IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE Optmal Confguraton of e EDCA for Real-Tme and Data Traffc Pablo Serrano, Member, IEEE, Albert Banchs, Member, IEEE, Paul Patras, Student Member, IEEE, and Arturo Azcorra, Senor Member, IEEE Abstract The enhanced dstrbuted channel access (EDCA) mechansm of the IEEE e standard provdes qualty-ofservce (QoS) support through servce dfferentaton by usng dfferent medum-access-control (MAC) parameters for dfferent statons. The confguraton of these parameters, however, s stll an open research challenge, as the standard provdes only a set of fxed recommended values that do not take nto account the current wreless local area network (WLAN) condtons and, therefore, lead to suboptmal performance. In ths paper, we propose a novel algorthm for EDCA that, gven the throughput and delay requrements of the statons that are present n the WLAN, computes the optmal confguraton of the EDCA parameters. We frst present a throughput and delay analyss that provdes the mathematcal foundaton upon whch our algorthm s based. Ths analyss s valdated through smulatons of dfferent traffc sources (both data and real tme) and EDCA confguratons. We then propose a mechansm to derve the optmal confguraton of the EDCA parameters, gven a set of performance crtera for throughput and delay. We assess the effectveness of the confguraton provded by our algorthm by comparng t aganst 1) the recommended values by the standard, 2) the results from an exhaustve search over the parameter space, and 3) prevous confguraton proposals, whch are both standard and nonstandard complant. Results show that our confguraton outperforms all other approaches. Index Terms Enhanced dstrbuted channel access (EDCA), IEEE , performance analyss, qualty-of-servce (QoS), wreless local area network (WLAN). I. INTRODUCTION THE IEEE e supplement [1], whch s ncluded n the new revson of the standard [2], provdes wreless local area networks (WLANs) wth qualty-of-servce (QoS) support n the two access mechansms specfed: the enhanced dstrbuted channel access (EDCA) and the hybrd coordnaton functon controlled channel access. Our focus s on the former, whch s an extended verson of the wdely supported dstrbuted coordnaton functon (DCF) mechansm. Manuscrpt receved March 17, 2009; revsed August 18, 2009, November 19, 2009, and January 28, 2010; accepted January 31, Date of publcaton February 17, 2010; date of current verson June 16, Ths work was supported n part by the European Communty s Seventh Framework Program (FP7/ ) under Grant Agreement The vews and conclusons contaned here are those of the authors and should not be nterpreted as necessarly representng the offcal polces or endorsements, ether expressed or mpled, of the Ctzens Advanced Relatonshp Management Project or the European Commsson. The revew of ths paper was coordnated by Prof. J. L. P. Serrano s wth the Department of Telematcs Engneerng, Unversty Carlos III de Madrd, Leganés, Span (e-mal: pablo@t.uc3m.es). A. Banchs, P. Patras, and A. Azcorra are wth the Department of Telematcs Engneerng, Unversty Carlos III de Madrd, Leganés, Span, and also wth the IMDEA Networks, Leganés, Span (e-mal: banchs@t. uc3m.es; patras@t.uc3m.es; azcorra@t.uc3m.es). Dgtal Object Identfer /TVT Smlarly to the DCF, the EDCA mechansm s based on the carrer sense multple access wth collson-avodance (CSMA/CA) protocol. The man dfference s that, n the new standard, dfferent statons may contend wth dfferent values of these parameters, leadng to statstcal servce dfferentaton among flows (numercal values are provded n, e.g., [3] [6]). When deployng an EDCA WLAN, the man challenge s the confguraton of the contenton parameters, as the standard provdes only a set of recommended values. However, usng ths confguraton for every scenaro, regardless of, e.g., the number of statons or the traffc patterns, leads to suboptmal performance n most crcumstances. Therefore, a confguraton mechansm to derve the contenton parameters s needed. Furthermore, ths mechansm should not be based on heurstcs but rather on an analytcal model that provdes strong mathematcal foundatons to guarantee optmal performance. In ths paper, we buld upon our prevous work to acheve a twofold objectve. Frst, we present a novel analytcal model of EDCA performance that accounts for generc saturated and nonsaturated sources, and provdes the average throughput, the average delay, and the standard devaton of the delay as performance fgures. To our knowledge, ths s the most complete model of EDCA proposed to date and the only one that has all these features. Second, we use ths new analytcal model to develop a confguraton mechansm for the parameters of EDCA that, takng as nput the traffc requrements from both realtme and nonreal-tme statons, outputs the confguraton that maxmzes performance: It admts as many real-tme traffc statons as possble whle optmzng nonreal-tme throughput. To the best of our knowledge, ths s the frst approach to confgurng EDCA that covers all traffc types and s sustaned analytcally, thereby guaranteeng optmal performance. 1 The rest of ths paper s structured as follows. In Secton II, we revew the state of the art. In Secton III, we descrbe our analytcal model and valdate t through exhaustve smulatons. The optmal confguraton mechansm s ntroduced n Secton IV, along wth the results from the numercal search to prove the effectveness of our algorthm as well as a comparson aganst prevous approaches. Fnally, concludng remarks are gven n Secton V. 1 Note that the analytcal model requres a seres of assumptons. Therefore, when we use the term optmal confguraton, we are referrng to the confguraton that provdes the best performance accordng to ths model /$ IEEE

2 2512 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 II. STATE OF THE ART Here, we present the state of the art. We frst summarze the behavor of the EDCA mechansm, and then, we revew prevous analyses and approaches to confgure EDCA. A. IEEE e EDCA Here, we brefly summarze the EDCA mechansm as defned n the e standard. EDCA s a CSMA/CA-based protocol that extends the DCF by means of the parameters that are used to access the channel. The channel access s regulated by the channel-access functons (CAFs). To transmt ts frames, each CAF executes an ndependent back-off process that s regulated by a number of confgurable parameters. For the confguraton of these parameters, the standard groups the CAFs by access categores (ACs) and assgns the same confguraton to all the CAFs of an AC. In ths paper, we assume, for smplcty, that each staton runs only one CAF, and therefore, we nterchangeably use the terms CAF and staton. 2 A staton of an access category (AC ) wth a new frame to transmt montors the channel actvty. If the channel s sensed dle for a perod of tme that s equal to the arbtraton nterframe space parameter of ths AC (AIF S ), the staton transmts. Otherwse, f the channel s sensed busy (ether mmedately or durng the AIF S perod), the staton contnues to montor the channel untl t s measured dle for an AIF S tme, and at ths pont, the back-off process starts. The arbtraton nterframe space AIF S takes a value of the form DIFS + nt e, where DIFS and T e are constants that are dependent on the physcal layer, and n s a nonnegatve nteger. 3 Upon startng the back-off process, the staton computes a random value that s unformly dstrbuted n the range (0,CW 1) and ntalzes ts back-off tme counter wth ths value. The CW value s called the contenton wndow and depends on the number of transmsson attempts for the current frame. At the frst transmsson attempt, CW s set to be equal to the mnmum contenton wndow parameter (CW mn ). As long as the channel s sensed dle, the back-off tme counter s decremented once for each tme nterval T e. When a transmsson s detected on the channel, the backoff tme counter s frozen and reactvated agan after the channel s sensed dle for a certan perod. Ths perod s equal to AIF S f the transmsson s receved wth a correct frame check sequence (FCS). Otherwse, ths perod s equal to EIFS DIFS + AIF S, where EIFS s another constant that s dependent on the physcal layer. As soon as the back-off tme counter reaches zero, the staton transmts ts frame n the next slot tme. A collson occurs when two or more statons smultaneously start a transmsson. An acknowledgment (Ack) frame s used to notfy the transmttng staton that the frame has been successfully receved. If the Ack 2 Note that, followng [7], the analyss here could easly be extended to the case of multple CAFs per staton. 3 Accordng to the IEEE e standard termnology, AIF S = SIFS + nt e,wheredifs = SIFS +2T e,andn 2. Wthout loss of generalty, n ths paper, we use the smplfed notaton AIF S = DIFS + nt e, wth n 0. s not receved wthn a tmeout, the staton assumes that the frame was not receved and reschedules the transmsson by reenterng the back-off process. After each unsuccessful transmsson, CW s doubled, up to a maxmum value that s gven parameter. If the number of faled attempts reaches a predetermned retry lmt R, the frame s dscarded. When the staton gans access to the channel, t s allowed to retan the rght to access t for a duraton that s equal to the transmsson opportunty lmt parameter (TXOP ).Note that the mpact of the TXOP parameter s typcally small n QoS-provsoned scenaros, as real-tme traffc parameters are usually set such that queues never grow above one packet, whereas for data traffc, ths parameter s set such that only one packet s transmtted upon accessng the channel to avod degradng the delay performance of real-tme traffc. Followng ths reasonng, n the rest of ths paper, we concentrate on the by the CW max analyss of the other three parameters,.e., CW mn and AIF S. B. Related Work, CW max, There are several analytcal models of EDCA performance avalable n the lterature [7] [20]. However, most of them [7] [14] are based on the unrealstc assumpton that all statons always have packets that are ready for transmsson (commonly referred to as saturaton condtons). Whle ths assumpton may be reasonable for data traffc, t does not hold for realtme traffc. On the other hand, prevous approaches assumng nonsaturated condtons [15] [20] are typcally vald only for Posson arrvals and fxed length packets. In contrast to these prevous papers, our analyss makes no assumptons about the arrval process and allows for varable packet lengths. The analyss presented n ths paper combnes and extends our prevous work, provdng the most comprehensve analyss of EDCA to date, ncludng generc traffc sources as well as the relevant metrcs for data and real-tme traffc (namely, the throughput, the average, and the standard devaton of the delay). In partcular, the analyss extends our prevous work as follows. In [20], we presented an analyss of EDCA under nonsaturated traffc condtons to model the throughput and the average delay. In ths paper, we also account for the standard devaton of the delay. In [13], we analyzed the average delay performance of EDCA. Whle [13] s lmted to saturaton condtons, the present analyss also consders nonsaturaton traffc. In [21], we analyzed the standard delay devaton when there s only voce traffc that s present n the WLAN. In ths paper, we extend ths analyss to the case where there are multple ACs. The dfferences between the model presented n ths paper and the prevous work are summarzed n Table I. We observe that the proposed model s more complete than any of the prevous models. Only recently has the challenge of confgurng the EDCA parameters been addressed [7], [21] [27]. However, the exstng approaches suffer from major drawbacks. Our prevous works n [7] and [22] are restrcted to data traffc, whereas our works

3 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC 2513 TABLE I COMPARISON BETWEEN THE ANALYTICAL MODELS OF EDCA PERFORMANCE n [21] and [23] are restrcted to voce traffc. The works n [24] and [25] only consder two traffc types,.e., voce and data, and do not allow dfferent types of real-tme and nonreal-tme 4 traffc. The default confguraton recommended by the standard [2], the one recommended n [26], and the adaptve mechansm n [27] consder all traffc types, but they are based on heurstcs and, therefore, do not guarantee optmal performance. Indeed, the performance evaluaton conducted shows that our proposal substantally outperforms these prevous proposals. In addton to the above, a number of modfcatons of the EDCA protocol have recently been proposed [28] [32]. These proposals have the major drawback of not beng standardcomplant and requrng modfcatons to the hardware and the frmware of the wreless cards, whch challenges ther practcal deployment. The proposal n [28] apples only to one AC, whereas the one n [29] supports only voce and best effort traffc. The approach proposed n [30] prevents data statons from transmttng when the contenton level exceeds a certan threshold, whch has the shortcomng of starvng them. Fnally, the approaches n [31] and [32] are based on heurstcs; our smulaton results show that our approach, even wthout ntroducng modfcatons to EDCA, clearly outperforms them. III. PERFORMANCE ANALYSIS Here, we consder a WLAN operatng under the EDCA mechansm and analyze the throughput and the delay of each AC n the WLAN. A. Defntons, Termnology, and Assumptons In the followng, we present the key defntons, termnology, and assumptons upon whch our analyss s based. A summary of the notaton and varables used n the analyss s provded n Table II. In partcular, our analytcal model takes the followng nput varables: the number of ACs n the WLAN (N); the number of statons of each AC (n s the number of statons of AC ); the average sendng rate of the statons of each AC (ρ ), ther frame length dstrbuton, and the average frame length (l ); the confguraton {CW mn,m,a } of each AC, where m s defned such that CW max =2 m CW mn, and A such that AIF S = DIFS + A T e ; 4 Throughout ths paper, we wll nterchangeably use the terms data and nonreal tme. TABLE II NOTATION USEDINTHEANALYSIS and provdes as output the throughput, the average delay, and the standard devaton for each AC. Note that our model can be appled to analyze generc source models. The only restrcton mposed on the sources s that they are ergodc; otherwse, the analyss could not rely on the statons average sendng rate. Our analyss s based on the followng defntons. Defnton 1: A slot tme s the tme nterval between two consecutve back-off counter decrements of a staton wth mnmal AIF S (.e., DIFS). We say that a slot tme s nonempty when t contans a collson or a successful transmsson and that t s empty otherwse. Defnton 2: A slot tme s a k-slot tme f t s preceded by k or more empty slot tmes. Defnton 3: The saturaton rate of an AC s the rate that the statons of ths AC would obtan f they always had a packet that s ready for transmsson. Based on these defntons, our analyss reles on a number of assumptons. Frst, we make the followng two key approxmatons around the noton of saturaton rate to compute the statons rates n the WLAN. As long as the average sendng rate of the statons of a gven AC falls below ther saturaton rate, we assume that the statons of ths AC see all ther packets served (.e., ther transmsson queue never overflows). We refer to such an AC as a nonsaturated AC. On the other hand, f the average sendng rate of the statons of the AC exceeds the saturaton rate, we consder that the statons of ths AC always have packets that are ready for transmsson (.e., ther transmsson queue never emptes). We refer to such an AC as saturated.

4 2514 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 Fg. 1. k-slot tmes and probablty of transmsson (example wth k =2). In addton to the above two approxmatons, our analyss further reles on the followng addtonal assumptons that have already been used n prevous works n the lterature. Back-off tmes follow a geometrc dstrbuton (.e., a staton transmts upon decrementng ts counter wth an ndependent probablty). Ths assumpton was frst used n the analyss n [33] for the DCF, and snce then, t has been used n most of the analyses of EDCA (see, e.g., [8] [10]). Although back-off tmes actually follow a unform dstrbuton, all these works have shown that ths assumpton leads to accurate results. Each packet transmsson attempt colldes wth an ndependent probablty. Ths assumpton, whch s ntally used n [34], has been the bass of most of the WLAN performance analyses so far. The length of a slot tme can be modeled wth a random varable that depends only on the statons that could potentally transmt n ths slot tme. Ths s also a common assumpton when analyzng the delay performance of EDCA (see, e.g., [11]). Fnally, at each transmsson attempt, the packet length follows a random varable that depends only on the consdered AC. Ths assumpton s necessary for the tractablty of the analyss and has been used and shown to be accurate n prevous analyses dealng wth varable packet lengths n WLANs (see, e.g., [20] and [34]). We buld our analyss upon the varable τ, whch s defned as the probablty that a staton of AC transmts upon a backoff counter decrement. Note that snce a staton wth A = k starts decrementng ts back-off counter only after k empty slot tmes followng a nonempty slot tme, we see that the back-off counter decrements of ths staton concde wth the boundares of the k-slot tmes. Therefore, a staton of AC, wth A = k, transmts n a k-slot tme wth probablty τ and does not transmt n any other slot tme (see Fg. 1). In the followng, we frst separately analyze the τ of a saturated AC and the τ of a nonsaturated AC and combne both analyses to compute the τ values of all the ACs n the WLAN. Then, based on these values, we calculate the throughput and delay performance of each AC. B. Pont of Operaton of the WLAN We frst compute the pont of operaton of the WLAN as gven by the transmsson probabltes τ s of all the ACs. We start wth the case of a saturated AC [13]. Wth the assumpton that each transmsson attempt colldes wth a constant and ndependent probablty, we can model the behavor of ths AC wth the same Markov chan as n [35, Fg. 5]. Then, the probablty that a staton of a saturated AC transmts upon a back-off counter decrement can be computed by means of (1), shown at the bottom of the page, whch s gven by [35], where p(c ) s the probablty that a transmsson attempt of a staton of AC colldes. We next focus on the analyss of a nonsaturated AC. The goal of ths analyss s to compute the probablty that a nonsaturated staton transmts n a slot tme,.e., τ nonsat. Note that, n contrast to the τ of a saturated staton, whch exclusvely depends on the back-off process, τ nonsat also accounts for the nactvty perods of the staton caused by ts queue beng empty. The followng lemma lets us compute the τ of a nonsaturated AC based on varables that, as shown n the Appendx, can be expressed as a functon of τ s and p(c ) s. Lemma 1: The τ of a nonsaturated AC s gven by 5 τ nonsat = ρ ( 1 p(c ) R+1) (p(s)t s + p(e)t e + p(c)t c ) l (1 τ ) n 1 A k=a p(δ k ) j Δ k \ (1 τ j) n j where p(s), p(c), and p(e) are the probabltes that a slot tme contans a successful transmsson, contans a collson, or s empty, respectvely, and T s, T c, and T e are the average slottme duratons n each case. Δ k s the set of ACs wth A k, and p(δ k ) s the probablty that a randomly chosen slot tme s allowed for transmsson to the set Δ k. Wth the above, we can express τ s as a functon of the rest of the τ s and p(c ). To buld a system of equatons, we need to express p(c ) as a functon of the rest of the τ s. We compute p(c ) as a functon of the probablty of an empty k-slot tme [whch s denoted by p(e t k )]asfollows.ak-slot tme s empty as long as 1) the consdered staton does not transmt, and 2) no other staton transmts. The latter can be expressed as a functon of p(c ) by notng that the probablty of a collson corresponds to the case when some other staton transmts. Thus whch yelds (2) p(e t k )=(1 τ )(1 p(c )) (3) p(c )=1 p(e t k) 1 τ. (4) 5 The proofs of all lemmas are derved n the Appendx. τ sat = 2 ( 1 2p(c )(1 p(c ) R+1) CW mn (1 (2p(c ) m +1 )(1 p(c ))+(1 2p(c )(1 p(c ) R+1 )+CW mn 2 m p(c ) m +1 (1 2p(c )(1 p(c ) R m ) (1)

5 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC 2515 Fg. 2. Probablty of an empty k-slot tme (example wth k =1). Now, let us focus on the probablty that a gven k-slot tme s empty. If the prevous k-slot tme was nonempty, n ths k-slot tme, only the ACs wth A k may transmt. If the prevous k-slot tme was empty, the gven k-slot tme s preceded by k +1or more empty slot tmes, whch s exactly the defnton of (k +1)-slot tme, and therefore, such a k-slot tme s empty wth probablty p(e t k+1 ). Applyng ths reasonng (see Fg. 2), p(e t k ) can be wrtten as p(e t k )=(1 p(e t k )) (1 τ j ) nj + p(e t k )p(e t k+1 ). j Δ k Note that, f A s the largest A n the WLAN, n a A-slot tme, all statons may transmt; therefore, the followng holds: p(e t A )= (1 τ j ) nj. (6) j Δ A Startng from τ, wth (6), we can compute p(e t A ). Then, wth (5), we can compute p(e t A 1 ). Applyng ths recursvely, we can compute p(e t k ) k. Then, p(c ) can be computed usng (4), and fnally, τ can be obtaned from (1). We next combne the analyses for a saturated and a nonsaturated AC to obtan all τ s n the WLAN under statonary condtons. From the above, we have a method to compute the τ of a saturated and of a nonsaturated AC; the remanng challenge les n determnng whch ACs are saturated and whch are not. For ths purpose, we proceed step by step as follows. In the frst step, we consder that all ACs are saturated. Note that, from (1) and (2), we can express each τ of a saturated (or nonsaturated) AC as a functon of all τ s. Therefore, we have a system of N nonlnear equatons on τ s that can be resolved usng numercal technques. Once the τ values have been derved, we compute the throughput of all ACs by usng Lemma 2. We next compare the throughputs aganst the sendng rates. If the throughput of an AC s larger than ts sendng rate, we consder from ths step on that ths AC s not saturated and move t to the set of nonsaturated ACs. In the second step, we take the new sets of saturated and nonsaturated ACs resultng from the frst step and repeat the throughput computaton. Next, we agan compare the throughputs obtaned n the prevous step for the saturated ACs aganst ther sendng rates and move those ACs whose (5) throughputs are larger than ther sendng rates to the set of nonsaturated ACs. 6 The above s teratvely done untl the resultng throughputs of all the saturated ACs are smaller than ther sendng rates. Ths last scenaro represents a stable soluton, and therefore, the values from ths step gve us the throughput that each AC wll obtan n the WLAN under statonary condtons. Note that, as the number of ACs N s lmted to four by the standard, the above procedure requres, n the worst case, that we resolve, at most four tmes, a system of no more than four equatons, and therefore, the computatonal complexty s low. C. Throughput and Delay Analyss Once the values τ s have been derved, we can analyze the throughput and the delay performance of the WLAN. More specfcally, n the followng, we analyze the average throughput, the average servce delay, and the standard devaton of the delay. 7 The throughput r s gven by the followng lemma. Lemma 2: The average throughput r that a staton from AC experences s gven by r = l A k=a p(δ k )p(s Δ k ) (7) (s)t s + p(c)t c + p(e)t e where p(s Δ k ) s the probablty that, gven that only statons from set Δ k can transmt, there s a successful transmsson from AC. We next compute the delay performance of the WLAN. For ths purpose, we defne B,r as the average back-off counter before retry r, Tslot,k as the average duraton of a k-slot tme n whch the consdered staton of AC does not transmt, Tnter_tx,k and T nter,k as the average duratons of the tme between two k-slot tmes when the consdered staton transmts and does not transmt n the frst one, respectvely, and T s, and T c, as the average duratons of a slot tme that contans a success and a collson nvolvng a staton of AC. In Fgs. 3 and 4, we llustrate these delay components for a gven sequence of slot tmes. Based on these varables, Lemma 3 provdes the average value of the delay d. Lemma 3: The average delay experenced by a nondropped packet of a staton of AC s gven by 1 d = R j=0 (1 p(c (1 p(c )) p(c ) j )) p(c ) j j=0 ( j ( ( jt c, +T s, + T nter_tx,k+b,r T slot,k +Tnter,k)) ). r=0 6 Note that an AC that was not saturated n the prevous step can never become saturated agan. In fact, f such an AC always had packets that are ready for transmsson, t would obtan a throughput that s even larger than n the step where t became nonsaturated (snce n the current step, there are fewer saturated ACs). 7 Gven the average delay and ts standard devaton, t s possble to provde guarantees on the delay dstrbuton by means of the Chebyshev nequalty [36]. In ths paper, we do not dscuss ths further and smply assume that the average delay and the standard devaton are suffcent to provde real-tme traffc wth the desred servce guarantees. R (8)

6 2516 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 Fg. 3. Average delay components for the case of j retres. Fg. 4. Components of the delay (example wth k =2). Fnally, the followng lemma gves the value of the standard devaton of the delay. Lemma 4: The standard devaton of the delay s gven by R σd 2 j=0 = (1 p(c )) p(c ) j E [ (d,j ) 2] R j=0 (1 p(c (d ) 2 (9) )) p(c ) j where d,j s the delay that a frame from AC suffers n case of j retres. The above lemma termnates our performance analyss of EDCA. Secton III-D s devoted to the assessment of ts accuracy under dfferent traffc sources and EDCA confguratons. D. Performance Analyss Valdaton We valdate the accuracy of the model by comparng the analytcal values aganst those obtaned by means of smulatons. For ths purpose, we have mplemented the e EDCA protocol n OMNeT++. 8 The source code of our smulatons s avalable n our Web ste. 9 The smulatons are performed for a WLAN wth the medum-access-control (MAC) layer parameters of IEEE b [37]. We assume a channel n whch frames are only lost due to collsons. The queue sze of all of the statons s set equal to 100 packets. For the smulaton results, the average and 95% confdence nterval values are gven, although, n many cases, confdence ntervals are too small to be apprecated n the graphs. The values that are analytcally obtaned are plotted wth lnes, and the smulaton results are plotted wth ponts. 1) Data Traffc: Frst, we analyze our throughput model for the case when only data traffc s present n the network, wth no delay requrements. We have taken a fxed frame payload sze of 1500 B, and m =5(.e., CW max =2 5 CW mn ). We consder a scenaro wth four ACs,.e., {1,...,4}, wth n =2 statons each, sharng the channel wth a dfferent CW mn and AIF S each. Specfcally, we take CW mn =2 1 CW1 mn for {2, 3, 4} and A = 1 for {1,...,4}. Results are gven n Fg. 5. The smulatons Fg. 5. Valdaton of the throughput model for a scenaro wth four ACs, each usng a dfferent AIF S and CW confguraton. Fg. 6. Valdaton of the average delay model for a voce traffc scenaro wth dfferent confguratons of the CW used. performed valdate our model for data traffc, as smulaton results match the analytcal ones well. 2) Voce Traffc: Next, we valdate the accuracy of our analyss by comparng analytcal results aganst smulatons n a scenaro where only voce traffc s present. Followng the behavor of standard pulse-code modulaton codecs (e.g., G.711), voce sources generate one 80-B packet every 10 ms. Fgs. 6 and 7 plot the average and the standard devaton of the delay, respectvely, for dfferent confguratons of the CW mn parameter and dfferent numbers of voce statons. The three values that are chosen for the number of voce statons n {10, 15, 20} correspond to a low, medum, and heavly loaded WLAN, respectvely. We observe that the analytcal results match the smulatons remarkably well, whch confrms the accuracy of our analyss.

7 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC 2517 Fg. 7. Valdaton of the model for the standard devaton of the delay under voce traffc and dfferent CW confguratons. We observe from Fg. 6 that the evoluton of the delay versus CW shows a nonmonotonous behavor. Indeed, there s, at frst, a steep decrease n the delay, reachng the mnmum value, and then there s a slow ncrease. Ths s caused because, wth small CW values, there are many collsons n the WLAN, whch cause congeston. When usng larger CW, collsons take place less frequently, and the WLAN moves out of a congested stuaton; the steep decrease corresponds to ths change from congeston to out of congeston. Then, after reachng the mnmum value, there s a graceful degradaton of the delay, whch s caused by the use of larger back-off counters than needed to prevent congeston. 10 3) Voce and Data Traffc: Next, we valdate the model for the case of a WLAN operatng wth both data and voce traffc. The valdaton s performed usng two ACs, both wth the same number of statons. The frst group (voce statons) transmts 80-B packets every 10 ms. The second group (data statons) transmts accordng to a Posson process wth an average rate of 500 kb/s and the packet lengths derved from the measurements n [38]. For valdatng our model, we perform the followng experments. Frst, we perform an experment to valdate the analyss of the dfferentatng effect of the AIF S parameter. To ths am, both ACs have the same contenton wndow confguraton CW mn =32, m =5. Regardng the A parameter, the voce AC s always confgured wth A =0, whereas for the confguraton of the data AC, we use two dfferent values: A =1(small dfferentaton), and A =5(large dfferentaton). Smlarly, we assess whether our model captures the dfferentatng effect of the CW parameter by means of the followng confguraton: A =0for the two ACs and CW mn =16, m =1for voce, whereas for data traffc, we use CW mn =32, m =4n one case and CW mn = 64,m=4n the other case. 10 For a detaled analyss of ths behavor, see [21]. Fg. 8. Valdaton of the average delay model for a mxed scenaro wth voce and data statons and dfferent AIF S dfferentaton. Fg. 9. Valdaton of the average delay model for a mxed scenaro wth voce and data statons and dfferent CW dfferentaton. The results for the average delay are shown n Fgs. 8 and 9. As the results from the analytcal model closely follow the smulaton values, we conclude that the proposed model s also vald for ths case. It s worth remarkng the degree of servce dfferentaton that the AIF S and CW parameters provde: For the case of AIF S, the dfferentaton s strong only when there s enough traffc on the WLAN (.e., n s relatvely large). On the other hand, the CW parameter provdes a larger level of dfferentaton. The evaluaton of the analyss of the standard devaton of the delay s depcted n Fgs. 10 and 11. As n the prevous case, the model closely follows the smulaton results, whch confrms the valdty of our analyss for ths performance metrc as well. We further observe that, compared wth the average delay, the standard devaton s more senstve to the ncrease n the load. 4) Mxed Traffc: We fnally valdate our model for the more general case, wth up to four traffc classes of dfferent characterstcs, whch we name voce, vdeo, data, and background, respectvely. In the frst AC (voce), 80-B packets are generated every 10 ms. In the second AC (vdeo), we model vdeo traffc wth a varable bt-rate source sendng varable-sze packets at

8 2518 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 Fg. 10. Valdaton of the model of the standard devaton of the delay for a mxed scenaro wth voce and data statons and dfferent AIF S confguratons. Fg. 12. Valdaton of the average delay model for a scenaro wth four ACs confgured accordng to the standard recommended values. Fg. 11. Valdaton of the model of the standard devaton of the delay for a mxed scenaro wth voce and data statons and dfferent CW confguratons. TABLE III EDCA CONFIGURATION Fg. 13. Valdaton of the model for the standard devaton of the delay for a scenaro wth four ACs confgured accordng to the standard recommended values. a constant nterarrval tme. The average bt rate of the source s set equal to 250 kb/s, and the packet length dstrbuton s taken from the vdeo traffc measurements n [39]. In the thrd AC (data), statons always have a packet that s ready for transmsson, modelng the behavor of a data transfer. Packet szes are taken from the data traffc measurements n [38]. In the fourth AC (background), statons always have 1000-B packets that are ready for transmsson. The confguraton of each AC s derved from the recommendatons gven n the e standard for b (see Table III). Experments are performed for a varyng number of statons per AC (each AC has n statons). Fgs. 12 and 13 plot the average and the standard devaton of the delay, respectvely. The valdaton of the throughput model s depcted n Fg. 14. Fg. 14. Valdaton of the throughput model for a scenaro wth four ACs confgured accordng to the standard recommended values. We observe from the fgures that EDCA s effectve n provdng servce dfferentaton. Both n terms of the throughput and the delay, hgher prorty ACs always perform better than lower prorty ones. Furthermore, hgher prorty ACs also saturate later: AC 3 (data) saturates for n > 4, whereas ACs 1

9 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC 2519 and 2 (voce and vdeo) saturate for n > 6 (AC 4 s, by defnton, always saturated). Beyond ths saturaton pont, the throughput of all ACs gradually decreases wth n, whereas the delay ncreases drastcally. For all cases, the analytcal results match the smulatons remarkably well, confrmng the accuracy of our model. IV. OPTIMAL CONFIGURATION Here, we present an algorthm to fnd the optmal confguraton of the EDCA parameters under a general scenaro wth multple real-tme and data ACs. The objectves of our algorthm are gven as follows. 1) Meet the requrements of the real-tme traffc. More specfcally, the confguraton should provde real-tme statons wth the requred throughput and delay guarantees. 2) Maxmze the admssblty n the network. Specfcally, we am to admt as many real-tme statons as possble whle satsfyng the prevous objectve. 3) Maxmze the throughput that s receved by the data traffc whle meetng the prevous two objectves. For throughput allocaton, we use the common weghted max-mn far allocaton crteron [40] [42]. Ths maxmzes the mnmum r /w n the system, wth r beng the throughput that s allocated to entty and w beng the entty s weght. In our case, the enttes are the WLAN statons, and the allocated throughput s the saturaton throughput of a staton. A. Consderatons for Optmal Confguraton Before proceedng wth the desgn of our algorthm, we make the followng consderatons on the confguraton of some of the EDCA parameters. Ths smplfes the desgn of the algorthm and reduces ts computatonal cost. The consderatons for the data ACs are the followng. From (1), we have that τ can be adjusted as a functon of two parameters,.e., CW mn and m. As a consequence, we have one degree of freedom when settng these parameters to obtan the desred τ. Followng ths, we fx m =0. Then, by substtutng m wth 0 n (1), we compute the CW mn value that leads to τ opt as follows: CW = 2 τ opt 1. (10) A = A d : Followng the proof n [7], the throughput of the data statons s maxmzed when they all use the same A settng. TXOP =1packet. Ths ensures that a staton transmttng data sends only one packet upon accessng the channel and, thus, reduces the delay that s nflcted on real-tme traffc. For the case of real-tme ACs, we make the followng consderatons. A =0: The optmal settng for ths parameter s ts mnmum possble value, namely, AIF S = DIF S, as otherwse, addtonal tme s unnecessarly lost after every transmsson. CWj mn = CWj max = CW j : When the number of statons n the channel s unknown, CW max s typcally set larger than CW mn so that after a collson, the CW ncreases, and thus, the probablty of a new collson s reduced. However, ths s not necessary n our case, as the number of statons s known, and therefore, ther CW mn can be drectly confgured for optmal operaton. In addton, f we set CW max larger than CW mn, the delay of the packets that suffer one or more collsons drastcally grows, whch harms jtter performance. TXOP j = TXOP max : Consderng the strct delay requrements of real-tme traffc, the EDCA parameters wll be chosen such that the transmsson queues of the statons almost never grow to more than one packet (n partcular, ths holds for the confguratons that we later propose). In the eventual case that queues grow above one packet, t s desrable that, upon accessng the channel, all watng packets are transmtted to mnmze ther delay. To acheve ths, we set the TXOP parameter to ts maxmum allowed value. Followng the above consderatons, our algorthm provdes the confguraton for the followng set of parameters that are left open: the A confguraton for the data statons, the CW parameters for each of the real-tme ACs, and the CW for each data AC. B. Optmal Confguraton Algorthm The proposed algorthm s based on a numercal search that we perform over the τ of one data AC, whch we take as reference. In each step of the search, gven the value of the τ of ths reference AC, we need to compute the τ j of the other ACs. To obtan the τ j of the other data ACs, we apply the max-mn far allocaton crteron to the throughput expresson gven n (7), whch yelds [7] τ (1 τ j ) τ j (1 τ ) = w. (11) w j Once the τ j s of each data AC are known, the other τ l s can be obtaned as follows. Neglectng the probablty of a drop due to reachng the maxmum retry lmt, we have r ρ. Furthermore, by applyng (7) to r l /r k and makng the approxmaton p(s l )/p(s k ) τ l /τ k, we obtan τ l ρ l/l l (12) τ k ρ k /l k where, hereafter, we wll denote the rght-hand sde of the above equaton by K l. Wth the above, we can derve a thrd-order equaton to approxmately calculate τ k of a reference real-tme AC, gven all τ s of the data ACs. Ths thrd-order equaton s obtaned from settng the output rate of a staton of AC k equal to ts nput rate,.e., r k = ρ k (13) where r k s computed by makng the followng smplfcaton to the expresson of (7): We dstngush two types of slots,.e., the ones where only real-tme statons can transmt and the

10 2520 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 ones where data statons can transmt, and then compute the numerator and the denomnator of (7) by condtonng them to these two types of slots. Ths yelds r k = p(δ real)p(s k Δ real )+p(δ data )p(s k Δ data ) l k (14) p(δ real )T slot,r + p(δ data )T slot,d where p(δ real ) s the probablty that, n a slot tme, only realtme ACs can transmt, p(δ data ) s the probablty that data statons can also transmt, p(s k Δ real ) and p(s k Δ data ) are the success probabltes of a staton of AC k for each of the two cases, and T slot,r and T slot,d are the average slot duratons, respectvely. The probablty p(δ real ) s computed as follows. We frst calculate the exact expresson for the probablty of beng n a state n whch only real-tme ACs can transmt, and then, we perform a frst-order approxmaton of the Taylor expanson of ths expresson. The result s the followng: p(δ real ) A d(1 p(e Δ data ) A d (1 p(e Δ data )) (1 p(e Δ data )) A 2 d 2((1 p(e Δ data )A d +1) 2 τ k + (1 + p(e Δ data)) A d l Δ real n l K l 2((1 p(e Δ data )A d +1) 2 τ k (15) where Δ real s the set of the real-tme ACs, and p(e Δ data ) s the probablty that a slot n whch all ACs can transmt s empty,.e., p(δ data ) s smply computed as p(e Δ data )= (1 τ k ). (16) k p(δ data )=1 p(δ real ). (17) The probablty p(s k Δ real ) corresponds to the probablty that a staton of AC k transmts and that no other real-tme staton transmts,.e., p(s k Δ real )=τ k (1 τ k ) n k 1 (1 τ l ) n l l Δ real \k τ k 1 (n k 1)τ k l Δ real \k n l K l τ k. (18) By consderng that the probablty that no other staton transmts s approxmately p(e Δ data ), the probablty p(s k Δ data ) corresponds to the probablty that a staton of AC k transmts and that no other staton,.e., real-tme or data, transmts,.e., p(s k Δ data ) τ k p(e Δ data ). (19) Fnally, we can calculate T slot,r and T slot,d as a secondorder expresson n τ k by consderng the dfferent lengths of the transmssons that we can have n a slot tme and the correspondng probabltes. Based on the above analyss, our optmal confguraton mechansm s descrbed by Algorthm 1 and s summarzed as follows. Gven a reference data AC and a reference real-tme AC k, a search s performed on all A s values specfed n the standard (lne 4). For each A value, a golden secton search s performed on the τ to maxmze the throughput allocaton crteron (lne 5). For each value of τ,theτ j of the remanng data ACs s computed wth (11) accordng to the allocaton crteron (lne 7). Next, the transmsson probablty τ k of the reference realtme AC s computed wth (13) (lne 9), and from ths, the remanng τ l s of the other real-tme ACs are then computed by applyng (12) (lne 11). Wth all the τ s, we proceed to compute the CW values that guarantee delay performance to real-tme statons. Followng the explanatons n [21], there s a range of CW values that provde the desred QoS performance. To compute ths range of CW values, we use the delay analyss of Lemmas 3 and 4 to obtan the confguratons that lead to the desred delay performance. Wth the alreadycomputed τ s and the settng CW mn = CW max, ths can be effcently done usng (8) and (9). From all the CW values, we choose the maxmum one for each AC (lne 14) snce, followng the dscusson n [21], these are the ones that lead to a WLAN operatng as far as possble from nstablty. We next check that the values of CW obtaned n the prevous step satsfy the requrement that, even n the cases where the real-tme statons become saturated, ther throughput n saturaton r j (sat) s larger than ther nput rate ρ j (lne 18) snce, followng [43], ths guarantees that the proposed confguraton s ndeed stable. If ths condton s not met, then ths confguraton s not further consdered n the search. Next, τ s are used to compute the weghted rate r /w of each data AC (lne 23). Note that the golden secton search of lne 5 maxmzes the mnmum of these values. Therefore, f the current confguraton provdes better performance than the ones prevously evaluated n the search, t s saved (lnes 25 30). Fnally, once the search ends, the best confguraton s returned through the EDCA parameters (lne 37). If the search provdes no confguraton, ths means that there exsts no confguraton that satsfes the sources requrements, and therefore, the request that trggered ths search has to be rejected. Algorthm 1 Optmal confguraton of EDCA parameters 1: Take data AC as a reference 2: Take real-tme AC k as a reference 3: max 0 4: for A =0to 15 do 5: whle Golden secton search on τ do 6: for each data AC j do 7: τ j w j τ /(w + τ (w j w )) (11)

11 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC : end for 9: Compute τ k (13) 10: for each real-tme AC j do 11: τ l τ k K (12) 12: end for 13: for each real-tme AC j do 14: Compute CW j to fulfll 15: the delay requrement Lemmas 3 and 4 16: end for 17: for each real-tme AC j do 18: f r j (sat) <ρ j then 19: The τ value s not a possble value. Skp. CW j corresponds to saturaton. 20: else 21: for each data AC j do 22: Compute r j /w j 23: end for 24: f mn{(r /w )} > max then Save confguraton 25: max mn{(r /w )} 26: A max A 27: τ data max τ data 28: CW real tme max 29: end f 30: end f 31: end for 32: end whle 33: end for 34: CW data 2/τ data max 1 35: return A, CW data, CW real tme CW real tme C. Optmal Confguraton Valdaton Here, we valdate our optmal confguraton algorthm by means of smulatons for dfferent traffc scenaros. More specfcally, we assess through smulatons the performance of the confguraton resultng from our algorthm and compare t aganst the best performance obtaned by performng an exhaustve search over the EDCA parameters. 1) Data Traffc: We frst assess the performance of our algorthm for a scenaro where only data statons are present. We consder a scenaro where four ACs wth n statons each always have a 1500-B frame that s ready for transmsson. In these crcumstances, and wth no real-tme traffc n the WLAN, the only relevant metrc of performance s the maxmum mn(r /w ), accordng to the max-mn far allocaton crteron. Results are shown n Table IV for n = {2, 10} statons per AC and dfferent throughput allocaton weghts w s. They show that the confguraton algorthm maxmzes throughput performance as the gan obtaned when usng the exhaustve search s neglgble. 2) Voce Traffc: Next, we evaluate the performance of our algorthm for voce traffc. We valdate the algorthm by comparng the performance of our confguraton (CW algorthm ) aganst the result of performng an exhaustve search over the CW mn space and choosng the best CW mn value,.e., CW exhaustve. We perform ths experment for three df- TABLE IV ALGORITHM VALIDATION FOR DATA TRAFFIC SCENARIO TABLE V ALGORITHM VALIDATION FOR VOICE TRAFFIC SCENARIO ferent qualty crtera, rangng from a more strngent requrement (E[d max ],σ max 2.5 ms) to a more relaxed one (E[d max ],σ max 5 ms) [21]. Smulaton results, whch are presented n Table V, show that 1) the proposed confguraton s always very close to the one obtaned from the exhaustve search, and 2) our algorthm admts as many voce calls as the exhaustve search whle meetng the desred qualty crtera. 3) Voce and Data Traffc: To valdate the proposed algorthm for a scenaro n whch the WLAN operates under both data and voce traffc, we perform the followng experment. We consder two ACs, both wth the same number of statons and the followng characterstcs. The frst AC transmts 80-B packets every 10 ms. We consder two dfferent delay requrements for ths AC: 1) E[d], σ d 2.5 ms, and 2) E[d], σ d 5 ms. The second AC models the behavor of a data transfer by always havng a 1000-B packet that s ready for transmsson. Agan, we compare the results from our confguraton aganst those provded by the best confguraton found by means of an exhaustve search over the CW mn of the data and voce ACs, and the A parameter of the data AC. The results are shown n Table VI: Wth the proposed confguraton, the qualty crtera are always met, and the throughput obtaned by data statons s very close to that provded by the confguraton resultng from the exhaustve search. We, therefore, conclude that the proposed confguraton algorthm maxmzes the performance of the WLAN. 4) Mxed Traffc: Fnally, to valdate the proposed algorthm under the most generc scenaro, we consder a WLAN wth the four ACs defned n Secton III-D4, each of them wth the same number of statons n. For the real-tme ACs, we consder the

12 2522 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 TABLE VI ALGORITHM VALIDATION FOR DATA AND VOICE TRAFFIC SCENARIO TABLE VII ALGORITHM VALIDATION FOR MIXED TRAFFIC SCENARIO statons (n klobts per second) resultng from our algorthm and from the other fve mentoned approaches. From the results gven n the table, we conclude that our algorthm clearly outperforms the other proposals snce 1) wth our approach, real-tme statons always see ther delay guarantees satsfed; 2) our approach provdes data statons wth a substantally larger throughput than any other approach meetng the delay requrements 11 ; and 3) t also provdes a much larger admssblty regon. In partcular, wth our approach, we can admt up to n =10statons, whle none of the other proposals can admt more than n =6 statons (.e., our approach can admt at least 66% more statons). The reason for ths s that the other approaches are based on heurstcs that do not guarantee optmal performance, n contrast to ours, whch s based on an analytcal model that guarantees optmal performance. E. Implementaton Consderatons followng delay requrements: E[d 1 ], σ d,1 5 ms and E[d 2 ], σ d,2 20 ms and, for the data ACs, the followng weghts: w 3 =2, and w 4 =1. The throughput and delay results obtaned wth the proposed algorthm are gven n Table VII. The results valdate the proposed algorthm snce they satsfy all the requrements. In all scenaros, the average and the standard devaton of the delay obtaned wth our confguraton are below the desred values, whch shows that the confguraton meets the requred delay guarantees. Furthermore, an exhaustve search has been conducted, whch has shown that no other confguraton can admt more statons whle satsfyng the delay requrements. Ths proves that the confguraton maxmzes the admssblty regon by admttng as many statons as possble. Fnally, by comparng the throughput performance obtaned through exhaustve search aganst our results, we conclude that we also maxmze the mn(r /w ) for data ACs. D. Comparson Aganst Other Approaches We next compare the performance of the confguraton resultng from our algorthm aganst the followng approaches. two other avalable approaches for the confguraton of the EDCA parameters, namely, the standard recommended set of values [2] and the recent proposal n [26]; the adaptve confguraton schemes n [27], [31], and [32], whch am to provde QoS guarantees n EDCA WLANs. It s worth notng that the approaches n [31] and [32] requre ntroducng changes to the e standard, whch challenges ther practcal use. The scenaro that we choose for ths comparson s the mxed traffc scenaro of Secton IV-C4 snce ths s the most complete of the scenaros used n the valdaton of the algorthm. Table VIII gves the average delay of voce and vdeo flows (n mllseconds), as well as the total throughput gven to data We assess the computatonal cost of the algorthm by measurng the number of floatng-pont operatons (flops) requred by a MATLAB mplementaton to execute t. For all the presented experments, the algorthm requres approxmately 90 kflops. Assumng a WLAN access pont wth a 10-Mflops/s CPU, t would take 9 ms to perform an admsson control decson, whch s fully acceptable n a realstc scenaro. We conclude from ths experment that the computatonal complexty of the proposed algorthm s suffcently low to allow ts practcal use n today s hardware platforms. V. C ONCLUSION As the EDCA mechansm of e becomes wdely avalable, the need for a confguraton algorthm to tune the MAC parameters and boost WLAN performance arses. We have shown that a proper confguraton of EDCA can lead to performance gans of 66% over the standard recommended values. We beleve that these gans represent a strong motvaton for the deployment of EDCA WLANs to effcently use the scarce wreless medum. In ths paper, we have presented an algorthm to confgure an EDCA WLAN that acheves a twofold objectve: 1) It maxmzes the admssblty regon of real-tme traffc, and 2) t optmzes the throughput performance of data traffc. To buld ths algorthm, we have presented the most comprehensve analyss of EDCA performance to date. Ths analyss, as proven by exhaustve smulatons, can accurately model throughput and delay performance of real-tme and nonreal-tme traffc. We have used ths analyss to desgn an optmal confguraton algorthm for EDCA. In contrast to prevous work, whch s typcally heurstc or measurement-based, ours s a mathematcally supported mechansm that tunes the EDCA parameters to maxmze performance. By means of the analytcal model, 11 Although, for the n =10case, data statons receve a larger throughput wth [31] than wth our confguraton, voce and vdeo statons suffer much larger delays. Addtonally, they also suffer a drop rate above 20% (not shown n the table), whch results n our approach actually provdng better total throughput performance.

13 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC 2523 TABLE VIII COMPARISON AGAINST OTHER APPROACHES we have derved an effcent algorthm whose complexty s well suted for low computaton capacty devces and can be mplemented n realstc scenaros. We have shown that the performance of our algorthm s almost dentcal to the one obtaned through exhaustve numercal searches. APPENDIX Lemma 1: The τ of a nonsaturated AC s gven by τ nonsat = ρ ( 1 p(c ) R+1) (p(s)t s + p(e)t e + p(c)t c ) l (1 τ ) n 1 A k=a p(δ k ) j Δ k \ (1 τ. j) n j (20) Proof: Accordng to Secton III-A, a staton of a nonsaturated AC sees that all the traffc t sends served ether because ts packets are successfully transmtted or because they are dscarded when reachng the retry lmt due to sufferng R +1 collsons. Hence, the followng holds: ρ ( 1 p(c ) R+1) = r (21) where r s the throughput that s experenced by a staton of AC, whch s gven by (7), ρ s ts average sendng rate, and p(c ) R+1 corresponds to the probablty that a packet of ths staton s dscarded upon reachng the retry lmt. To prove the lemma, we need to derve the dfferent varables n (7). The probablty p(e) s, by defnton, p(e t 0 ),asall slot tmes are 0-slot tmes. Ths has already been computed n Secton III-B. To compute the rest of the varables n (7), we proceed as follows. Frst, let us defne p(t k ) as the probablty that a slot tme s a k-slot tme. Snce a slot tme s a k-slot tme f and only f the prevous slot tme s a (k 1)-slot tme and t s empty, whch occurs wth a probablty p(e t k 1 ),ths probablty can be expressed as p(t k )=p(t k 1 )p(e t k 1 ). (22) Startng from p(t 0 )=1 (whch holds by defnton) and recursvely applyng the above, t follows that k 1 p(t k )= p(e t j ). (23) j=0 The probablty that a random slot tme contans a success of a gven staton of AC can be computed (by applyng the total probablty theorem) as p(s )= A k=a p(δ k )p(s Δ k ) (24) where p(s Δ k ) s the probablty that a slot tme n whch ths set of ACs may transmt contans a success of a gven staton of AC. A slot tme s allowed for transmsson to the set Δ k (wth k<a)ftheslottmesak-slot tme but not a (k +1)-slot tme. 12 For k = A, we have that n an A-slot tme, allacsare allowed to transmt. Thus { p(tk ) p(t p(δ k )= k+1 ), k < A (25) p(t A ), k = A. The probablty p(s Δ k ) corresponds to the case when the consdered staton transmts and no other staton of set Δ k does,.e., p(s Δ k )=τ (1 τ ) n 1 (1 τ j ) n j. (26) j Δ k \ The probablty that a slot tme contans a success can be computed as the sum of the ndvdual success probabltes,.e., p(s) = Δ A n p(s ) (27) where, wth our defnton of A, Δ A denotes the set of all ACs. The probablty that a slot tme contans a collson can be obtaned from p(c) =1 p(e) p(s). (28) The average duraton of a success T s can be computed by summng the dfferent possble duratons weghted by ther probabltes,.e., T s = n p(s ) p(s) T s, (29) Δ A where T s, s the average duraton of a success of a staton of AC, whch s calculated accordng to the followng expresson gven by [7]: T s, =T PLCP + H + l C +SIFS+T PLCP+ ACK C +DIFS (30) where T PLCP s the physcal-layer convergence protocol preamble and header transmsson tme, H s the MAC overhead (header and FCS), ACK s the sze of the acknowledgment frame, and C s the channel bt rate. 12 Note that a slot tme that s a k-slot tme but not a (k +1)-slot tme s preceded by exactly k empty slot tmes, and therefore, only the ACs wth A k (.e., the ACs of set Δ k ) may transmt n such a slot tme.

14 2524 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 To compute the average duraton of a collson T c, we note that ths s gven by the largest packet length nvolved. Followng ths, we can compute T c by summng the possble collson duratons weghted by ther probabltes,.e., T c = l L p(c, t = l) Tc l (31) p(c) where p(c, t = l) s the probablty that a slot tme contans a collson n whch the length of the longest packet nvolved s equal to l, Tc l s the duraton of ths collson, and L s the set of packet lengths. Tc l s computed as (see [7]) Tc l = T PLCP + H + l + EIFS (32) C and p(c, t = l) s computed, applyng the total probablty theorem, as p(c, t = l) = A p(δ k )p(c, t = l Δ k ) (33) k=0 where p(c, t = l Δ k ) s the probablty that, gven that only statons of set Δ k may transmt, a slot tme contans a collson n whch the longest packet nvolved s of length l. To obtan p(c, t = l Δ k ), we sweep along all the statons that may transmt and compute the probablty that 1) the consdered staton transmts a packet of length l, and 2) some other staton transmts a packet but wth length that s no longer than l. Let us defne S k as the set of statons of Δ k and p(t j = l) as the probablty that the length of a transmsson from staton j s l. Then p(c, t = l Δ k )= j S k τ j p(t j = l)p(tx l S k,j) (34) where p(tx l S k,j) accounts for the probablty that there s at least one transmsson from the set S k (wthout staton j)but of a sze that s less than or equal to l. To compute ths probablty, we calculate the probablty that no staton transmts a packet that s longer than l and subtract from ths the probablty that no staton transmts. In partcular, for the computaton of the frst term, we ndex all the statons and refer wth S k,j to the set of statons of S k wth an ndex that s smaller than j; then, we compute the probablty that statons of S k,j do not transmt a packet that s longer than or equal to l and the probablty that statons wth hgher ndex than j do not transmt a packet that s longer than l, 13.e., p(tx l S k,j)= (1 τ m p(t m l)) m S k,j (1 τ m p(t m >l)) (1 τ m ). (35) m S k \S k,j j m S k \j Fnally, expressng r as a functon of the varables computed n (22) (35) and substtutng these nto (20) yeld ρ ( 1 p(c ) R+1) = τ (1 τ ) n 1 l A k=a p(δ k ) j Δ k \ (1 τ j) n j. (36) (p(s)t s + p(e)t e + p(c)t c ) The proof follows. Lemma 2: The average throughput r that a staton from AC experences s gven by r = l A k=a p(δ k )p(s Δ k ). (37) p(s)t s + p(c)t c + p(e)t e Proof: We compute the throughput r followng [34]: We dvde the average payload nformaton transmtted by AC n a slot tme E[payload per slot] over the average duraton of a slot tme E[slot length],.e., r = E[payload per slot]. (38) E[slot length] The average payload nformaton transmtted by AC s gven by E[payload per slot] =l p(s ) (39) whle the average length of a slot tme s gven by E[slot length] =p(s)t s + p(c)t c + p(e)t e (40) where the probabltes and average duratons have already been derved n the proof of Lemma 1. By combnng the above equatons, we obtan r = l p(s ) p(s)t s + p(c)t c + p(e)t e. (41) The proof follows. Lemma 3: The average delay experenced by a nondropped packet of a staton of AC s gven by 1 d = R j=0 (1 p(c ))p(c ) j ( jt c, +T s, + R j=0 (1 p(c ))p(c ) j j ( ( T nter_tx,k+b,r T slot,k +Tnter,k)) ). r=0 (42) Proof: To compute the average delay of a nondropped packet d, we use the total probablty theorem as follows: R j=0 d = (1 p(c )) p(c ) j d,j R j=0 (1 p(c (43) )) p(c ) j 13 The dstncton n (35) between the statons wth ndexes that are smaller and larger than j s made to avod countng more than once the event when two or more statons transmt a packet of length l. where d,j s defned as the average delay of a staton of AC n case the frame suffers j retres. Ths delay s computed as

15 SERRANO et al.: OPTIMAL CONFIGURATION OF e EDCA FOR REAL-TIME AND DATA TRAFFIC 2525 (see Fg. 3) j ( ( d,j = T nter_tx,k+b,r T slot,k +Tnter,k)) +jtc, +T s,. r=0 (44) To complete the proof of the lemma, we need to compute the components of (44). T s, s gven by (30). B,r s computed usng the followng gven n [13]: B,r = CWmn 2 mn(m,r) 1. (45) 2 T c, s computed by applyng the total probablty theorem A k=a T c, = T c,,k p(δ k ) A (46) k=a p(δ k ) where T c,,k s the average duraton of a collson n whch a staton of AC s nvolved when only the ACs of set Δ k may transmt. Ths s computed as follows: T c,,k = l L T cp(c l,t= l S k ) l L p(c (47),t= l S k ) where p(c,t= l S k ) s the probablty that a slot tme n whch a staton of AC transmts and the statons of set S k may transmt contans a collson of length l. Ths s computed by dstngushng between the case that a staton of AC transmts a frame of sze l [wth probablty p(t = l)] orsmaller[wth probablty p(t <l)],.e., p(c,t=l S k ) =p(t =l) m S k \ j S k \ (1 τ m p(t m >l)) + p(t <l) τ j p(t j =l) T slot,k m S k \{S k,j,j} m S k,j \ m S k \ (1 τ m ) (1 τ m p(t m l)) (1 τ m p(t m >l)). (48) s computed as the sum of probabltes of success, empty, and collson multpled by the average slot-tme duraton n each case,.e., st slot,k = p(s S k,)t s,k + p(e S k,)t e +(1 p(s S k,) p(e S k,)) T c,k (49) where p(e S k,) and p(s S k,) are the probabltes that a k-slot tme n whch the consdered staton does not transmt The condton that the consdered staton does not transmt holds untl the end of the proof. s empty and contans a success, respectvely, and T s,k and T c,k are the average slot-tme duratons of a success and a collson, respectvely. T s,k s computed by applyng the total probablty theorem,.e., T s,k = A j=k p(δ j) m Δ j n m, p(s m Δ j,)t s,m p(s S k,) (50) where n m, = n m δ m (the Kronecker functon δ m accounts for the fact that the consdered staton does not transmt), p(s m Δ j,) s the probablty that gven the set Δ j can transmt but staton dd not transmt, there s a success from AC m,.e., p(s m Δ j,)=τ m (1 τ m ) n m, 1 j Δ k \m (1 τ j ) n j, (51) and p(s S k,) s computed by addng the success probabltes of each AC,.e., p(s S k,)= T c,k where A p(δ j ) j=k s computed smlarly to (50),.e., T c,k = p(c, t = l S k,)= m Δ j n m, p(s m Δ j,)t s,m. (52) A j=k l L T l cp(c, t = l S j,)p(δ j ) A j=k l L p(c, t = l S j,)p(δ j ) j S k \ (53) τ j p(t j = l)p(tx l S k,,j) (54) s the probablty of a collson of sze l n a k-slot, wth p(tx l S k,,j) beng the probablty that at least one staton other than and j transmts a frame of smaller than or equal to l, whch s computed followng (35). Fnally, we compute p(e S k,) by applyng a smlar reasonng to (3),.e., T nter,k p(e S k,)= p(e t k) 1 τ. (55) s computed as follows. If the gven slot tme s empty, whch occurs wth probablty p(e S k,), then T 0. Otherwse, T nter,k nter,k = s, by defnton, equal to Tnter_tx,k. Thus T nter,k =(1 p(e S k,)) T nter_tx,k. (56) The above reles on Tnter_tx,k, whch s the tme between a nonempty tmeslot and the next k-slot. To compute t, we consder the number of j empty slots that follow the transmsson(s) and dstngush two cases: 1) when the number of j empty tmeslots s equal to k and, therefore, the tme untl the next k-slot s composed of exactly k empty slot tmes and 2) when j<kand, therefore, the tme s composed of j empty slot tmes, a nonempty slot where only statons from

16 2526 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 S j can transmt, and an addtonal tme that s, by defnton,. Ths way T nter_tx,k T nter_tx,k = k p(e S j,)kt e j=0 ( k 1 j ) + p(e S l,)(1 p(e S j+1,)) j=0 l=0 (jt e + Tslot_tx,j + Tnter_tx,k ) (57) where Tslot_tx,j s the average duraton of a nonempty slot tme preceded by a nonempty k-slot tme followed by j empty slot tmes, whch s computed as the probablty that such a slot tme contans a collson multpled by the average duraton n ths case, plus the probablty that t contans a success multpled by the correspondng average duraton,.e., T slot,tx,j ( m S = 1 j n m τ m (1 τ m ) n m 1 p S j \m (1 τ ) p) n p 1 m S j (1 τ m ) n m Tc,j m S + j n m τ m (1 τ m ) n m 1 p S j \m (1 τ p) n p 1 m S j (1 τ m ) n m T s,j. (58) Equatons (57) and (58) can be reduced to a frst-order equaton on Tnter_tx,k, from whch we can solate ths term and then derve Tnter,k. By combnng all the above equatons, we obtan the expresson for the average delay gven by the lemma, as well as the computaton of all the terms of ths expresson. The proof follows. Lemma 4: The standard devaton of the delay s gven by R σd 2 j=0 = (1 p(c )) p(c ) j E [ (d,j ) 2] R j=0 (1 p(c (d ) 2. (59) )) p(c ) j Proof: To compute the standard devaton of the delay,.e., σ 2 d, we use the followng statstcal relatonshp between the average and the second-order moment: σ 2 d = E [ (d ) 2] (d ) 2. (60) We already have computed d n (8), and therefore, the remanng challenge s to compute the second order of the average delay,.e., E[(d ) 2 ]. To ths am, we proceed smlarly to (43),.e., E [ R (d ) 2] j=0 = (1 p(c )) p(c ) j E [ (d,j ) 2] R j=0 (1 p(c. (61) )) p(c ) j To compute E[(d,j ) 2 ], we rewrte d,j n (44) as d,j = T s, + jt c, + jt nter_tx,k + d,j bo (62) where d,j bo s the average tme spent n back-off counter decrements for AC n case of j retres,.e., d,j bo = p(bo = n AC, j retx) n (T slot,k + Tnter,k ) ( + + T slot,k + Tnter,k ) }{{} n tmes (63) where p(bo = n AC, j retx) s the probablty that the total number of back-off counter decrements after j retressn.ths s computed through j convolutons of the dfferent unform dstrbutons that the staton may use to compute ts back-off counter,.e., p(bo = n AC, j retx) =U ( 0,CW mn 1 ) ( ) U 0, 2 mn(j,m) CW mn 1. (64) Wth the above, we proceed as follows to compute E[(d,j ) 2 ]: E [ (d,j ) 2] =(d,j ) 2 + σ 2 d,j (65) where σd 2,j s gven by the sum of the varances of the components of (62). Wth our assumpton that slot-tme duratons are ndependent σ 2 d,j = jσ 2 T c, + σ 2 T s, +(j +1)σ 2 T nter_tx,k + σ 2. (66) d,j bo Gven the prevous expressons, the computaton of E[(d ) 2 ] (and, therefore, the analyss of the standard devaton of the delay) s laborous but straghtforward, as t bascally nvolves redong the analyss of the average delay but computng secondorder moments and varances. By combnng all the above equatons, we obtan the expresson for the average delay gven by the lemma, as well as the computaton of all the terms of ths expresson. The proof follows. REFERENCES [1] Amendment to Standard for Informaton Technology. LAN/MAN Specfc Requrements Part 11: Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) specfcatons: Medum Access Control (MAC) Enhancements for Qualty of Servce (QoS), IEEE Std WG, Nov [2] IEEE Standard for Informaton Technology-Telecommuncatons and Informaton Exchange Between Systems-Local and Metropoltan Area Networks-Specfc Requrements Part 11: Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcatons, IEEE Std (Revson of IEEE Std ), 12, [3] S. Mangold, S. Cho, G. Hertz, O. Klen, and B. Walke, Analyss of IEEE e for QoS Support n Wreless LANs, Wreless Commun., vol. 10, no. 6, pp , Dec [4] S. Cho, J. Prado, and S. Shankar, IEEE e contenton-based channel access (EDCF) performance evaluaton, n Proc. IEEE ICC, 2003, pp [5] A. Grlo and M. Nunes, Performance evaluaton of IEEE e, n Proc. PIMRC, Lsboa, Portugal, Sep. 2002, pp [6] D. Gu and J. Zhang, A new measurement-based admsson control method for IEEE wreless local area networks, n Proc. IEEE PIMRC, Sep. 2003, pp [7] A. Banchs and L. Vollero, Throughput analyss and optmal confguraton of e EDCA, Comput. Netw., vol. 50, no. 11, pp , Aug

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In 2007, he was a Vstng Researcher wth the Computer Network Research Group, Unversty of Massachusetts, Amherst, whch was partally supported by the Spansh Mnstry of Educaton under a José Castllejo grant. He has over 20 scentfc papers n peer-revewed nternatonal journals and conferences. Hs current work focuses on performance evaluaton of wreless networks. Dr. Serrano serves as a Techncal Program Commttee member of several nternatonal conferences, ncludng the IEEE Global Telecommuncatons Conference and the IEEE Conference on Computer Communcatons. Albert Banchs (M 04) receved the Telecommuncatons Engneerng and Ph.D. degrees from the Polytechncal Unversty of Catalona, Barcelona, Span, n 1997 and 2002, respectvely. In 1997, he was a Vstng Researcher wth the Internatonal Computer Scence Insttute, Berkeley, CA. In 1998, he was wth Telefonca I+D and, from 1998 to 2003, wth NEC Europe Ltd., Hedelberg, Germany. Snce 2003, he has been wth the Unversty Carlos III of Madrd, Leganés, Span. Snce 2009, he has been a Deputy Drector wth Insttuto Madrleño de Estudos Avanzados (IMDEA) Networks, Leganés. He has authored over 50 publcatons n peer-revewed journals and conferences. He s the holder of four patents (two of them granted). Prof. Banchs has been a Guest Edtor for two dfferent ssues: one specal ssue of IEEE Wreless Communcatons Magazne, and a dfferent specal ssue of Elsever Computer Networks. He has served on the Techncal Program Commttee (TPC) of a number of conferences and workshops, ncludng the IEEE Conference on Computer Communcatons, the IEEE Internatonal Conference on Communcatons, and the IEEE Global Telecommuncatons Conference. He s the TPC Char for European Wreless Hs Ph.D. thess receved the natonal award for Best Thess on Broadband Networks.

18 2528 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 Paul Patras (S 08) receved the Telecommuncatons Engneerng degree n 2006 from the Techncal Unversty of Cluj-Napoca, Cluj-Napoca, Romana, and the M.Sc. degree n telematcs engneerng n 2008 from the Unversty Carlos III of Madrd, Leganés, Span, where he s currently workng toward the Ph.D. degree. Snce 2007, he has been a Research Assstant wth IMDEA Networks, Leganés. Hs current research nterests nclude performance optmzaton n IEEE wreless local area networks, adaptve medum-access control mechansms, qualty-of-servce provsonng n wreless mesh networks, prototype mplementaton, and testbeds. Arturo Azcorra (SM 02) receved the M.Sc. degree n telecommuncatons engneerng and the Ph.D. degree from the Unversdad Poltécnca de Madrd, Madrd, Span, n 1986 and 1989, respectvely, and the MBA degree from the Insttuto de Empresa, Madrd, n He has recently been apponted the Drector General for Technology Transfer and Entrepreneural Development wth the Spansh Mnstry of Scence and Innovaton. As a result, he s on leave from hs double appontment as a Full Professor (wth Char) wth the Telematcs Engneerng Department, Unversty Carlos III of Madrd, Leganés, Span, and as the Drector of IMDEA Networks, Leganés. He founded the not-for-proft nsttute n 2006 and has conducted hs research actvtes there snce ts ncepton. He has publshed over 100 scentfc papers n books, nternatonal magaznes, and conferences. Dr. Azcorra s a member of the Assocaton for Computng Machnery Specal Interest Group on Data Communcaton. He has partcpated n and drected 49 research and technologcal development projects, ncludng the European Strategc Program on Research n Informaton Technology, R&D n Advanced Communcaton for Europe, Advanced Communcatons Technologes and Servces, and Informaton Socety Technologes programs. He has coordnated the Content Dstrbuton Network Research and Emergng Networkng Experments and Technologes European Networks of Excellence. He has served as a Program Commttee Member for numerous nternatonal conferences, ncludng several edtons of the IEEE Conference Protocols for Multmeda Systems, Interactve Dstrbuted Multmeda Systems, Qualty of Future Internet Servces, the Conference on Emergng Networkng Experments and Technologes, and the IEEE Conference on Computer Communcatons.