An Analytical Model for the Capacity Estimation of Combined VoIP and TCP File Transfers over EDCA in an IEEE e WLAN

Transcription

1 An Analytcal Model for the Capacty Estmaton of Combned VoIP and TCP Fle Transfers oer EDCA n an IEEE e WLAN Sr Harsha, Anurag Kumar, Vnod Sharma, Department of Electrcal Communcaton Engneerng Indan Insttute of Scence, Bangalore , Inda Emal: {harshas, anurag, nod}@ece.sc.ernet.n Abstract In ths paper we deelop and numercally explore the modelng heurstc of usng saturaton attempt probabltes as state dependent attempt probabltes n an IEEE e nfrastructure network carryng packet telephone calls and TCP controlled fle downloads, usng Enhanced Dstrbuted Channel Access EDCA. We buld upon the fxed pont analyss and performance nsghts n [1]. When there are a certan number of nodes of each class contendng for the channel.e., hae nonempty queues, then ther attempt probabltes are taken to be those obtaned from saturaton analyss for that number of nodes. Then we model the system queue dynamcs at the network nodes. Wth the proposed heurstc, the system eoluton at channel slot boundares becomes a Marko renewal process, and regenerate analyss yelds the desred performance measures. The results obtaned from ths approach match well wth ns2 smulatons. We fnd that, wth the default IEEE e EDCA parameters for AC 1 and AC 3, the oce call capacty decreases f een one fle download s ntated by some staton. Subsequently, reducng the oce calls ncreases the fle download capacty almost lnearly by 1/3 Mbps per oce call for the 11 Mbps PHY. I. INTRODCTION In order to guarantee the QoS requrements n IEEE WLANs, the IEEE e group has deeloped MAC enhancements to support QoS senste applcatons and has proposed the IEEE e standard [2]. Ths standard ntroduces an enhanced, dstrbuted, contenton-based access scheme, called Enhanced Dstrbuted Channel Access EDCA, that offers the possblty to defne four dfferent classes of serce at the MAC layer so that QoS requrements of the multmeda traffc can be supported n addton to data traffc. At the MAC layer, each serce class s called an access category AC, and serce between classes s dfferentated by dfferent set of parameters to contend for the channel. Performance analyss of IEEE e WLANs has become an acte research area. Whle many smulaton studes hae been reported [3], [4], [5], [6], t s mportant to deelop analytcal models. An analytcal modelng exercse prodes nsghts nto the workng of the system and leads to a more general understandng of the effects of arous parameters, and desgn choces, than many smulaton runs. Further, these models may prode general gudelnes for admsson control and MAC parameter optmzaton, and may lead to deas for noel adapte MAC algorthms. The aalablty of good analytcal models s also useful for deelopng fast smulatons [7], [8], [9]. Model based performance analyss of EDCA e WLANs hae been proposed n [10], [11], [12], [13], [1]. Robnson and Randhawa [11] and Zhu and Chlamtac [12] consder a WLAN wth saturated nodes nodes that always hae packets to transmt. Ramayan et al. [1] extend the fxed pont analyss of Kumar et al. [14] for a sngle cell IEEE e WLAN wth saturated nodes and propose a general fxed pont analyss that captures the dfferentaton by mnmum contenton wndow CW, maxmum CW and arbtrary nterframe space AIFS. Wth real traffc, howeer, the nodes are not always saturated. Shankar et al. [13] ealuate the VoIP capacty n e WLAN, but n a scenaro where other classes of traffc are not coexstent n the WLAN. Clfford et al. [15] hae proposed a model for e for dfferent classes of traffc when the nodes are nonsaturated. Ths model yelds throughputs of arous flows. The authors do not model the buffer dynamcs for dfferent traffc types. Our Contrbuton: We prode a model that can predct the performance of a sngle cell nfrastructure IEEE e WLAN, under a scenaro where VoIP and TCP controlled data traffc are carred oer EDCA. We model the queue dynamcs at dfferent nodes as per the consdered applcaton traffc. sng the model, we fnd the maxmum number of oce calls that can be carred wth and wthout fle downloads and the aggregate fle download throughput for each number of admssble oce calls. We take adantage of the fact that the e MAC layer works on system slot boundares. A system slot s the tme unt employed for dscrete-tme backoff countdown. We replace the real WLAN wth a system where each staton transmts ts head-of-lne packet f t has one n a slot wth a probablty that depends only on the set of statons contendng for the channel at that tme,.e., the set of statons that hae packets to send. These attempt probabltes are approxmated usng the saturaton analyss n [1]. The nterals between the nstants at whch our Marko chan s embedded are random, but together these consttute a Marko renewal process. We wll show by smulatons that such an approach s ald and prodes good nsghts nto the performance of e WLANs /06/$ IEEE. 178

2 ... QAP AC 3 QAP QAP AC 3 AC 3 AC 1 AC 1 QSTA 1 QSTA N AC 1 t QSTA t 1... QSTA t N t Fg. 1. An IEEE e WLAN model scenaro where VoIP calls and TCP traffc are serced on EDCA Paper Outlne: In Sec II we dscuss the approach for modelng along wth the obseratons and assumptons of the network and the traffc. In Sec III we formulate a Marko renewal framework, by usng the state dependent attempt probabltes of [1]. In Sec IV we dere the performance measures, namely, the VoIP call capacty and the TCP throughput. In Sec V we dere three more measures namely, the attempt rate of nodes wth access category 1 AC 1, the attempt rate of nodes wth AC 3 and the system collson rate, n order to aldate the model. Ths s followed by numercal and smulaton results for all the measures so dered. Lastly, n Sec VI we conclude wth the lstng of useful modelng and performance nsghts obtaned n ths analyss. II. THE MODELING APPROACH We study the performance of a sngle cell nfrastructure e WLAN that uses EDCA, when both AC 3 and AC 1 are used. Whle IEEE e also defnes TXOPs as an optonal feature, for smplcty, we do not use TXOP n our model. We follow the modelng approach of Kurakose [16] and Harsha et al. [17], where only the IEEE WLAN s analyzed for oce traffc and for TCP traffc separately. The approach of [16] and [17] can be brefly explaned as follows: 1 Embed the number of acte nodes at channel slot boundares. The channel slot boundares are those nstants of tme when an actty ends. The actty could be a successful transmsson or a collson or no transmsson an dle slot. 2 If n nodes are acte.e., hae non empty queues at a channel slot boundary, then the attempt probablty of a node s taken to be β n. Ths s the approxmaton from Banch [18] and Kumar et al. [14] where f there are n saturated nodes, the attempt probablty of each node s β n. 3 se these attempt probabltes to model the eoluton of the number of contendng nodes at channel slot boundares. Ths yelds a Marko renewal process. 4 Obtan the statonary probablty ector π of ths Marko chan. 5 se Marko regenerate argument to obtan the performance measures. In case of e WLANs, due to dfferent parameters, each AC has a dfferent attempt probablty, that further depends on the number of nodes n other ACs. The attempt probabltes obtanable from [14] do not consder the dfferentaton n the parameters and hence cannot be used. We approach ths problem by ncorporatng the attempt probablty alues obtaned from the fxed pont analyss n [1]. We buld a model that can use the results of [1]. A. The Network Scenaro and Modelng Obseratons Consder an nfrastructure IEEE e WLAN, whch has VoIP and TCP traffc, both serced on EDCA. The VoIP traffc and TCP traffc could be handled at the same node. Then we hae multple queues per node. It has been shown n the ournal erson of [1] that wth ncrease n the number of nodes, the performance of the multple queues per node case concdes wth the performance of the sngle queue per node case, each node wth one queue of the orgnal system; bascally the probablty of rtual collson wthn a node s small. Ths obseraton leads to substantal reducton n complexty of our analyss. We make use of ths obseraton and consder the VoIP traffc and TCP traffc as orgnatng from dfferent nodes. Thus, let N be the number of full duplex CBR VoIP calls n the WLAN, nolng N number of e complant wreless statons QSTAs, each carryng one VoIP call. Smlarly let N t be the number of QSTAs downloadng TCP traffc n the WLAN, each hang one sesson. The e complant access pont QAP can be ewed as two nodes: QAP hang a queue for AC 3 VoIP traffc for all VoIP calls, and the other, QAP t, hang a queue for AC 1 TCP traffc to sere all TCP downloads. Ths model s llustrated n Fg. 1. Note that at any tme the WLAN n Fg. 1 can be seen to consst of N + N t +2 nodes. Lets call the QSTAs wth AC 3 as QST A and QSTAs wth AC 1 as QST A t. We assume that there are no bt errors, and packets n the channel are lost only due to collsons. B. VoIP Traffc Each VoIP call results n two RTP/DP streams, one from a remote clent to a wreless QSTA, and another n the reerse drecton. We consder that each call uses the IT G711 codec. Packets are generated eery 20 ms. Includng the IP, DP and RTP headers, the sze of the packet emtted n each call n each drecton s 200 bytes eery 20 ms. As a QoS requrement we demand that the probablty that a packet s transmtted successfully wthn 20 ms s close to 1. Whle a more relaxed delay QoS may seem approprate, we hae obsered through smulatons that een an obecte of Probdelay 100ms s small, yelds no ncrease n the call capacty. Snce the packets wll experence delays n the rest of the network also, ths seems lke a reasonable delay target to achee. Ths QoS obecte also smplfes the modelng snce, f the QoS obecte s met, the probablty of more than one packet of a call n a queue s small. Thus, f the QoS target s met, wheneer a new packet arres at a QST A,t /06/$ IEEE. 179

3 ... V V V V V,T V,T V,T V,T V,T V,T... L t... V: nodes wth only AC3 can attempt V,T: nodes wth AC 3 or AC 1 can attempt Idle slot collson successful transmsson by AC 3 successful transmsson by AC 1 Fg. 2. An eoluton of the channel actty wth two ACs n e WLANs. wll fnd the queue empty wth a hgh probablty. Hence, the followng three assumptons wll be acceptable n the regon where we want to operate: 1 the buffer of eery QST A has a queue length of at most one packet, and 2 new packets arrng to the QST A s arre only at empty queues. The latter assumpton mples that f there are kqsta s wth oce packets then, a new oce packet arral comes to a k +1 th QST A. 3 Snce the QAP handles packets from N streams, there can be up to N packets of dfferent calls n the QAP. Thus we expect that QAP s the bottleneck for oce traffc, and we assume that t wll contend at all tmes at least when N s large. Ths s a realstc assumpton near system capacty. As mentoned earler, packets arre eery 20 ms n eery stream. We use ths model n our smulatons. Howeer, snce our analytcal approach s a Marko chans, we assume that the probablty that a oce call generates a packet n an nteral of length l slots s p l = 1 1 λ l, where λ s obtaned as follows. Each system slot n b s of 20μs duraton hereafter denoted as δ. Thus n 1000 system slots there s one arral. Therefore, for the b PHY we take λ = Ths smplfcaton turns out to yeld a good approxmaton. C. TCP Controlled Fle Downloads Each QST A t has a sngle TCP connecton to download a large fle from a local fle serer. Hence, the QAP t delers TCP data packets towards the QST A t s, whle the QST A t s return TCP ACKs. Here we assume that when a QST A t recees data from the QAP t, t mmedately sends an ACK,.e., we do not model delayed ACKs here, though the delayed ACKs case can also be done see [16]. We assume that the QAP t and the QST A t s hae buffers large enough so that TCP data packets or ACKS are not lost due to buffer oerflows. Snce, by assumpton, there are no bt errors, packets n the channel are lost only due to collsons. Also, we assume that these collsons are recoered by the MAC before TCP tmeouts occur. As a result of these assumptons, for large fle transfers, the TCP wndow wll grow to ts maxmum alue and stay there. As N t s ncreased ths assumpton s close to what happens n realty. We then adopt an obseraton made by Bruno et al. [19]. Snce all nodes wth AC 1 ncludng the QAP t wll contend for the channel and no preference s gen to the QAP t, most of the packets n the TCP wndow wll get backlogged at the QAP t. The QAP t s buffer s sered FIFO, and we can assume that the probablty that a packet transmtted by the QAP t to a partcular QST A t s 1 N t. Thus t s apparent that the larger the N t, the lower s the probablty that the QAP t sends to the same QST A t before receng the ACK for the last packet sent. Then t s assumed that the probablty that any QST A t has more than one ACK s neglgble. We can thus smply keep track of the number of QST A t wth ACKs. If there are seeral QST A t s wth ACKs then the chance that QAP t succeeds n sendng a packet s small. Thus the system has a tendency to keep most of the packets n the QAP t wth a few QST A t s hang ACK to send back. Ths results n a closed system, wheren each tme the QAP t succeeds, t actates a QST A t hang an ACK packet and each tme a QST A t succeeds, the number of non-empty QST A t s reduces by one. Thus for the QST A t s that are downloadng fles, our modelng assumptons are: 1 A QST A t has ether 0 or 1 ACK packet wantng to be sent to the QAP t. 2 When the QAP t sends a data packet t s assumed to be destned to a QST A t that has no ACK queued. III. THE ANALYTICAL MODEL A. An Embedded Chan The eoluton of the channel actty n the network s as n Fg. 2., 0, 1, 2, 3,..., are the random nstants where ether an dle slot, or a successful transmsson, or a collson ends. Let us defne the tme between two such successe nstants as a channel slot. Thus the nteral [ 1, s called the th channel slot. Let the tme length of the th channel slot be L see Fg. 2. Let be the number of non-empty QST A s and Y be the number of non-empty QST A t s at the nstant. Thus 0 N and 0 Y N t. Let B be the number of new VoIP packet arrals at all the QST A s, n the channel slot. Let V be the number of departures from QST A s, V tap tst A be the number of departures from QAP t and V be the number of departures from QST A t s, n the th channel slot. We know that at most one departure can happen n any channel slot. The mplcaton of access dfferentaton through AIFS s that the ACs wth larger AIFS alues cannot contend n those slots that were preceded by some actty.e., successful transmsson or collson. After eery actty successful transmsson or collson on the channel, AC 1 nodes wat for an addtonal system slot before contendng for the channel. Fg. 2 shows the eoluton of the channel actty when AC 3 and AC 1 queues are acte. Note that at the nstants 4, 6, 7 and 10, only AC 3 nodes can contend for the channel, /06/$ IEEE. 180

4 Prob B +1 = b/y =n ; L +1 = l = N n p l b 1 p l N n b 1 b whereas AC 1 nodes hae stll to wat for one more system slot to be able to contend. At other nstants, 5, 8, 11 and 13, nodes wth AC 3 or AC 1 can attempt. The AC attempt probabltes obtaned from [1] are condtoned on when an AC can attempt. We use the arable Y s to keep track of whch ACs are permtted to attempt n a channel slot. Let Y s =1denote that the precedng channel slot had an actty and so n the begnnng of the th channel slot, only nodes wth AC 3 can attempt. Let Y s =0denote that the precedng channel slot remaned dle and hence, at the begnnng of the th channel slot any node can attempt. Thus Y s {0, 1}. Then we hae the followng dynamcs. +1 = V +1 + B +1 Y +1 = Y tst A V +1 + V tap +1 wth the condton that V tst A +1 + V +1 + V tap +1 {0, 1}. Snce the probablty wth whch a packet arres at a node n a channel slot of length l s p l and we assume that packets arre at only empty QST A s, B can be modeled as hang a bnomal dstrbuton and the condtoned probablty ProbB +1 /Y,L +1 =n,l s gen by Equaton 1. B. Marko Property a State Dependent Attempt Probabltes For determnng the expressons of V tst A +1, V +1 and V tap +1, we use the attempt probabltes of [1]. Let be the attempt probablty of a node wth AC 3 and β n +1,n t+1 be the attempt probablty of a node wth AC 1, when there are n VoIP calls and n t TCP sessons n the network. These attempt probabltes are condtoned on the eent that the ACs can attempt. Note that the addton of one n the subscrpts s so as to nclude the QAP and QAP t, whch by assumpton, always contend. The alues, β β n +1,n t+1 n +1,n t+1 for AC 3 and β n +1,n t+1 for AC 1 are obtaned from saturaton fxed pont analyss of [1] for all combnatons of n,n t. Our approxmaton s that the state dependent alues of attempt probabltes from the saturated nodes case can be used for a WLAN where the nodes are not saturated, by keepng track of the number of nonempty nodes n the WLAN and takng the state dependent attempt probabltes correspondng to ths number of nonempty nodes. For conenence, let us defne the followng probablty functons depctng the acttes n the channel slot +1: η t be the probablty that all nodes wth AC 1 reman dle; α be the probablty that any one QST A attempts whle QAP s dle; α t be the probablty that any one QST A t attempts whle QAP t s dle; σ be the probablty that the QAP attempts and all QST A s are dle; σ t be the probablty that the QAP t attempts and all QST A t s are dle; ζ be the probablty that there s a collson amongst nodes wth be the probablty that there s a collson amongst QST A t s; ψ 1 be the probablty that there s a hybrd collson nolng nodes wth AC 3 ncludng QAP and QST A t s excludng QAP t ; ψ tap be AC 3; ζ t,y the probablty that there s a hybrd collson between QAP t and any other node. The expressons for these functons are gen n Appendx. We can express the condtonal dstrbutons V tst A +1, V +1 and V tap +1 usng these functons. V s 1 f a QST A wns the contenton for the channel and 0 otherwse. Then, V +1 = 1 w.p. α 1 w.p. α 0 otherwse,y,y η t f Y s =0 f Y s =1 tst A Smlarly, V and V tap are expressed as follows: { tst A 1 w.p. α V = t,y η,y f Y s = otherwse { V tap = +1 1 w.p. σ t,y η,y f Y s =0 0 otherwse Y s +1 takes the alues n {0, 1} wth the followng probabltes: { Y s 0 w.p. +1 = η η t 1 otherwse wth the ntal state, Y s 0 =0. Wth the bnomal dstrbuton for oce packet arrals assumed aboe and the state dependent probabltes of attempt, t s easly seen that {,Y s ; 0} forms a fnte rreducble three dmensonal dscrete tme Marko chan on the channel slot boundares and hence s poste recurrent. The statonary probabltes π n,n t,n s of the Marko Chan {,Y s ; 0} can then be numercally determned usng expressons for dstrbutons of B, V, V tap and tst A V and the functons n the Appendx. C. The Marko Renewal Process In ths subsecton we use the state dependent attempt probabltes to obtan the dstrbuton of the channel slot duraton. On combnng ths wth the Marko chan n Sec III-B, we fnally conclude that {,Y s ;, =0, 1, 2,...} s a Marko renewal process. We use the basc access mechansm for the TCP traffc. Ths shall facltate the aldaton of analytcal results /06/$ IEEE. 181

5 EL +1/Y s =0 = η η t +T s η t α +σ + T s tst A η α t +T s tap η σ t + T c short η ζ t + T c oce η t ζ +ψ 1 + T c longφ tap EL +1/Y s =1 = η +T s α +σ + T c oceζ 2 P Y +1 = y, +1 l/y 0 = y 0, 0 = u 0, Y 1 = y 1, 1 = u 1,..., Y = y, = u = P Y +1 = y, +1 l/y = y, = u 3 through smulatons by the ns-2 wth EDCA mplementaton [20], that supports only basc access mechansm and not RTS/CTS mechansm. Howeer, our analyss can be worked out for RTS/CTS mechansm as well. When basc access mechansm s used, there shall be collsons between three knds of packets. The longest collson tme s seen when QAP t packet colldes wth a packet of any other node. A smaller collson tme s seen when VoIP packet colldes wth a packet of any other node except wth packet of QAP t. The shortest collson tme s seen when only packets of QST A t s collde. Then L n system slots takes one of the seen alues: 1 f t s an dle slot, T s f t corresponds to a successful transmsson of a AC 3 node, T s tap f t corresponds to a successful transmsson of QAP t, T s tst A f t corresponds to a successful transmsson of QST A t, T c short f t corresponds to a collson between QST A t s, T c oce f t corresponds to a collson amongst nodes wth AC 3 or between AC 3 nodes and any QST A t and T c long f t corresponds to a collson between QAP t and any other QST A. The condtonal expectaton of L +1 s gen by Equaton 2 that uses the followng notatons: T s = T P +T PHY + L MAC+L oce +T SIFS +T P +T PHY + L ACK C c + T AIF S3 ; T s tst A = T P +T PHY + L MAC+L TCPACK +T SIFS +T P + T PHY + L ACK C c + T AIF S1 ; T s tap = T P +T PHY + L MAC+L IPH +L data +T SIFS +T P + T PHY + L ACK C c + T AIF S1 ; T c oce = T P +T PHY + L MAC+L oce +T EIFS +T AIF S3 ; T c short = T P + T PHY + L MAC+L TCPACK T AIF S1 ; + T EIFS + T c long = T P + T PHY + L MAC+L IPH +L data T AIF S1 ; + T EIFS + T EIFS = T P + T PHY + L ACK C c + T SIFS. See Table I for meanng and alues of arous parameters. We thus obsere Equaton 3 and so conclude that {,Y s ;, =0, 1, 2,...} s a Marko renewal process wth L = 1 beng the renewal cycle tme. Parameter Symbol Value PHY data rate 11 Mbps Control rate C c 2 Mbps PLCP preamble tme T P 144μs PHY Header tme T PHY 48μs SIFS Tme T SIFS 10μs AIFS3 Tme T AIF S3 50μs AIFS1 Tme T AIF S1 70μs G711 packet sze L oce 200 Bytes Data packet sze L data 1500 Bytes MAC ACK Packet Sze L ACK 112 bts MAC Header sze L MAC 288 bts TCP ACK sze L TCPACK 320 bts AC3 Mn. CW CW mn AC3 7 AC3 Max. CW CW maxac3 15 AC1 Mn. CW CW mn AC1 31 AC1Max. CW CW maxac TABLE I PARAMETERS SED IN ANALYSIS AND SIMLATION FOR EDCA E WLAN IV. VOIP CAPACITY AND TCP THROGHPT A. Call Capacty Let A be the reward when the QAP wns the channel contenton n th channel slot. If we hae 1 = n, Y 1 = n t and Y s 1 = n s at the 1 th channel slot boundary, then, 1 w.p. σ n,n t η t n,n t f n s =0 A = 1 w.p. σ n,n t f n s =1 0 otherwse Let A denote the cumulate reward of the QAP untl tme t. Applyng Marko regenerate analyss [21], we obtan the serce rate of the QAP, Θ AP VoIP N,N t,asgen by Equaton 4. Snce the rate at whch a sngle call sends data to the QAP s λ, and the QAP seres N such calls the total arral rate to the QAP s N λ. Ths rate should be less than Θ AP VoIP N,N t for stablty. Thus, a permssble combnaton of N VoIP calls and N t TCP sessons, whle meetng the delay QoS of VoIP calls, must satsfy Θ AP VoIP N,N t >N λ /06/$ IEEE. 182

6 A Θ AP VoIP N,N t = lm where, E n,n t,n s A = E A / 1,Y 1,Ys 1 =n,n t,n s a.s. = N Nt n =0 N Nt n =0 1 n t=0 n π s=0 n,n t,n s E n,n t,n s A 1 n t=0 n π s=0 n,n t,n s E n,n t,n s L, E n,n t,n s L = E L / 1,Y 1,Ys 1 = n,n t,n s 4. Prob B AP +1 = b/x AP = x; L +1 = l = N x p l b 1 p l N x b 6 b R lm a.s. = N Nt 1 N n =0 n t=0 n s=0 n AP =0 π n,n t,n s,n AP N Nt 1 N n =0 n t=0 n s=0 n AP =0 π n,n t,n s,n AP E n,n t,n s,n AP R E n,n t,n s,n AP L 7 The aboe nequalty defnes the admsson regon for VoIP. Note that we are assertng that the N that satsfes nequalty 5 also ensures the delay QoS. Ths s based on the obseraton n earler research [22] that when the arral rate s less than the saturaton throughput then the delay s ery small. Remark: The model dscussed aboe does not ge the TCP download throughput. Ths s due to the fact that we assume that the oce queue of the AP s saturated all the tme. But actually, the VoIP queue of AP saturates only at system capacty [16]. Thus f we follow the aboe method to obtan analytcal TCP download throughput, we obtan an underestmated throughput. Ths problem can be soled by consderng that QAP s not saturated and we consder ths case n the followng subsecton. B. TCP Throughput Dependng on whether the QAP queue contans a packet, the total number of nonempty nodes wth AC 3 wll be n case no packet s there n QAP queue or +1 f QAP queue has at least one packet. We then need to know the state of the QAP queue so as to know the number of nonempty nodes wth AC 3, at the channel slot boundares. Therefore, we ntroduce another arable to track the number of packets n the QAP queue. Let X be the number of packets n the QAP queue, B AP be the number of new packets arrng at the QAP queue and V AP be the number of departures from QAP at the end of th channel slot. Then, the set of eoluton equatons are: V +1 = Y +1 = Y V X +1 = X +1 + B +1 tst A V tap V AP +1 + B AP +1 wth the condton that V tst A +1 + V +1 + V tap +1 + V AP +1 {0, 1}. On smlar lnes as B, B AP can be modeled as hang a bnomal dstrbuton. Obsere that f x packets are already there n QAP queue, at most N x packets can arre before the QoS delay bound of the earlest arred packet gets exceeded. sng the earler defnton of p l, the condtonal probablty probb AP +1 /X AP,L +1 s gen by Equaton 6. In order to take nto account the fact that QAP may or may not be acte at any channel slot boundary, defne Z := +1,fX AP 0and Z := f X AP = 0. Then the functons n the Appendx need a modfcaton. Instead of β Y +1,Y +1, we now hae to use β Z Wth the aboe change ncorporated, V AP +1 s gen as: V AP +1 = 1 w.p. σ Z 1 w.p. σ Z 0 otherwse,y,y,y +1. η tz f Y s =0 f Y s =1 We agan see that, under our model for the attempt probabltes, {,Y s,x AP ; 0} forms a fnte rreducble four dmensonal dscrete tme Marko chan on the channel slot boundares and hence s poste recurrent. The statonary probabltes π n,n t,n s,n AP can be numercally obtaned. If R be the reward and L be the cycle tme n th channel slot, n ths context, applyng Marko regenerate analyss [21], mean reward rate s gen by Equaton 7, where R s the cumulate reward untl tme t. We use ths equaton to obtan arous measures of nterest. Let us defne T to be the reward when the QAP t wns the channel contenton n th channel slot and T denote the cumulate reward of the QAP t untl tme t. If there are Z 1 = n AC 3 nodes acte, Y 1 = n t QST A t s acte and Y s 1 = n s, then, { 1 w.p. σt n T =,n t η n,n t f n s =0 0 otherwse Θ AP data N,N t n Mbps, s then gen as: Θ AP data N,N t = L data δ T lm where we use Equaton 7 to ealuate lm t T t, wth R = T /06/$ IEEE. 183

7 V. MODEL VALIDATION AND NMERICAL RESLTS A. Attempt and Collson Rates In order to aldate and show the accuracy of the model, we now analytcally dere three other measures: the attempt rate of AC 3 nodes, the attempt rate of AC 1 nodes, and the total collson rate n the WLAN. We compare the numercal results wth that obtaned from the smulatons. 1 Attempt Rate: Let S be the number of attempts process of AC 3 nodes,.e., S counts the number of AC 3 nodes that attempt n the channel slot,. Let, as before, Z 1 = n and Y 1 = n t. Then S = w.p. n β n,n t+1 1 β n,n t+1 n Let S denote the cumulate reward of number of attempts of AC 3 nodes untl tme t. Then the total attempt rate of AC 3 nodes, Φ N,N t s QAP serce rate, Θ AP VoIP, Load arral rate at QAP n pkts per slot QAP load arral rate QAP serce rate for N t = 0 QAP serce rate for N = 1 t QAP serce rate for N t = Number of oce calls, N, as AC 3 on e EDCA Fg. 3. The serce rate Θ AP V oip appled to the QAP s plotted s the number of oce calls, N for dfferent number of TCP sessons N t. Also shown s the lne N λ. The pont where the lne N λ crosses the cures ges the maxmum number of calls supported. VoIP packet sze s 200B G711 Codec; data packet sze s 1500 Bytes; PHY data rate s 11Mbps and basc rate s 2Mbps. Φ N,N t = 1 δ lm S 9 S and we use Equaton 7 to ealuate lm, wth R = S. Smlarly, let S be the number of attempts process of AC 1 nodes,.e., S counts the number of AC 1 nodes that attempt n the channel slot,. Then S = { w.p. nt+1 0 otherwse β n,n t+1 1 β n,n t+1 nt f Y s =0 The total attempt rate of AC 1 nodes, Φ t N,N t s then Φ t N,N t = 1 δ lm S 10 S and we agan use Equaton 7 to ealuate lm, wth R = S. 2 Collson Rate: Let C be the number of collsons process n the WLAN,.e., C counts the total number collsons n the WLAN n the channel slot,. For nstance, f fe nodes are noled n a collson n the th channel slot, then C =5.IfE n,n t,n s,n AP C s the state dependent mean number of collsons, E n,n t,n s,n AP C = ES + S 1 ProbS =1;S =0 1 ProbS =0;S =1 Let enote the cumulate reward of number of collsons n the WLAN, untl tme t. Then, f ΓN,N t s the system collson rate n the WLAN, C ΓN,N t = lm 11 C and agan we use Equaton 7 to ealuate lm, wth R = C. B. Numercal Results We present the results obtaned from the analyss and smulaton. The smulatons were obtaned usng ns-2 wth EDCA mplementaton [20]. The VoIP traffc was consdered on AC 3 and the TCP traffc was consdered on AC 1. The PHY parameters confrm to the b standard. See Table I for the alues used n smulaton. 1 VoIP Capacty: In Fg. 3, we show the analytcal plot of QAP serce rate s. the number of calls, N for three dfferent alues of N t {0, 1, 10}. From Fg. 3, we note that the QAP serce rate crosses the QAP load rate, after 12 calls for N t = 0. Ths mples that a maxmum of 12 calls are possble whle meetng the delay QoS, on a e WLAN when no TCP traffc s present on AC 1. When one TCP sesson s added to the WLAN.e., N t =1, the QAP serce rate crosses below the QAP load rate, after 10 calls. Ths mples that only 10 calls are possble when any TCP sesson s added to the WLAN. The same s the case een when 10 TCP sessons are added to the WLAN. Remark: The analyss represented by Fg. 3, assumes that the QAP s saturated. It s for ths reason that the QAP serce rate exceeds the load arral rate for small N. The crossoer pont would howeer correctly model the alue of N beyond whch oce QoS wll be olated. From Fg. 3, we obsere that for each alue N, wth ncrease n the alue of N t from zero to a non-zero alue, the serce rate aalable to the QAP decreases. Ths s, of course, because the QAP needs to serce the TCP traffc also. Howeer, the cures of N t =1and N t =10are ery close. The effect of one TCP transfer s the same as that of 10 TCP transfers. Partly, the reason s that QAP t queue s already saturated wth 1 TCP. By addng more TCP transfers a few more QSTAs begn to contend, but ths number wll not change much wth ncreasng N t see also Kurakose [16] /06/$ IEEE. 184

8 QAP delay, N=0 t QSTA delay, N t =0 QAP delay, N=1 t QSTA delay, N t =1 QAP delay, N t =10 QSTA delay, N t = analyss: oce analyss: data smulaton: oce wth 95% CI smulaton: data wth 95% CI Pdelay > 20ms Φ, Φ t n attempts per sec Number of VoIP calls, N, as AC 3 on e EDCA Number of VoIP calls, N, as AC 3 on e EDCA Fg. 4. Smulaton results showng probablty of delay of QAP and QSTA wth AC 3, beng greater than 20ms s the number of calls N for dfferent alues of N t. Analyss and smulaton use VoIP packet sze = 200B G711 Codec; TCP download packet sze = 1500B Basc access mechansm; PHY data rate = 11Mbps and basc rate = 2Mbps. Fg. 6. Analyss and smulaton results showng attempt rates of AC 3 nodes and AC 1 nodes, for dfferent alues of N and N t =10. PHY data rate s 11Mbps and basc rate s 2Mbps. 600 analyss smulaton wth 95% CI analyss smulaton, wth 95% CI 500 Θ AP data n mbps Γ n collsons per sec Number of VoIP calls, N, as AC 3 on e EDCA Number of VoIP calls, N, as AC 3 on e EDCA Fg. 5. Analyss and smulaton results showng total download throughput obtaned by QST A ts for dfferent alues of N and N t =10. VoIP packet sze s 200B G711 Codec; data packet sze s 1500 Bytes; PHY data rate s 11Mbps and basc rate s 2Mbps. Smulaton results for the QoS obecte of Probdelay 20ms for the QAP and the QST A sareshownnfg.4. Note that the Probdelay : QAP 20ms s greater than Probdelay : QST A 20ms for gen N and that the QAP delay shoots up before the QST A delay, confrmng that the QAP s the bottleneck, as per our assumptons. It can be seen that wth and wthout TCP traffc, there s a alue of N at whch the Probdelay 20ms sharply ncreases from a alue below Ths can be taken to be the oce capacty. In case of no data traffc, we obtan 12 calls, matchng the analyss result and when there s data traffc, we get 9 calls, one less than the analyss result. 2 TCP Throughput: For the data packet length of 1500 bytes, usng IEEE b PHY parameters, wth PHY data rate of 11Mbps, we numercally calculate the total download throughput for TCP traffc fxed at N t =10 usng Equaton 8, for aryng number of oce calls. The analytcal plot has been gen n Fg. 5 and the fgure also shows the smulated TCP download throughput wth 95% confdence nterals. Fg. 5 shows that the reducton of TCP throughput wth Fg. 7. Analyss and smulaton results showng collson rate n the WLAN, for dfferent alues of N and N t =10. PHY data rate s 11Mbps and basc rate s 2Mbps. ncreasng N s almost lnear at the rate of 1 3 Mbps per VoIP call. Remark: Fg. 5 can also be used for admsson control of VoIP calls n order to guarantee a net mnmal throughput to the data traffc. For nstance f at least 2 Mbps of aggregate TCP throughput s to be allotted to data traffc then Fg. 5 says that only 7 VoIP calls should be admtted. 3 Attempt and Collson Rates: In order to aldate the model, we numercally calculate the attempt rates of AC 3 nodes and AC 1 nodes usng Equaton 9 and Equaton 10 respectely and compare them wth the smulatons. Fg. 6 shows the attempt rates obtaned from analyss and smulatons for AC 3 and AC 1 nodes for dfferent alues of N and N t =10. We further calculate the system collson rates for dfferent alues of N and N t =10, usng Equaton 11. Fg. 7 shows the collson rates obtaned from analyss and smulatons. Remark: From Fg. 6 and 7 we conclude that the analytcal model not only predcts the performance measures well but certan other measures such as attempt rate and collson rate are also captured well. Ths shows that the model captures the behaour of the system qute well. It can be obsered from Fg. 4 that the Probdelay : /06/$ IEEE. 185

9 QST A 20ms begns to rse from N = 9 onwards. Ths mples that the model assumpton that the QST A s hae at most one packet fals oer N =9calls. Oer the operatng pont, the QST A s wll start bufferng more than one packet. Ths s gettng reflected n the attempt rates and system collson rate, after N =9, where the error between the analytcal alue and stmulaton alue ncreases. VI. CONCLSION In ths paper we proded an analytcal model for obtanng the capacty of VoIP calls and the TCP controlled download throughput n EDCA e WLAN, when both VoIP and data traffc are present. The analyss proceeds by modelng the eoluton of the number of contendng QSTAs at channel slot boundares. Ths yelds a Marko renewal process. A regenerate analyss then yelds the requred performance measures. In case of VoIP capacty, the analytcal results match wth those obtaned from smulatons, whle oerestmatng the number of VoIP calls by ust 1 call, when TCP sessons are added to the WLAN. In case of TCP download traffc, the error n download throughput s wthn 5% n the regon of operaton,.e. up to 9 VoIP calls. Our work prodes the followng modelng nsghts: The dea of usng saturaton attempt probabltes as state dependent attempt rates yelds an accurate model n the unsaturated case. sng ths approxmaton, an IEEE e nfrastructure WLAN can be well modeled by a multdmensonal Marko renewal process embedded at channel slot boundares. We also obtan the followng performance nsghts: nlke the orgnal DCF, the EDCA mechansm supports the coexstence of VoIP connectons and TCP fle transfers; but een 1 TCP transfer reduces the VoIP capacty from 12 calls to 9 calls. Subsequently the VoIP capacty s ndependent of the number of TCP transfers see Fg. 4. For an 11 Mbps PHY, the fle download throughput reduces lnearly wth the number of oce calls at the rate of 1 3 Mbps per addtonal oce call from 0 to 9 calls. Our ongong work wll extend the analyss n ths paper to the case when data traffc s both ways nstead of ust download traffc. We also are workng on fndng the capactes of e WLANs for real tme and streamng deo sessons n the EDCA framework. In related work, we hae also proded an analytcal model for IEEE e nfrastructure WLANs usng HCCA, wth oce beng carred n contenton free perod and TCP data n the remanng tme usng EDCA. ACKNOWLEDGMENT Ths work s based on research sponsored by Intel Technology, Inda. REFERENCES [1] V. Ramayan, A. Kumar, and E. Altman, Fxed Pont Analyss of Sngle Cell IEEE e WLANs: nqueness, Multstablty and Throughput Dfferentaton, n Proceedngs ACM Sgmetrcs, 05. Journal erson submtted, [2] Wreless LAN Medum Access Control MAC Qualty of Serce Enhancements, IEEE Std e, [3] S. Cho, J. Prado, S. S. N, and S. Mangold, IEEE e Contentonbased Channel Access EDCF performance Ealuaton, IEEE Internatonal Conference on Communcatons, pp , May [4] P. Garg, R. Dosh, R. Greene, M. Baker, M. 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10 APPENDIX The expressons for arous probabltes defned n III-B are as follows: η = 1 β η t = 1 β α α t = = Y σ = β σ t = β ζ = ζ t = ψ 1 = +1,Y +1,Y β +1,Y +1 β +1,Y +1 +1,Y +1 +1,Y =2 Y =2 +1 =1 Y =1 ψ tap = β +1 Y Y +1 +1,Y +1 Y +1,Y +1 Y +1,Y +1 Y +1,Y +1 Y 1 β 1 β 1 β 1 β Y +1 Y Y Y +1,Y +1 β +1,Y +1 η t 1 β β +1,Y +1,Y +1 Y + η =1 Y + +1 =1 Y =1 Y +1 β +1,Y +1 1 β β +1,Y +1 1 β +1 =1 Y β +1,Y β +1,Y +1 1 β +1,Y +1 Y +1 +1,Y +1 Y β Y +1 β +1,Y +1,Y +1 Y +1 +1,Y +1 Y β +1 1 β β +1,Y +1 1 β +1 1 β +1,Y +1 Y +1,Y +1 Y +1 +1,Y +1 Y +1,Y +1 Y /06/$ IEEE. 187