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678IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 4, MAY 2007A Cross-Layer Approach for WLANVoice Capacity PlanningYu Cheng, Member, IEEE, Xinhua Ling, Student Member, IEEE, Wei Song, Lin X. Cai,Weihua Zhuang, Senior Member, IEEE, Xuemin Shen, Senior Member, IEEEAbstract— This paper presents an analytical approach todetermining the maximum number of on/off voice flows that canbe supported over a wireless local area network (WLAN), undera quality of service (QoS) constraint. We consider multiclassdistributed coordination function (DCF) based medium accesscontrol (MAC) that can provision service differentiation viacontention window (CW) differentiation. Each on/off voice flowspecifies a stochastic delay bound at the network layer as theQoS requirement. The downlink voice flows are multiplexed atthe access point (AP) to alleviate the MAC congestion, wherethe AP is assigned a smaller CW compared to that of themobile nodes to guarantee the aggregate downlink throughput.There are six-fold contributions in this paper: 1) a nonsaturatedmulticlass DCF model is developed; 2) a cross-layer framework isproposed, which integrates the network-layer queueing analysiswith the multiclass DCF MAC modeling; 3) the channel busynessratio control is included in the framework to guarantee theanalysis accuracy; 4) the framework is exploited for statisticalmultiplexing gain analysis, network capacity planning, contentionwindow optimization, and voice traffic rate design; 5) a head-ofline outage dropping (HOD) scheme is integrated with the APtraffic multiplexing to further improve the MAC channel utilization; 6) performance of the proposed cross-layer analysis andthe associated applications are validated by extensive computersimulations.Index Terms— Cross-layer analysis, WLAN voice capacity,contention window optimization, head-of-line outage dropping,nonsaturated MAC modelingI. I NTRODUCTIONIN RECENT years, extensive efforts have been made bothin academia and industry to provision voice over InternetProtocol (VoIP) over IEEE 802.11 wireless local area networks (WLANs) [1]–[4]. In order to support the toll-qualityvoice or other multimedia applications with quality of service(QoS) requirements, the WLAN is required to provision somequantitative performance guarantees, e.g. packet loss rate,delay bound, or delay jitter. For Internet QoS provisioning,a bottleneck link is usually modeled as a queueing system atthe network layer for QoS analysis. The traffic arrival processin voice/video applications is usually bursty with variabledata rate [5], [6]; a proper service rate falling between theManuscript received May 15, 2006; revised December 3, 2006.Y. Cheng is with the Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA (email:cheng@iit.edu).X. Ling, W. Song, L. X. Cai, W. Zhuang, and X. Shen are with theDepartment of Electrical and Computer Engineering, University of Waterloo,Waterloo, ON N2L 3G1, Canada (email: {x2ling, wsong, lcai, wzhuang,xshen}@uwaterloo.ca).Digital Object Identifier 10.1109/JSAC.2007.070505.average arrival rate and the peak rate, which is defined asthe effective bandwidth [7], needs to be determined to satisfythe quantitative QoS requirements. Given the link capacity,which is constant in wireline networks, the network capacityin terms of the number of effective-bandwidth guaranteed (i.e.,QoS guaranteed) traffic flows can then be obtained.With the WLAN Internet access, the wireless link involvedin the end-to-end path is prone to become a bottleneckdue to the limited spectrum, channel contention delays, andpossible collisions. The QoS analysis and flow (or call) levelcapacity planning in the WLAN in fact incurs a cross-layerdesign problem, where the effective bandwidth required bythe network layer for QoS guarantee needs to be provisionedby the medium access control (MAC) layer under the calladmission control (CAC). To the best of our knowledge, therewas no such a cross-layer analytical tool available before ourwork presented in this paper, by which we can determinethe network capacity and the proper configuration of theMAC, according to network-layer QoS requirements. TheIEEE 802.11 MAC protocol contains two access modes, themandatory distributed coordination function (DCF) mode andthe optional point coordination function (PCF) mode. In thispaper, we consider the 802.11 DCF.The DCF mode is contention based and distributed and,hence, renders effective resource allocation and quantitativeQoS control very difficult. Most of the previous works onthe DCF MAC performance analysis, e.g. [8]–[10] and thereferences therein, focus on deriving the channel throughputor average delay from a Markov chain under saturated inputtraffic. While the saturated modeling is applicable for bulkdata transfer applications, it is hardly valid for real-timevoice/video applications that are normally associated with abursty arrival process. It is very difficult, if not impossible, toderive an efficient analytical tool from the saturated modelingfor effective bandwidth provisioning and call-level networkcapacity analysis.In [11], [12], a simple yet accurate analytic model isdeveloped for evaluating the 802.11 DCF in nonsaturated case,where each node is modeled as a discrete time G/G/1 queue1.While the nonsaturated model is used in [11], [12] to derive theMAC service time distribution for input traffic with a generalarrival distribution, no hint is provided there on how to applythe model to analytically obtain a capacity region under certain1 According to the standard Kendall’s notation, for G/G/1 and G/D/1queueing systems, “G” stands for a “general” distribution, “D” stands fora “deterministic” service time, and “1” represents the number of servicechannel.c 2007 IEEE0733-8716/07/ 25.00

CHENG et al.: A CROSS-LAYER APPROACH FOR WLAN VOICE CAPACITY PLANNINGQoS requirements. In [2], it is shown that the maximum DCFMAC capacity and satisfying QoS performance can only beachieved in the nonsaturated case. It is also shown that, when aWLAN works in the proper operation range under CAC, eachpacket sees an approximately constant service rate; thereforethe G/G/1 queue at each node can be well approximated bya G/D/1 queue. Inspired by the above results, we present inthis paper that the queueing analysis at the network layer canbe combined with the nonsaturated DCF MAC modeling toform a cross-layer analytical framework to investigate thestatistical multiplexing gain, QoS guarantee, and call-levelnetwork capacity over the WLAN. While the proposed crosslayer framework is generic in traffic models and applications,we focus on the voice over WLAN in this paper.It should be emphasized that maintaining the WLAN withinthe proper unsaturated operation range by CAC is essentialfor generating accurate analytical results from the proposedcross-layer framework; otherwise, the heavy MAC collisionwill lead to large service time fluctuation and invalidate theG/D/1 modeling. The simulation studies in [2] show that, at theoptimal operation point, the channel busyness ratio (CBRO)is stable around 0.9 (without request/clear to send, RTS/CTS)or 0.95 (with RTS/CTS) independent of the packet size andnumber of mobile nodes. Such an observation is exploited in[1] for a measurement-based call admission and rate controlin voice/data integrated WLANs. In this paper, we integratethe CBRO control within the cross-layer framework, wherethe admission region (or call-level network capacity) takingaccount of the statistical multiplexing among on/off voiceflows can be accurately and analytically calculated.The packet-level buffering and QoS adaption are commonly used to improve the sustainability of a multimediaIP application session under various network load conditions.However, it has been manifested [1]–[3], [11], [12] that theQoS performance over the DCF MAC shows a “good-or-bad”sharp-turning behavior around the operation point, in whichcase the QoS adaption is ineffective. We demonstrate in thispaper that downlink traffic multiplexing at the AP, in twoway conversations, can improve the channel utilization andfacilitate the downlink QoS adaption by adjusting the resourceallocation to the AP. Moreover, the aggregate downlink rateat the AP is differentiated with the per-flow uplink rate at amobile node by a multiclass DCF MAC that provisions servicedifferentiation via contention window (CW) differentiation.We extend the nonsaturated DCF modeling of [11], [12] toinclude the class differentiation. Given the packet-level QoSrequirements, both the network capacity and the MAC layercontention windows for the AP and the mobile nodes canbe jointly determined from our cross-layer framework. Inaddition, we investigate a head-of-line outage dropping (HOD)scheme, where a head-of-line packet being served by the MAClayer will be dropped when it exceeds the delay bound. Weshow that the QoS of the WLAN applying the HOD schemedegrades gradually instead of the sharp-turning behavior asthe traffic load increases, which can considerably facilitate theQoS adaption and the measurement-based admission control.In Section II, we give more review on related work.Section III describes the system model. Section IV presentsthe nonsaturated DCF model with class differentiation. In679Section V, the nonsaturated DCF model is combined withthe CBRO control and network layer queueing analysis toform the cross-layer analytical framework. Applications of theframework to statistical multiplexing gain analysis, networkcapacity planning, voice codec rate design are also presented.In Section VI, extensive numerical analysis and computersimulation results are presented to demonstrate the analysisaccuracy and the efficiency of the HOD scheme, statisticalmultiplexing gain, and contention window optimization. Section VII gives the concluding remarks.II. R ELATED W ORKA comprehensive discussion of the cross-layer optimizationissues for efficient wireless multimedia transmissions is givenin [13]. Various possible interactions from the physical layer(PHY) up to the application layer (APP) in the wirelessprotocol stack are addressed in [14]–[16]. However, little workon NET/MAC cross-layer design for provisioning QoS guaranteed realtime applications, as demonstrated in this paper,had been reported in the literature.The DCF MAC has been enhanced to provision servicedifferentiation, e.g. in [17], [18] and the references therein.The standardized differentiation mechanisms, as defined in theenhanced distributed channel access (EDCA) of IEEE 802.11e,include differentiating CW backoff parameters, interframespacing before data transmission (arbitration interframe space,AIFS), and channel holding times upon the successful channel access (transmission opportunity, TXOP). In this paper,we extend the nonsaturated DCF modeling of [11], [12] toanalyze a DCF MAC with CW differentiation. While the CWdifferentiation is only a subset of the differentiation schemesprovided by EDCA, it should not be difficult to includeAIFS differentiation into the analytical framework. IntegratingTXOP into the nonsaturated DCF model is still an open issue.The CW differentiated DCF provides us simple yet effectiveservice differentiation MAC, which facilitates our effort inrevealing insight into the NET/MAC cross-layer design.The voice capacity of WLANs has been investigated bymeasurement studies or analytical estimation under simplifiedassumptions of channel collision [19]–[21]. However, all thestudies deal with constant-rate voice flows and do not considerthe possible statistical multiplexing gain achievable by exploiting the on/off effect in voice. While the capacity region ofon/off voice flows has been studied by computer simulations in[1], the capacity region and associated statistical multiplexinggain are analytically determined under a QoS specificationin this paper. It is shown in [3] that the unbalanced trafficdistribution due to downlink aggregation can easily makeAP the QoS bottleneck under the standard 802.11 DCF. Weshow in this paper that the CW differentiation can provisiona fair resource sharing between the uplink and downlinktraffic. A multiplexing-multicast (M-M) scheme is proposedin [4] to improve the downlink performance by aggregatingpackets from multiple voice flows into a big multicast packet.While the study in [4] focus on suppressing the packetheader overhead by multicasting, we emphasize the statisticalmultiplexing gain by traffic aggregation.In WLANs, the excessive packet delay due to heavy collision tends to result in head-of-line (HOL) blocking problem

680IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 4, MAY 2007[22], where the subsequent packets in the queue have to waitbefore the HOL packet is served or dropped. The HOD schemeproposed in this paper to address the HOL blocking issue isclosely related to the active queue management scheme [23],[24] that has been well studied in wireline networks; however,there is no much work quantitatively demonstrating the effectof HOD over a WLAN. Particularly, this paper is the firstwork (as far as we know) that reveals the effect of HOD inalleviating the “good-or-bad” sharp-turning DCF behavior.III. S YSTEM M ODELIn this paper, we develop an analytical framework forWLAN voice capacity planning. A typical application of thenetwork capacity planning is to determine the call-level network capacity or the admission region, which guarantees thepacket-level QoS for each admitted VoIP flow. The analyticalframework can also help to determine the MAC protocolconfiguration parameters, i.e. the contention window, to tunethe WLAN into the optimal operation point for maximumadmission region. Another typical scenario in network planning is the rate planning. In telephone networks, the calllevel capacity is usually planned by the Erlang-B formula toguarantee a target call blocking probability. In order to fitthe predetermined call-level capacity and the packet-level QoSrequirements, the voice traffic source rate (i.e. the codec rate)needs to be determined properly.A. IEEE 802.11 DCF MACThe basic access mode of the IEEE 802.11 MAC layerprotocol is Carrier Sense Multiple Access with CollisionAvoidance (CSMA/CA) protocol based distributed coordination function. In the DCF mode, each time the channel issensed idle for a time interval exceeding a DCF InterFrameSpace (DIFS), the node starts a new or continues an existingbackoff stage. The time immediately following an idle DIFS isslotted, and a node is allowed to transmit only at the beginningof each time slot. At each backoff stage, a random backoffcounter is uniformly chosen from [0, CW 1], where CWis the contention window size in terms of time slots in thecurrent stage. The backoff counter decreases by one for eachidle time slot and stops when the channel is sensed busy. Whenthe backoff counter reaches zero, the node starts transmissionat the beginning of the next time slot. After a successfultransmission, the contention window is reset to CWmin ; thereceiver will send back an acknowledge (ACK) frame upon thesuccessful receipt of the data frame after a Short InterFrameSpace (SIFS). If the sender does not receive the ACK within acertain time, i.e. ACK timeout, it assumes a collision and thenarranges a retransmission according to a new backoff stagewith doubled contention window size up to CWmax . A dataframe is dropped when the retransmission limit is reached.The DCF MAC also specifies the optional request-tosend/clear-to-send (RTS/CTS) mechanism to solve the hiddenterminal problem. In the proposed analytical model, we do notconsider RTS/CTS for simplicity. However, the model can beextended to include the RTS/CTS mechanism.B. Multiclass DCFWith the DCF MAC, all nodes have the same priority toaccess the channel and achieve the same quality of serviceon average. Such a homogeneous access mode is unfavorablewhen different nodes have different service requirements.Particularly in our case, the AP needs to handle aggregateddownlink flows, corresponding to a much larger traffic loadthan that from a mobile node; it is preferable that the MACallocates the AP a larger serving capacity to guarantee thedownlink throughput. Therefore, we consider an enhancedDCF with class differentiation for more effective QoS provisioning and higher resource utilization.In the multiclass WLAN, mobile nodes belonging to different classes may have different traffic arrival processeswith different QoS requirements. The multiclass DCF assigns different contention windows to different classes, withthe contention windows sizes properly designed to satisfyQoS requirements with efficient resource utilization. Basically,classes with smaller contention windows have a higher priorityto access the channel and therefore occupy a larger portion ofthe serving capacity. We will show that the optimal contentionwindow for each class can be analytically determined tomaximize the resource utilization under the QoS constraints.IV. N ONSATURATED M ULTICLASS DCF M ODELA. Average Backoff TimeWe consider a WLAN supporting S classes with DCF,where class i has Ni nodes, i 1, 2, · · · , S. Time is discretized into slots, and each node is modeled as a discrete timeG/G/1 queue. Assume there is no link layer fragmentation,and one IP packet corresponds to one link layer frame. For aclass-i node, the average traffic arrival rate is λi packets/slot.Define the packet service time as the period from the instantthat a packet begins to be serviced by the MAC layer to theinstant that it is either successfully transmitted or droppedafter several retransmissions. At the steady state, a classi node achieves an average service rate of µi packets/slotand correspondingly a queue utilization ratio of ρi λµii . Tomaintain a stable queue, it is required that ρi 1. Accordingto queueing theory, ρi is also equal to the probability thatthe queue is busy, when the buffer size is large enough toguarantee a lossless system [5].A class-i node is assigned a minimum contention windowof CWi,min . All the classes have the same retransmissionlimit of mr (equal to 7 in 802.11 DCF) and the samemaximum backoff stage of mb (equal to 5 in 802.11 DCF).Therefore, the maximum contention window of a class-i nodeis CWi,max 2mb CWi,min . The contention window for thekth round (re)transmission of a class-i packet isCWi (k) min(CWi,max , 2k 1 CWi,min ), k 1, · · · , mr 1(1)with the backoff counter randomly chosen over [0, CWi (k) 1]. Let pi denote the packet collision probability seen bya class-i node, and assume that the collision probabilitiesassociated with different nodes are independent of each other.The average backoff time of the node in terms of time slots

CHENG et al.: A CROSS-LAYER APPROACH FOR WLAN VOICE CAPACITY PLANNINGis then given byWi mr 1 pk 1(1 pi )I{k mr 1}ik j 1k 1CWi (j) 12(2)where the indicator I{A} is equal to 1 if A is true, and equalto 0 otherwise. The indicator is used to include the case thata packet is dropped when the retransmission limit is reached.B. Packet Collision ProbabilityWe now derive the collision probability of a tagged class-inode. Let qi denote the probability that a class-i node transmitsa packet in a certain slot. A collision occurs if at least oneof the remaining nodes also transmits in the same time slot.Therefore,S Ni 1pi 1 (1 qi )(1 qj )Nj .(3)j 1,j iConditioning on a busy or non-empty queue, the transmission probability of a class-i node can be approximated byτi E[Ai ]W i E[Ai ](4)where E[Ai ] is the average number of transmission attemptsthe node made during the backoff time. With the collisionprobability pi for each transmission attempt, we haveE[Ai ] mr 1 kpk 1(1iI{k mr 1} pi )k 1r1 pmi .1 pi(5)As the node is busy with probability ρi and there is notransmission when the node queue is empty, we can obtainthe unconditional transmission probabilityqi ρi · τi λi τi /µi .(6)Substituting (6) into (3), we havepi 1 (1 τiλi Ni 1)µiS j 1,j i(1 τjλj Nj) ,µji 1, · · · S.(7)C. Average Packet Service TimeTo obtain the QoS of each node over the WLAN, we needto solve the average packet service time so that the G/G/1queue can be analyzed. During the time interval of 1/µi , thefollowing events may occur: a successful transmission by the tagged class-i node successful transmissions by the remaining nodes collisions due to multiple simultaneous transmissions channel idlingWe assume that an admission control scheme is implementedto keep each node in the stable state, i.e., ρi 1 (i 1, · · · , S), and no packet loss happens. Thus, the averagenumber of packets successfully transmitted by a class-j nodeduring 1/µi is λj /µi . Letting TSi denote the transmissiontime of a class-i packet (assuming a constant packet size forsimplicity), the total average transmission time during 1/µiSis [1 (Ni 1) µλii ]TSi µ1i j 1,j i Nj λj TSj .681Before a node successfully transmits a packet, the packetmay experience collisions. Letting TCi denote the collisiontime that a class-i node experiences upon each transmissioncollision, the average collision time till the successful transmission2 can be calculated asmr 1 T Ci (k 1)TCi · pk 1(1 pi )ik 1rpipi [1 (mr 1)pm mr pimr 1 ]iTCi TC . 1 pi1 pi i(8)Thus, the total average collision time during 1/µi is 12 [(1 (Ni 1) λµii )T Ci µ1i Sj 1,j i Nj λj T Cj ]. The factor “ 12 ”is used to get rid of the repetitive count of the collisiontime, considering that most of the collisions occur due tosimultaneous transmissions from two nodes.Based on the above analysis, we can obtain the averagepacket service time for class i 1, · · · , S as Sλi1 1 1 (Ni 1)Nj λj TSj T Si µiµiµij 1,j i S1 λi1 T Ci Nj λj T Cj W i1 (Ni 1)2µiµij 1,j i(9)where TSi and TCi (T Ci ) can be obtained from the packetlength of each class given.For all the classes, given the arrival rates λ [λ1 , λ2 , · · · , λS ], the minimum contention windows CW [CW1,min , CW2,min , · · · , CWS,min ], the numbers of nodes [N1 , N2 , · · · , NS ], (7) and (9) can be solved numericallyNto obtain p [p1 , p2 , · · · , pS ] and µ [µ1 , µ2 , · · · , µS ]. Notethat τi in the equations is a function of pi by combining (2),(4), and (5). With µ solved, the QoS of each node can thenbe obtained by analyzing the G/G/1 queue [11], [12].V. C ROSS -L AYER A NALYTICAL F RAMEWORKIn the previous section, the DCF MAC model is developedfrom the perspective of QoS analysis, which will be integratedwith the network-layer queueing analysis in this section toform a cross-layer analytical framework for network capacityplanning. Specifically, each node in the WLAN under consideration is modeled as a G/D/1 queue, with CAC beingapplied to maintain the WLAN at a nonsaturated operationpoint. For the given traffic arrival process, the single-serverqueueing analysis techniques is used to determine the appropriate service rates µ [µ1 , µ2 , · · · , µS ] that satisfy the QoSrequirements of all the classes. With µ [µ1 , µ2 , · · · , µS ],(7) and (9) are then used to compute p [p1 , p2 , · · · , pS ] [N1 , N2 , · · · , NS ]. In theand the admission region Nfollowing, we focus on voice capacity analysis to illustratethe applications of the cross-layer framework. Before goinginto details of the cross-layer framework, we first give a morethorough examination of the optimal operation point.2 The collision time associated with the dropped packets is ignored. Whenthe admission control is applied to maintain the collision probability at a smallvalue, the packet dropping probability at the MAC layer is negligible.

682IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 4, MAY 2007A. Optimal Operation Point of a WLAN310CBRO (VS TS VC TC )/TsimCU VS TS /Tsim110010 110 210 3(10)10(11)where VS and VC denote the numbers of successful andcollided transmissions, respectively, in a simulation run, andTsim denotes the system time duration of the simulation runfor a given flow number.From the simulations, we find that the CU starts to dropwhen the CBRO exceeds 0.9 under 76 voice flows, which isconsistent with the simulation results presented in [1]. Thereason for the decreasing CU beyond the optimal operationpoint (identified by the CBRO of 0.9) is that the traffic loadis too high to be effectively handled by the DCF MAC. Thecurves of the packet service time are shown in Fig. 13 . Inthe unsaturated region below the OOP, the average packetservice time is small (implying a short contention delay) andremains steady (reflected by a very small standard deviation).The packet sojourn time (i.e., departure time - arrival time) isalmost equal to the packet service time (i.e., departure time- MAC service start time), implying a queueing delay closeto zero. However, in the operation region exceeding the OOP,the MAC channel becomes saturated due to a large numberof collisions, which results in sharply increased packet servicetime and sojourn time. It is noteworthy that the “good-or-bad”sharp turning behavior at the MAC layer makes the networklayer queueing system ineffective. Such a contradiction can besolved by downlink traffic multiplexing at the AP.Mean of the service timeStandard deviation of the service timeMean of the sojourn timeStandard deviation of the sojourn time210Delay of voice packets (s)We demonstrate the constraint effect of the optimal operation point (OOP) through simulating an 802.11b WLAN(without RTS/CTS) supporting on/off voice flows. Each nodein the WLAN generates a single on/off flow; the on/offparameters and voice source packet rate follow those used in[1]. The constant voice packet size and therefore the constantTS and TC are considered. More details of our simulationsystem are given in Section VI. In simulations, the channelbusyness ratio and channel utilization (CU) are estimated by 410Fig. 1.1020303 The results in Fig. 1 are slightly different from those presented in Fig. 3 in[1], because we use an infinite buffer in the simulations, and do not considerbackground data traffic.708090Performance in a WLAN supporting on/off voice flows.service rate of the downlink queue should be properly provisioned to guarantee the QoS requirements of all the downlinkflows, which is to be achieved by properly configured CWdifferentiated multiclass DCF MAC. In addition, the MACshould be maintained operating at the OOP for maximumresource utilization and valid G/D/1 queueing analysis.For each voice flow, the on and off periods are exponentiallydistributed with average durations of ton and tof f , respectively; the activity factor is pon ton /(ton tof f ). At theon state, voice packets are generated at a constant rate ofRp packets/slot. Considering that N ( 1) on/off flows aremultiplexed at the AP, the QoS is to guarantee a stochasticdelay bound d, i.e.,P {D d} (12)where D is the queueing delay and the delay bound violationprobability. If the queue service rate is µ packets/slot, the delayviolation probability can be equivalently mapped to bufferoverflow probability at dµ,P {Q dµ} B. Traffic Multiplexing at APAs we know, each VoIP conversation incurs two VoIPflows, uplink and downlink, respectively. We consider thecase that each mobile node communicates through the APwith a correspondence node (CN) outside the WLAN. Withthe standard DCF MAC, in order to achieve symmetric datarate in uplink and downlink directions, each downlink voiceflow needs to occupy a separate queue at the AP for channelcontention. In practice, all the downlink flows are multiplexedinto a single downlink queue for simplicity, although trafficmultiplexing tends to make AP the performance bottleneckover the standard DCF MAC [3]. Another benefit of trafficmultiplexing at AP is to alleviate the MAC congestion; withN mobile nodes considered, the number of contending queuescan be reduced to N 1 instead of 2N queues in the caseof separate downlink queues. With traffic multiplexing, the405060Number of voice flows(13)where Q is the queue length of a node.It is well-known that a conservative approximation of theoverflow probability for on/off sources takes an exponentialexpression (equations (3-42) and (3-43) in [5]), i.e., N (1 ρ)(α β)x(14)P {Q x} exp N Rp µwhere ρ pon N Rp /µ is the utilization ratio, and α 1/ton ,β 1/tof f are the transition rates between the on and offstates, respectively. After some manipulations of (14), we have N d(µ/pon N Rp )P {Q dµ} exp (15)tof f (N Rp µ)Combining (13) and (15), the minimum service rate requiredto guarantee the QoS is given byµ N Rp (tof f log N d).tof f log N d/pon(16)

CHENG et al.: A CROSS-LAYER APPROACH FOR WLAN VOICE CAPACITY PLANNINGC. Cross-Layer AnalysisThe network layer bandwidth requirement should be satisfied by the MAC layer. In addition, the multiclass DCFMAC is used to provision the service differentiation betweenthe AP and the mobile nodes; the AP is assigned of class1 with a minimum contention window of CW1,min , and allthe mobile nodes are assigned of class-2 with a minimumcontention window of CW2,min rCW1,min . The factor r isthe CW differentiation ratio between the two classes. Considera constant voice packet size, and use µ1 and µ2 to denote theaverage packet service rate achieved by the MAC for the APand a mobile node, respectively. In a WLAN supporting Nmobile nodes (i.e. 2N on/off voice flows), we can form across-layer analytical framework including the following setof equations:N Rp (tof f log N d)(17)tof f log N d/ponpon Rp Np1 1 (1 τ2)(18)µ2pon N Rppon Rp (N 1)p2 1 (1 τ1)(1 τ2)(19)µ1µ2 1pon Rp1pon Rp TS NTS TC NTC W1µ1µ12µ1(20) pon Rppon N Rp1 1 (N 1)TS TS µ2µ2µ2 pon N Rp1pon RpTC TC W21 (N 1)2µ2µ2(21)11 W 1 ) µ2 ( W 2)(22)µ1 (µ1µ21 W 2 ) 0.9(23)µ2 (µ2In the cross-layer framework, (18) to (21) are the simplifications of the multiclass D

678 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 4, MAY 2007 A Cross-Layer Approach for WLAN Voice Capacity Planning Yu Cheng, Member, IEEE, Xinhua Ling, Student Member, IEEE, Wei Song, Lin X. Cai, Weihua Zhuang, Senior Member, IEEE, Xuemin Shen, Senior Member, IEEE Abstract—This paper presents an analytical approach to determining the maximum number of on/off voice flows .

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Lung anatomy Breathing Breathing is an automatic and usually subconscious process which is controlled by the brain. The brain will determine how much oxygen we require and how fast we need to breathe in order to supply our vital organs (brain, heart, kidneys, liver, stomach and bowel), as well as our muscles and joints, with enough oxygen to carry out our normal daily activities. In order for .