Modeling and Analysis of Slow CW Decrease for IEEE WLAN

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1 Modeling and Analyi of Slow CW Decreae for IEEE 82. WLAN Qiang Ni, Imad Aad 2, Chadi Barakat, and Thierry Turletti Planete Group 2 Planete Group INRIA Sophia Antipoli INRIA Rhône-Alpe Sophia Antipoli, France Grenoble, France {qni, cbarakat, turletti}@ophia.inria.fr imad.aad@inrialpe.fr Abact The IEEE 82. Medium Acce Conol (MAC) protocol provide a contention-baed diibuted channel acce mechanim for mobile tation to hare the wirele medium, which may inoduce a lot of colliion in cae of overloaded active tation. Slow Contention Window (CW) decreae cheme i a imple and efficient olution for thi problem. In thi paper, we ue an analytical model to compare the low CW decreae cheme to the IEEE 82. MAC protocol. Several parameter are invetigated uch a the number of tation, the initial CW ize, the decreae factor value, the maximum backoff tage and the coexitence with the RequetToSend and ClearToSend (RTS/CTS) mechanim. The reult how that the low CW decreae cheme can efficiently improve the throughput of IEEE 82., and that the throughput gain i higher when the decreae factor i larger. Moreover, the initial CW ize and maximum backoff tage alo affect the performance of low CW decreae cheme. Keyword - IEEE 82.; DCF; low CW decreae cheme; RTS/CTS I. INTRODUCTION In recent year, IEEE 82. wirele LAN (WLAN) [] ha emerged a one of the mot deployed wirele acce technologie all over the world. Thi technology provide people with a ubiquitou environment in office, hopital, campue, factorie, airport and tock market. The IEEE 82. tandard provide both Medium Acce Conol (MAC) layer and the phyical (PHY) layer pecification for WLAN. IEEE 82. MAC ha defined two medium acce coordination function: the contention-baed Diibuted Coordination Function (DCF) and the contention-free baed Point Coordination Function (PCF) []. 82. can operate both in DCF mode and PCF mode. Every 82. tation hould implement DCF mode, which i baed on the Carrier Sene Multiple Acce with Colliion Avoidance (CSMA/CA) protocol []. Unlike DCF, the implementation of PCF i not mandatory in the tandard. In thi paper, we limit our invetigation to the DCF and correponding enhanced cheme. In the DCF cheme, all tation compete for the reource and channel with the ame prioritie. The number of colliion increae with the number of tation. Throughput degradation and high delay are caued by the increaing time needed by contending tation to acce the channel. Although the RequetToSend and ClearToSend (RTS/CTS) cheme i known to provide better performance than baic acce cheme in ome cae [2], it induce a coniderable overhead when packet ize i mall. Recently, IEEE 82. Tak Group e (TGe) ha been working on a new mechanim, the Enhanced Diibuted Coordination Function (EDCF), to enhance the performance of 82. DCF [4]. However, latet reearch work [8, 9] have hown that EDCF only reduce the internal colliion within a tation, and external colliion between tation remain high in ad-hoc network. Thi motivate the reearch on the low Contention Window (CW) decreae cheme [9]. To analyze the performance of 82. DCF, [2] propoe an analytical model for the computation of 82. aturation throughput. Thi model make the following aumption: Ideal channel condition (i.e. no hidden terminal and capture), a fixed number of tation and each mobile tation alway have packet to end. [3] extend thi model further to conider the cae of dynamic number of tation. The active tation are modeled with a Continuou Time Markov Chain Single Server Queue (CTMC-SSQ) proce. [5] extend the model in [2] to conider the frame retanmiion limit, which i pecified in the 82. tandard. [6] analyze the throughput and fairne iue of the DCF function concerning the effect of hidden terminal and capture. [7] ue a p-peritent protocol to tudy the maximum protocol capacity of 82.. The author in [7] claim that thi method give very cloe approximation of the 82. tandard protocol if the average backoff interval i alway the ame. Unlike 82., they propoe to compute the optimized contention window ize that maximize the channel utilization. But thi cheme require the knowledge of the number of active tation, which i difficult to obtain in real implementation. The low CW decreae cheme in [9] i impler than the one in [7], ince it only require multiplying the previou CW by a contant decreae factor to compute the new CW after ucceful anmiion. Given that there are no analytical model to analyze the performance of low CW decreae cheme, we preent in thi paper a Markov chain

2 model that allow thi analyi. Our analytical model i baed on the one propoed in [2], which ha already proven good performance reult. The ret of thi paper i organized a follow. Section II decribe the low CW decreae cheme briefly. Section III derive our analytical model. Section IV how the numerical reult of the model and analyze the performance of the low decreae cheme. Section V conclude the paper. II. SLOW CW DECREASE SCHEME In a diibuted 82. DCF mode, a mobile tation ha no knowledge of the number of other contending terminal. Thu, the MAC layer adapt it CW to the current congetion level by doubling it CW upon each colliion, and by reetting it upon each ucceful anmiion. Doubling the CW aume that each unucceful anmiion indicate a high congetion level. On the conary, when a node ucceed to anmit a packet, it aume the congetion level decreaing and reet it CW ize to it minimal value: CW min. However, when a anmiion ucceed at a given CW, thi doe not correpond to a congetion level decreae, but to a convenient CW value. Therefore the CW value hould be kept the ame a long a the congetion level remain the ame. Normally, congetion level i not likely to drop harply. By reetting the CW to CW min, a node take the rik of experiencing colliion and reanmiion until it reache the high CW value again, wating time and channel bandwidth. Although a pot backoff, i.e. DIFS plu backoff after a ucceful anmiion, i ued in the tandard to help low-tart after each ucceful anmiion [], thi i not enough to avoid colliion. Slow CW decreae cheme provide a olution to thi problem. The main advantage of low CW decreae cheme i more colliion avoidance during congetion, which reult in le colliion and reanmiion, and hence in a better throughput. The diadvantage i keeping high CW value when congetion level harply drop, increaing the overhead and maybe decreaing the throughput. The low CW decreae cheme induce then a adeoff between wating ome backoff time and riking a colliion following a packet anmiion. [9] propoe three different low CW decreae cheme: multiplicative CW decreae cheme, linear CW decreae cheme and adaptive CW decreae cheme. In thi paper, we propoe a Markov model to analyze the performance of the multiplicative low CW decreae cheme and we denote thi cheme a SD cheme. Let δ be the contant low decreae factor in the range of (,). The SD cheme tudied in thi paper i defined a follow: CW new = max (CW min, δ CW old ), after each ucceful anmiion, CW new = 2 CW old, after each unucceful anmiion. III. ANALYTICAL MODEL OF SLOW CW DECREASE (SD) SCHEME Our analyi i divided into two part: Firt, we tudy the behavior of a ingle mobile tation with a SD Markov model, and we compute the tationary probability that the tation anmit a packet in a randomly choen lot time. Thi probability doe not depend on the acce mechanim (with or without RTS/CTS cheme). Second, by tudying the event occurring within a lot time, we expre the channel throughput a a function of with and without RTS/CTS cheme. We get then a ytem of two equation that we olve for the channel throughput by getting rid of. A. Analyi of packet anmiion probability We make the ame aumption a [2]. A fixed number n of contending tation i conidered and the anmiion queue of each tation i alway nonempty. Each packet ha to wait for a random backoff time decrement to zero before being anmitted. The lot time i defined a, and p denote the probability that a packet collide. A lot time i equal to real PHY lot time if no packet are anmitted. If a packet i anmitted, i equal to the buy period until the channel i idle again. We define two tochatic procee to model the protocol behavior, ee Fig.. Firt, b(t) repreent the backoff counter of the time a tation ha to wait before it can anmit. Thi proce ha the range from to the current CW ize. Another tochatic proce (t) i defined a the backoff tage at a different CW level. (t) cale from to m, with m being the maximum CW tage. (-p)/w (-p)/w 2 (-p)/w g (-p)/w g+ (-p)/w m-g,,,2,w -2,W -, g, g+, m-g, m+-g, m+-g, m+-g,2 m,, g, g+, m-g, p/w p/w 2 p/w g p/w g+ p/w m-g p/w m+-g (-p)/w m+-g, W m+-g -2 m+-g, W m+-g - p/w m m, m,2 m,w m -2 m,w m - p/w m Fig. Markov chain model for the SD cheme With thee aumption, the bi-dimenional tochatic proce {(t), b(t)} fulfill the propertie of a homogenou dicrete Markov chain. The Markovian property doe not hold for the proce b(t) alone, which i dependent on the backoff tage hitory. For implicity, we write W i intead of CW i and W intead of CW min. Since the contention window double after each colliion, we can write W i = 2 i W, where i m. The maximum backoff tage m i the value uch that CW max =2 m W. We uppoe that the contant decreae factor δ ha a power of two form δ = /(2 g ), where the contant factor

3 g i a poitive integer with g>. Thi choice of δ limit the number of tate of the Markov chain and implifie the analyi, without impacting the reult. Another reaon for chooing δ a power of two come from implementation requirement. Current IEEE 82. contention window updating algorithm are implemented in hardware, where power of two multiplicative factor can be eaily upported. Thu, the new CW value when a packet i correctly anmitted will be: CW new = max (W, δ W i ) = max(w, 2 i-g W ) = max(w, W i-g ). Conider the anition of the SD cheme between lot time. Fig. explain the behavior of the Markov chain. The only non-null one-tep anition probabilitie are: P {i, k i, k+} =, k [,W i 2], i [,m] P {, k i, } = ( p)/ W, k [,W ], i [, g ] P {i-g, k i, } = ( p)/ W i-g, k [,W i-g ], i [g, m] P {i, k i, } = p/ W i, k [, W i ], i [, m] P {m, k m, } = p/ W m, k [, W m ]. () The firt equation in () account for the fact that the backoff timer ha not yet reached and that it i decremented by at the beginning of each lot time. The econd and third equation are pecific to the SD cheme. The econd equation account for the fact that when δ W i i maller than W, we reet W i to W, and a new backoff i uniformly choen in the range [, W ]. The third equation account for the fact that when δ W i i larger than W, we decreae W i lowly to the new value W i-g and we chooe the new backoff counter randomly in the range [, W i-g ]. The fourth and the fifth equation correpond to the cae where a colliion occur. Let π i.k = lim P{ ( t) = i, b( t) = k}, i [, m], k [, W i ], t be the tationary diibution of the chain. A the Markov Chain i ergodic, thi diibution exit and i unique. Firt, we expre all π i,k a a function of π,, then we ue the normalization equation to olve for π,, and hence for all π i.k. From the Markov chain above, we can ee that the incoming affic to tage i from either tage i+g after a ucceful anmiion, or from tage i- after a colliion, i uniformly diibuted over all poible backoff value at thi tage. Afterward, the counter i decremented by one and finally reache tate (i,). So, the tationary probability π i, i given by: g π, = (-p) j= π i, = p π i-, + (-p) π i+g,, < i (2) π i, = p π i-,, m-g < i < m p p π m-, = ( p) π m, π m, = π m,, i = m. p The firt equation in (2) account for the fact that tage can only be reached from tage j (j ) in the SD cheme, the tage j (j > g) can not directly decreae to tage. The econd equation in (2) ay that when < i g, there are two π j, different input: from the previou tage with colliion probability p and from tage i + g after a ucceful anmiion with probability -p. For i larger than m-g, there will be no input from tage i + g, becaue i + g i bigger than the maximum tage number m. For i = m, we fall into a pecial cae, ince after a colliion the contention window remain at thi tage. Now, according to the Markov chain regularitie, for each k [,W i -], π i, k can be written a: g ( p) π j, i = W k j= i π i, k = p π i, + ( p) π i+ g, < i m g (3) Wi p π < < i, m g i m p ( π m, + π m, ) i = m. The ratio before the parenthei account for the diibution of probabilitie for each tate in a tage. When we move in a tage to the right, the tate probability decreae by /W i, ince we do not get the input of the previou tate in the ame tage. From there, we can obtain the relation between π i,k and π i, : π i,k = [(W i k)/ W i ] π i,. Uing (2), we obtain the term on the right-hand ide of the parenthei in (3). By combining (2) and (3), one can compute all tationary probabilitie a a function of π, and p. In oppoite to [2], obtaining cloed-form expreion doe not eem poible, o we proceed by olving the ytem numerically with Matlab: firt we olve formula in (2) to obtain π i, that are only dependent on π, and p. Then we plug them into (3) to obtain π i,k that are only dependent on π, and p. π, i finally computed by uing the normalization condition: m W i i= k = π =. (4) i, k Now we compute, the probability that a tation anmit in a lot time. Thi probability i imply the um of probabilitie of all (i,) tate, m τ = π i, = f ( p, W, g, m). (5) i= Thi expreion of i a function of p, which i unknown. Let u aume independence of all tation haring the medium, i.e. the probability that a tation encounter a contention i independent of the tatu of the other tation. All tation anmit packet in a lot time with the ame probability. Conider that a tation anmit a packet in a lot time. p i then the probability that at leat one other tation anmit a packet in the ame lot time: p = ( τ) (n-). (6) We obtain therefore a non-linear ytem of two equation (5) and (6), that we can olve for p and. Thi ytem certainly ha a olution, ince the expreion of p a a function of i continuouly increaing with, with p = for = and p =

4 for =. A ufficient condition for thi olution to be unique i that the expreion of a a function of p given in (5) i continuouly decreaing. Our numerical reult in ection IV how that a unique olution for our model alway exit. B. Throughput Denote by S the normalized ytem throughput, which i defined a the fraction of time the channel i ued to anmit payload uccefully. Conider a random lot time, let P be the probability that there i at leat one anmiion in thi lot time, and let P be the probability of one ucceful anmiion given that there i at leat one anmiion. Note that P =-(-τ) n and n nτ ( τ ) P = ( τ ) PP E[P] S = ( P ) σ + P PT + P ( P ) T n c. Hence,, (7) where T i the average time the channel i ened buy becaue of a ucceful anmiion, and T c i the average time the channel i ened buy by each tation during a colliion. We ue in our analyi the value of T and T c computed in [2]. Note that the throughput expreion (7) doe not pecify the acce mechanim employed. To account for whether RTS/CTS cheme i ued or not, we only need to pecify the correponding value T and T c [2]. IV. NUMERICAL ANALYSIS We ue the Matlab tool to olve our model for the throughput of the channel. The 82. WLAN ytem parameter ued in the model are reported in Table. We tudy the performance impact of the SD cheme on 82. throughput for everal ytem parameter, uch a with or without RTS/CTS mode, the number of tation, the CW min value, the maximum backoff tage number m, and the value of SD factor g. Note that g= mean CW new =.5 CW old, which i the lowet decreae cheme we conider in thi paper. Our numerical reult how that in all cae, g= achieve the bet performance in term of throughput. We validate thi reult with n imulation and obtain a channel throughput very cloe to what i predicted by our model. The reult of the imulation are not included in thi paper for lack of pace. TABLE SIMULATION PARAMETERS Packet payload 884 bit MAC header 272 bit PHY header 28 bit ACK 2 bit+phy header RTS 6 bit+phy header CTS 2 bit+phy header Channel bit rate Mbit/ Propagation Delay µ Slot time 5 µ SIFS 28 µ DIFS 28 µ A. Without RTS/CTS mechanim Fig. 2 how the aturation throughput for tandard 82. and for the SD cheme. The figure report ix different value for the number of tation n: 5,, 5, 2, 3 and 5. We clearly ee how the throughput decreae when n increae (more contention) and how the total throughput of the SD cheme i alway higher than that of the baic 82. acce cheme, epecially for the mallet value of g (g=). For example, when n =5, the throughput gain of the SD cheme over tandard 82. i about 28% for g =, about 3% for g=2, about 6% for g=3, and about % for g=5. Saturation throughput (Mbit/) Compariion between DCF and SD cheme, CWmin =8, m =6 g =, SD Fig. 2 Saturation throughput for SD and 82. Fig. 3 decribe the impact of the initial CW ize (W ) on the SD cheme for different value of g. We et the maximum number of backoff tage to 6, i.e. W m =2 6 W. The initial CW ize ongly affect the SD gain. For example, when n =5, a high throughput gain (28%) i obtained with a mall initial CW (W =8), and the gain decreae to 4% with a large initial CW ize (W =28). A large initial CW reduce the number of colliion, which make the SD cheme le effective than the cae when a mall initial CW i ued and the number of colliion i high. Throughput Gain (%) The impact of CWmin on SD, n =5, m = Initial ize of the backoff window (CWmin) g = g = 2 g = 3 g = 4 g = 5 Fig. 3 Throughput gain v. initial CW ize To better undertand the above reult, we tudy the following two meaure: i). The average number of idle lot time per ucceful anmiion, which can be expreed a: P ) /( P P ) ; ( ii). The average channel time wated in colliion per ucceful anmiion, which i expreed a: T c ( ). P Fig. 4 and Fig. 5 how the idle time and the colliion time veru the number of tation, for the SD cheme with 5 different value of g and for the 82. cheme when W =8. We oberve that the SD cheme lightly increae the idle

5 time but ignificantly decreae the colliion probability. For example, when n=5 and g=, the idle channel time for the SD cheme i.6 lot time longer than 82., and the time wated in colliion for the SD cheme i about 38 lot time horter than 82.. A mentioned in Section II, the SD cheme involve a adeoff between wating ome backoff time and riking a colliion followed by the reanmiion. Idle channel time per packet TX (lot time) Idle Time, CWmin =8, m =6 g =, SD Fig. 4 Idle lot time per packet anmiion (W =8) Channel time wated in colliion (lot time) g =, SD 82. Colliion Time, CWmin =8, m = Fig. 5 Channel time wated in colliion (W =8) B. With RTS/CTS mechanim Fig. 6 compare the SD throughput gain obtained with and without the ue of the RTS/CTS mechanim. The gain without RTS/CTS i much higher than when RTS/CTS i ued. Thi mean that the SD cheme i more ueful when the RTS/CTS i not ued. The reaon i that RTS/CTS reduce the colliion time to a mall value, which make the ue of SD le effective ince the colliion time i already mall. Throughput Gain (%) The impact of RTS/CTS on SD, CWmin=8, m =6 g =, without RTS/CTS g =, with RTS/CTS V. CONCLUSION Thi paper preent an analytical model for the low CW decreae cheme, which ha been propoed to improve the performance of the baic IEEE 82. MAC. Our model take into account the different parameter that affect the channel throughput, uch a the number of mobile tation, the initial CW ize, the decreae factor value, the maximum number of backoff tage and the ue of RTS/CTS. The numerical reult we obtained how that the Slow CW Decreae (SD) cheme improve the throughput of IEEE 82. in all cae, epecially when the number of tation i large. Another finding i that the SD cheme ignificantly increae the throughput of baic CSMA/CA mode when uing a large decreae factor (e.g. δ=.5), while it i not very helpful when the RTS/CTS mode i ued ince the colliion time i mall with RTS/CTS. In addition, the initial CW ize and the maximum backoff tage alo affect the performance of the SD cheme and the gain in throughput. Future work will include the modeling analyi of the SD cheme with the effect of hidden terminal, and the impact of the SD cheme on fairne iue. ACKNOWLEDGMENT The author would like to thank Romain Zanolla and Marco Schmitt for their earlier work on Matlab code. REFERENCES [] IEEE Std , Part :Wirele LAN Medium Acce Conol (MAC) and Phyical Layer (PHY) pecification, 999 [2] G. Bianchi. Performance analyi of the IEEE 82. diibuted coordination function. IEEE Journal on Selected Area In Communication, Vol. 8. No. 3, March 2 [3] C. H. Foh and M. Zukerman. Performance analyi of the IEEE 82. mac protocol. Proceeding of the EW 22 Conference, Florence, Italy, pp. 84-9, February 22 [4] IEEE 82. WG, Draft Supplement to Part : Wirele Medium Acce Conol (MAC) and Phyical Layer (PHY) pecification: Medium Acce Conol (MAC) Enhancement for Quality of Service (QoS), IEEE 82.e/Draft 4., Februray 23 [5] H. Wu, Y. Peng, K. Long, S. Cheng and J. Ma. Performance of reliable anport protocol over IEEE 82. wirele LAN: analyi and enhancement. IEEE Infocom 2, New York, June 22 [6] H.S. Chhaya and S. Gupta. Performance modeling of the aynchronou data anfer method of IEEE 82. MAC protocol. Wirele Network, No. 3, pp , 997 [7] F. Cali, M. Conti, and E. Gregori. Dynamic tuning of the IEEE 82. protocol to achieve a theoretical throughput limit. IEEE/ACM Tranaction on Networking. Vol. 8, No. 6, December 2 [8] L. Romdhani, Q. Ni and T. Turletti, Adaptive EDCF: enhanced ervice differentiation for IEEE 82. wirele ad hoc network. IEEE WCNC 3, New Orlean, Louiiana, March 6-2, 23 [9] I. Aad, Q. Ni, C. Catelluccia, and T. Turletti. Enhancing IEEE 82. performance with low CW decreae. IEEE 82.e working group document 82.-2/674r, November, Fig. 6 SD throughput gain with and without RTS/CTS