs, APs, and MRs are given by Ps = 2.5e− 3, Pa = 7e−3, and Pri = [8.2e− 2, 7.3e− 2, 6.4e− 2, 5.5e− 2] for 1 ≤ i ≤ 4;the infinitesimal generator Qs of MMPPs is shown in the captionof the figures, representing different degrees of traffic burstinessand correlations.

Figs. 1 and 2 depict the analytical and simulation results for theaverage end-to-end delay, aggregate network throughput, and lossprobability as a function of the traffic rate of the UT in the hybridwireless networks. In these figures, the horizontal axis represents thetraffic rate λs1 at which the packets are generated by the UT whenMMPPs is at state 1. For the sake of clarity, we have deliberately set thearrival rate λs2 at state 2 as zero; otherwise, we need to use 3-D graphsto represent the results. To reduce the number of figures, as well as notto degrade the clarity of the figures, we depict the performance resultsof the average end-to-end delay and aggregate network throughputin one subfigure. Specifically, the left vertical axis in Figs. 1(a) and2(a) denotes the average end-to-end delay, and the right vertical axisrepresents the aggregate network throughput. The vertical axis inFigs. 1(b) and 2(b) denotes the results of loss probability. These figuresreveal that the analytical performance results closely match thoseobtained from the simulation, validating the accuracy of the developedanalytical model.

V. PERFORMANCE ANALYSIS

In this section, the developed model is used as a cost-effectivetool to investigate the impact of bursty and correlated traffic onthe performance of the hybrid wireless networks. To achieve thisgoal, Table I lists the performance results of the average end-to-end delay, aggregate network throughput, and loss probability of thehybrid wireless networks in the presence of bursty and correlatedMMPP arrivals with varying SCV of the interarrival time, i.e., C2

s .For specific illustration purposes, the performance results are shownin a 9 × 9 grid placement with eight UTs in each WLAN. Thepacket size is 8000 bits. The other system parameters, unless specifiedin Table I, are set the same as those presented in Section IV. Themean arrival rate of the MMPP traffic can be obtained according to(2). As shown in Table I, the increase in C2

s causes the significantgrowth in the average end-to-end delay and loss probability, as well asthe substantial decrease in the aggregate network throughput. This isbecause the larger C2

s can lead to a higher degree of traffic burstiness.The case C2

s = 1 corresponds to the scenario that the traffic followsa nonbursty Poisson arrival process (i.e., the assumption made in theprevious study [16]). The table reveals that the developed analyti-cal model manages to predict the increase in the end-to-end delayand loss probability, as well as the decrease in the network throughputfor hybrid wireless networks in the presence of bursty and correlatedtraffic, as compared with those predicted under the assumption ofPoisson traffic. The results highlight the importance of consideringthe traffic burstiness and correlations for developing the analytical

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Fig. 1. (a) Average end-to-end delay and aggregate network throughput and (b) loss probability for the hybrid wireless networks predicted by the model andsimulation in the hybrid wireless networks under bursty and correlated traffic with N = 8, ϕs1 = 0.09, and ϕs2 = 0.03.

Fig. 2. (a) Average end-to-end delay and aggregate network throughput and (b) loss probability for the hybrid wireless networks predicted by the model andsimulation in the hybrid wireless networks under bursty and correlated traffic with N = 15, ϕs1 = 0.7, and ϕs2 = 0.35.

TABLE IEFFECTS OF BURSTY AND CORRELATED TRAFFIC ON THE PERFORMANCE OF HYBRID WIRELESS NETWORKS

model to accurately and quantitatively capture the effects of the burstymultimedia traffic on the performance of hybrid wireless networks.

Since the traffic loads at the MRs located closer to the gatewaybecome higher, the packet delay experienced at these MRs increases.

This situation is exacerbated in the presence of bursty and correlatedtraffic. If additional MRs are deployed at the location under heavytraffic, the loads will be shared by more MRs. The developed analyticalmodel gives the quantitative relationship between the QoS metrics to

454 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 1, JANUARY 2013

be achieved in the hybrid wireless network and the number of MRsdeployed at the location with different hops to the gateway. Therefore,it can be extended and used to calculate the appropriate number ofMRs that should be deployed in the WMN subject to the specificQoS requirements.

VI. CONCLUSION

In this paper, a new analytical model has been developed to in-vestigate the performance measures, including the end-to-end delay,loss probability, and throughput in the hybrid wireless networks,where the mesh network is used to connect and integrate WLANs.This model is able to capture the bursty and correlated nature ofthe network traffic. Simulation experiments have been performed tovalidate the effectiveness and accuracy of the analytical model anddemonstrated that the performance results predicted by the analyticalmodel closely match those obtained from the simulation. The modelhas been used as a cost-effective tool to study the impact of burstyand correlated traffic on the performance of hybrid wireless networks.The results have emphasized the importance of considering and inves-tigating the impact of bursty and correlated traffic in hybrid wirelessnetworks.

REFERENCES

[1] I. F. Akyildiz and X. Wang, “A survey on wireless mesh networks,” IEEECommun. Mag., vol. 43, no. 9, pp. S23–S30, Sep. 2005.

[2] G. Bianchi, “Performance analysis of the IEEE 802.11 distributed coordi-nation function,” IEEE J. Sel. Areas Commun., vol. 18, no. 3, pp. 535–547,Mar. 2000.

[3] A. Boukerche, Handbook of Algorithms for Wireless Networking andMobile Computing. London, U.K.: Chapman and Hall, 2005.

[4] P. Chatzimisios, A. C. Boucouvalas, P. Raptis, K. Paparrizos, andD. Kleftouris, “Enhancing performance of the IEEE 802.11 distributed co-ordination function via packet bursting,” in Proc. IEEE Global Telecom-mun. Conf. Workshops, 2004, pp. 245–252.

[5] H.-W. Ferng and J.-F. Chang, “Connection-wise end-to-end performanceanalysis of queuing networks with MMPP inputs,” Perform. Eval., vol. 43,no. 1, pp. 39–62, Jan. 2001.

[6] W. Fischer and K. Meier-Hellstern, “The Markov-modulated Poisson pro-cess (MMPP) cookbook,” Perform. Eval., vol. 18, no. 2, pp. 149–171,Sep. 1993.

[7] S. Gollakota and D. Katabi, “Zigzag decoding: Combating hidden termi-nals in wireless networks,” in Proc. SIGCOMM, 2008, pp. 159–170.

[8] D. Gross and C. Harris, Fundamentals of Queueing Theory, 3rd ed.Hoboken, NJ: Wiley, 1998.

[9] H. Heffes, “A class of data traffic processes-covariance function charac-terization and related queueing results,” Bell Syst. Tech. J., vol. 59, no. 6,pp. 897–929, Jul./Aug. 1980.

[10] H. Hu, Y. Zhang, and H.-H. Chen, “An effective QoS differentiationscheme for wireless mesh networks,” IEEE Netw., vol. 22, no. 1, pp. 66–73, Jan./Feb. 2008.

[11] M. Iqbal, X. Wang, S. Li, and T. Ellis, “QoS scheme for multimediamulticast communications over wireless mesh networks,” IET Commun.,vol. 4, no. 11, pp. 1312–1324, Jul. 2010.

[12] J.-S. Liu and C.-H. R. Lin, “Achieving higher throughput in IEEE 802.11wireless local area networks with burst transmission methods,” IET Com-mun., vol. 3, no. 6, pp. 1050–1060, Jun. 2009.

[13] K.-H. Liu, X. Ling, X. Shen, and J. W. Mark, “Performance analysis ofprioritized MAC in UWB WPAN with bursty multimedia traffic,” IEEETrans. Veh. Technol., vol. 57, no. 4, pp. 2462–2473, Jul. 2008.

[14] A. K. Mahani, M. Naderi, C. Casetti, and C. F. Chiasserini, “MAC-layer channel utilisation enhancements for wireless mesh networks,” IETCommun., vol. 3, no. 5, pp. 794–807, May 2009.

[15] K. S. Meier-Hellstern, “The analysis of a queue arising in overflow mod-els,” IEEE Trans. Commun., vol. 37, no. 4, pp. 367–372, Apr. 1989.

[16] G. Min, Y. Wu, and L. T. Yang, “Performance modeling and analysisof integrated WLANs and Internet-access mesh networks,” Proc. CSE,pp. 1–8, 2009.

[17] D. Niyato and E. Hossain, “Integration of IEEE 802.11 WLANs withIEEE 802.16-based multihop infrastructure mesh/relay networks: Agame-theoretic approach to radio resource management,” IEEE Netw.,vol. 21, no. 3, pp. 6–14, May/Jun. 2007.

[18] M. Peltomaki, J. Koljonen, O. Tirkkonen, and M. Alava, “Algorithms forself-organized resource allocation in wireless networks,” IEEE Trans. Veh.Technol., vol. 61, no. 1, pp. 346–359, Jan. 2012.

[19] J. Robinson and E. W. Knightly, “A performance study of deploymentfactors in wireless mesh networks,” in Proc. IEEE INFOCOM, 2007,pp. 2054–2062.

[20] M. Vutukuru, H. Balakrishnan, and K. Jamieson, “Cross-layer wireless bitrate adaptation,” in Proc. SIGCOMM, 2009, pp. 3–14.

On the Performance of Transmit Antenna SelectionBased on Shadowing Side Information

Ahmet Yılmaz, Ferkan Yılmaz, Mohamed-Slim Alouini, andOguz Kucur

Abstract—In this paper, a transmit antenna selection scheme, which isbased on shadowing side information, is investigated. In this scheme, theselected single transmit antenna provides the highest shadowing coefficientbetween a transmitter and a receiver. By the proposed technique, the fre-quency of the usage of the feedback channel from the receiver to the trans-mitter and channel estimation complexity at the receiver can be reduced.We study the performance of our proposed technique, and in the analysis,we consider an independent but not identically distributed generalized-Kcomposite fading model. More specifically, exact and closed-form expres-sions for the outage probability, the moment-generating function, themoments of signal-to-noise ratio, and the average symbol error probability(SEP) are derived. In addition, asymptotic outage probability and SPexpressions are also presented to investigate the diversity order and thearray gain. Finally, our theoretical performance results are validated byMonte Carlo simulations.

Index Terms—Composite fading channels, diversity order, generalized-K, shadowing, transmit antenna selection (TAS).

I. INTRODUCTION

A significant improvement can be obtained in the performance ofwireless communication systems when multiple antennas are used atthe transmitter side [1], [2]. However, the employment of multipleantennas at the transmitter increases cost, complexity, and power con-sumption due to the increase in the number of required radio-frequency(RF) chains [3], [4]. Transmit antenna selection (TAS) reduces thenumber of RF chains as well as the cost, complexity, and powerconsumption since it relies on a single transmitter structure [3], [4].

Manuscript received December 16, 2011; revised June 2, 2012 and August 13,2012; accepted September 16, 2012. Date of publication September 21, 2012;date of current version January 14, 2013. This work was supported in part byKing Abdullah University of Science and Technology (KAUST) and conductedwhile A. Yılmaz was visiting KAUST. The review of this paper was coordinatedby Prof. L.-L. Yang.

A. Yılmaz and O. Kucur are with the Department of Electronics Engineering,Gebze Institute of Technology, Gebeze 41400, Turkey (e-mail: ahmetyilmaz@gyte.edu.tr; okucur@gyte.edu.tr).

F. Yılmaz and M.-S. Alouini are with King Abdullah University of Sci-ence and Technology, Thuwal 23955-6900, Saudi Arabia (e-mail: ferkan.yilmaz@kaust.edu.sa; slim.alouini@kaust.edu.sa).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2012.2220163

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