Effect of Contention Window on the Performance of IEEE WLANs

Transcription

1 Effect of Contention Window on the Pefomance of IEEE WLANs Yunli Chen and Dhama P. Agawal Cente fo Distibuted and Mobile Computing, Depatment of ECECS Univesity of Cincinnati, OH {ychen, Abstact In the IEEE 82.11, an exponential backoff has been adopted, which means wheneve a collision occus, the contention window (CW) of the station is doubled until it eaches the maximum value. The pupose of inceasing CW is to educe the collision pobability by distibuting the taffic into a lage time space. In this pape, we use a fixed contention window (FCW) scheme and then evaluate the pefomance of this scheme. Based on ou analysis, we detemine an optimal contention window (OCW). Futhemoe, we apply the OCW scheme to 82.11e EDCF. The esults show that the OCW scheme not only can effectively enhance the pefomance fo high pioity packets, but also can impove the oveall system pefomance. I. INTRODUCTION The IEEE standad defines a detailed medium access contol (MAC) and physical laye (PHY) specification fo wieless local aea netwoks (WLANs) [1]. WLANs ae gowing in populaity because of the convenience offeed in tems of suppoting mobility while poviding flexibility. In the IEEE MAC laye potocol, the basic access method is the distibuted coodination function (DCF) which is based on the mechanism of caie sense multiple access with collision avoidance (CSMA/CA). The standad also defines an optional point coodination function (PCF), which is a centalized MAC potocol suppoting collision fee and time bounded sevices. In this pape, we limit ou inteest to DCF. The DCF has two schemes fo packet tansmission. The basic scheme is a two-way handshaking technique. In this scheme, if a station has a packet to tansmit, it waits fo a DIFS idle duation of the medium and then tansmits its packet. When the packet is eceived This wok has been suppoted by Ohio Boad of Regents Doctoal Enhancement Funds and National Science Foundation unde Gant No. CCR successfully, the destination station sends a positive acknowledgement (ACK) to the sending station afte a shot intefame space (SIFS). The second scheme is based on a fou-way handshaking that avoids the "hidden teminals" poblem [2]. In this scheme, wheneve a packet is to be tansmitted, the tansmitting station fist sends out a shot equest-to-send (RTS) packet containing infomation on the length of the packet. If the eceiving station heas the RTS, it esponds with a shot clea-to-send (CTS) packet. Afte this exchange, the tansmitting station sends its packet. When the packet is eceived successfully, the eceiving station tansmits an ACK packet. This backand-foth exchange is necessay to avoid the "hidden teminals" poblem. In this pape, we assume that each station can hea each othe so that thee is no hidden teminal poblem in the system and we need only focus on the basic CSMA/CA. Souce Destination Othe DIFS Data SIFS ACK Defe access DIFS Fig. 1: Basic CSMA/CA CW Backoff afte defe Figue 1 illustates how basic CSMA/CA woks. CSMA/CA potocol woks on a "listen befoe talk" scheme. To tansmit a packet, a station must sense the medium and must ensue that the medium is idle fo the specified DCF intefame space (DIFS) duation befoe tansmitting. If a station having a packet to tansmit initially senses the medium to be busy; then the station waits until the medium becomes idle fo DIFS peiod, and then chooses a andom "backoff counte" which detemines the amount of time the station must wait until it is allowed to tansmit its

2 packet. Duing the peiod in which the medium is idle, the tansmitting station deceases its backoff counte. (When the medium becomes busy, its backoff counte is fozen. It can decease its backoff counte again only afte the medium is idle fo DIFS). This pocess is epeated until the backoff counte eaches to zeo and the station is allowed to tansmit. The idle peiod afte a DIFS peiod is efeed to as CW. The IEEE MAC laye potocol adopts exponential backoff. CW is initially assigned the minimum contention window size CW min. Then, the CW is doubled each time the station expeiences a collision until the CW eaches to CW max which is the maximum contention window size. When the CW is inceased to CW max, it emains the same even if thee ae moe collisions. Afte evey successful tansmission, CW is eset to the initial value CW min. A packet will be discaded if it cannot be successfully tansmitted afte it is etansmitted fo a specific ety times as defined in [1]. Recently, the concept of wieless netwoking has become immensely popula and thee is an inceased inteest in the tansmission of integated data and voice. Multimedia sevices (e.g., video, voice, audio, and data) ae gowing apidly in WLANs. Fo diffeent types of applications, thee ae diffeent equiements fo the quality of sevice (QoS). Fo example, eal-time applications such as voice ae delay sensitive. Howeve, the delay is not citical fo non eal-time applications such as ftp and some delays can be toleated [3]. The IEEE DCF can only povide best-effot sevice and cannot guaantee QoS. How to guaantee the QoS equiement has gained moe and moe attentions. IEEE 82.11e woking goup is engaged in such wok to enhance the MAC pefomance to suppot the integated sevice [4]. Till now, this goup poposed a daft of IEEE 82.11e, in which enhanced distibuted coodination function (EDCF) is included. The basic idea is to intoduce Taffic Categoies (TC) and povide diffeent pioities to diffeent TCs. In IEEE 82.11e EDCF, a new CW fo each TC is deived by newcw[tc] >= oldcw[tc]*2. IEEE 82.11e is simila to IEEE in that CW cannot exceed the CW max. The pefomance of DCF and EDCF has been widely investigated by both simulations and analytical models [5-18]. But all these papes used the exponential backoff. In [19], we discussed fixed contention window (FCW) scheme and intoduced an optimal contention window (OCW) scheme. The esults we have in [19] ae appoximate. A ecent wok [2] also focuses on the FCW and OCW, but it only consides satuation taffic and also gives an appoximate esult. Futhemoe, it employs a vey complicated Makov-chain to compute the thoughput which is not necessay because of the fixed contention window and the satuation taffic. In this pape, we use a much simple method to evaluate the pefomance of FCW scheme given the satuation taffic. Based on analytical equations, we get the OCW which can povide a much bette pefomance than exponential backoff. Moeove, we extend the OCW scheme to non-satuation taffic system and it is shown that OCW scheme still woks bette in this kind of system. We futhe apply the OCW scheme to 82.11e EDCF and the esults show an impovement in the pefomance ove exponential backoff. In the analysis of EDCF, we divide the taffic into two categoies: eal-time packets and non eal-time packets. The emainde of the pape is oganized as follows: In Section II, the pefomance of FCW scheme is evaluated and OCW is deived fom the equations. We investigate the pefomance of OCW fo 82.11e ECDF in Section III. In Section IV, we give the numeical esults and finally, we conclude the pape in Section V. II. FIXED CONTENTION WINDOW In this Section, we fist evaluate the pefomance of FCW scheme, and then we can obtain the OCW. In ou analysis, we use the fixed contention window W instead of the exponentially inceased contention window, which means that CW will emain the same when a packet expeiences a collision. We will show that by optimizing the CW, we can impove the pefomance ove the exponential backoff scheme. We assume that thee ae N stations in the system contending fo one shaed channel and each packet has a fixed length. We also assume that each station always has a packet available fo tansmission and no captue is pemitted which means that a station must wait a andom backoff time between two consecutive tansmissions. We define the delay D as the time inteval beginning fom a packet is eady to tansmit till it is eceived successfully. We denote the thoughput by S, which is defined as the faction of channel time occupied by valid tansmission. Because each station always has a packet available fo tansmission and no captue is pemitted, each packet will expeience at least one backoff. We assume that each packet collides with constant and independent pobability p. It is intuitive that this assumption leads 442

3 to moe accuate esults as long as W and N get lage [7]. To simplify the analysis, we assume that etansmission of a packet is attempted afte a collision has occued until it is successfully tansmitted, i.e., no packet is discaded. Since the contention window is W, the escheduling delay of a packet is unifomly distibuted with a mean W/2 slots; this in effect is identical to consideing that each station senses the channel in one slot with a pobability 2/W. We denote the pobability 2/W by τ. Then, a station tansmits its packet in a andomly chosen slot time with the pobability τ, and the collision pobability p is the pobability that at least one of the emaining N-1 stations also tansmits its packet duing this andomly chosen slot time (i.e., at least one of the othe stations also chooses this slot time to tansmit). This yields to p = 1 (1 τ) N-1. (1) Fo each packet, the aveage backoff counte is W/2. Accoding to [3], the aveage numbe of tansmissions befoe the backoff counte deceases to is p W/2. A tansmission is successful if thee is only one station tansmitting. Othewise, the tansmission collides with othe stations' tansmission. Let T p be the length of the packet tansmission time, T slot be the length of one slot (which is also the popagation delay), T DIFS be the length of DIFS, T SIFS be the length of SIFS, and T ACK be the length of ACK. In the analysis, the time is nomalized by T p. That is, the packet tansmission time is equal to 1, which is composed of 1/T slot slots. Accoding to basic CSMA/CA, the successful tansmission peiod (denoted by T) includes a DIFS delay, the packet tansmission time T p, a SIFS delay T SIFS, and the ACK tansmission time T ACK. In othe wods, the successful tansmission peiod has T slots. In the basic CSMA/CA, the collision occus in the packet tansmission. Then the sende will not eceive the ACK message afte a SIFS delay plus a popagation delay. Thus, the collision peiod (denoted by C) includes a DIFS delay, the packet tansmission time T p, a SIFS delay, and a popagation delay T slot. Theefoe, a packet waits fo p W/2 tansmissions befoe its backoff counte deceases to and the aveage tansmission peiod is p C+(1-p) T. A packet will ty 1/(1-p) times befoe it is successfully tansmitted. Thus, the aveage delay D fo a packet is given by W p 2 D = W T 2 slot [ p C + (1 p ) T ] T slot + [ p C + (1 p ) T ] T + slot 1. 1 p (2) Usually the length of ACK message is much shote than the length of the packet. Then, the collision peiod C is almost the same as the successful tansmission peiod T. Substituting p with (1) and C with T, we can get the following aveage delay afte some simplifications D 1 + (1 + τ ) T T (1 τ ) N 1 τ (1 τ ) = N 1 T slot, (3) whee τ is equal to 2/W and T is equal to (T DIFS + T p + T SIFS + T ACK ). Note that if T ACK is not vey shot as compaed to T p, we use (2) to compute D instead of (3). Since CSMA/CA is a andom access potocol, and each station is identical with each othe, the thoughput S is given as S N T D p =. (4) To impove the pefomance, we can minimize the aveage delay D by using an optimal CW (OCW) given N and T. We get the OCW by tying diffeent values of τ (=2/W) fo given N and T, and we use the W which makes the delay smallest as the OCW. Note that the aveage delay D will decease when W inceases fom 16, and afte it eaches the minimum value D will incease when W continues to incease. To get the OCW, we use an algoithm simila to the binay seach. The pseudo code is given in Algoithm 1. We obseved that in ou calculation, the delay changes just a little bit aound the OCW. Fo example, given T=19, C=14, T slot =.1 and N=2, we have D=25.9 if W=331, and D=25.9 if W=3. We just simply use 331 as the optimal contention window OCW (we pick the lage value as OCW when thee ae moe than one CW having the minimum delay because a lage CW is expected to educe collisions). The OCW can be pecomputed and stoed at each station. 443

4 Algoithm 1 δ=.1; W min =16; W max =124; W 1 =Wmin; W 5 =W max ; W 3 =(W 1 +W 5 )/2; W 2 =(W 1 +W 3 )/2; W 4 =(W 3 +W 5 )/2; W =W 1 ; W 6 =W 5 ; Compute delay D 1, D 2, D 3, D 4 and D 5 with W 1, W 2, W 3, W 4 and W 5 espectively; D =D 1 ; D 6 =D 5 ; Let D i =min{d 1, D 2, D 3, D 4, D 5 }; i=1,2,3,4,5 While D i -D i-1 > δ && D i -D i+1 > δ { W 1 =W i-1 ; W 5 =W i+1 ; W 3 =(W 1 +W 5 )/2; W 2 =(W 1 +W 3 )/2; W 4 =(W 3 +W 5 )/2; W =W 1 ; W 6 =W 5 ; Compute delay D 1, D 2, D 3, D 4 and D 5 with W 1, W 2, W 3, W 4 and W 5 espectively; D =D 1 ; D 6 =D 5 ; Let D i =min{d 1, D 2, D 3, D 4, D 5 }; } etun (W=W i+1 ); i=1,2,3,4,5 III. OPTIMAL CONTENTION WINDOW FOR 82.11E EDCF In 82.11e, sevice diffeentiation is implemented by classifying the taffic into taffic categoies (TC). Each TC has its own abitation intefame space (AIFS) and the minimum contention window. AIFS is at least DIFS and each TC can tansmit its packet o decease its backoff counte at least afte it senses the channel idle fo AIFS. Shote AIFS implies a highe pioity to access the channel. CW is used to detemine the backoff counte, so smalle CW means a highe pioity. In this pape, we only focus on CW to povide pioity e is simila to as they both adopt exponential backoff scheme. In ou discussion, we classify the taffic into two categoies: eal-time packets and non eal-time packets. We assume that thee ae N stations in the system and each station always has a packet eady to tansmit. We also assume that the atio of eal-time packets at each station is R. Fom Section II, we can get the OCW when thee ae N stations in the system. Then we let eal-time packets use R OCW as the contention window and non eal-time packets use OCW as the contention window. Since each packet collides with othe packets with the same pobability (it will be moe accuate if the OCW is lage enough), and a packet will initiate a new backoff wheneve a collision occus, the numbe of backoffs fo eal-time packets is the same as that fo non eal-time packets [3]. Thus, the contention window fo eal-time packets is always R of that fo non eal-time packets, and then the aveage delay fo eal-time packets is R of that fo non eal-time packets. Let D is the aveage delay fo eal-time packets, and D n is the aveage delay fo non eal-time packets, we have D =R D n. Since we apply the OCW (Note that OCW is also a FCW scheme) to the 82.11e, the aveage delay D between the eal-time packets and non eal-time packets can still be calculated by (2). Although a smalle contention window fo eal-time packets will cause moe collisions to the system, it will contibute a much shote delay fo the eal-time packets so that the aveage delay fo the whole system still emains the same. Ou simulation also validates this expectation. Theefoe, we have and D D n = R 2 R D + (1 R, ) (5) = D, (6) 2 R + (1 R ) whee D is given by (2). IV. NUMERICAL RESULTS This Section gives all the numeical esults. Since the thoughput is closely elated to the delay, we only focus on the delay in the following discussions. The paametes used fo analysis and simulations ae given in Table 1. Figue 2 compaes the pefomance between the optimal contention window scheme and the exponential contention window scheme. The esults show that the optimal contention window scheme geatly outpefoms the exponential contention window scheme. To validate (2), we fist get the optimal contention windows analytically accoding to the numbe of stations N. Then, we get the analytical delay. We un the simulation with the paametes of N and OCW. Figue 3 gives the analytical and simulation esults of optimal contention window. It can be seen that the esults ae matched vey well. 444

5 TABLE I. SYSTEM PARAMETERS Packet length 1 SLOT.1 SIFS.1 DIFS.3 AIFS.3 ACK.5 CW min 32 CW max 124 R.5 Although we only conside the satuation taffic in the analysis, whee each station always has a packet available to tansmit, we can easily expand it to nonsatuation taffic. Suppose that packets aive at each station with Poisson pocess. As in [19], we assume that the time is slotted with a slot size T slot. In this system, each station can be in one of two states: backlogged o thinking. In the thinking state, a station geneates a new packet in a slot with pobability g. A station is said to be backlogged if its packet eithe had a channel collision o has been blocked because of a busy channel. A backlogged station emains in that state until it completes successful tansmission of the packet, at which time it switches to the thinking state. If we assume that the total taffic load G is the Poisson pocess and g denote a packet aival ate duing a slot, then we have Mg=αG [19]. Due to the chaacteistics of CSMA/CA, hee G only eflects the total aive ate and it does not eflect the numbe of backlogged stations in the system. Fo example, when G is equal to o geate than 1, then the total aive ate is G, but thee will be moe than G stations having packets to tansmit. The eason is that CSMA/CA cannot guaantee a packet to be tansmitted immediately afte it is geneated. Thus, when G is geate than 1, the numbe of backlogged stations becomes lage so that we can appoximately conside the system as a satuation system and just apply the OCW to this case. Actually the system could be in the satuation state when G is lage enough. Ou simulation shows that almost all the stations will be backlogged if thee ae 15 stations, W is equal to 2, and G is lage than 3. When G is less than 1, the numbe of backlogged stations will not be lage enough, and then the pefomance will not be optimal if we still use OCW scheme by consideing the system as a satuation system fo this case. The simulation validates this fact but the esults show that even we apply the OCW to the system in which G is less than 1, the pefomance just degades a little bit as compaed to exponential contention window scheme. Figues 4 and 5 give details of the esults. In the simulation, we conside the system as a satuation system no matte what value the G is. As we can see, the OCW scheme woks bette when G is geate than 1, but woks wose than when G is less than 1 because we still conside the system as a satuation system fo this case. If we use the exponential contention window scheme when G is less than 1 and the OCW scheme when G is equal to o geate than 1, we can take advantage of both the OCW scheme and the scheme, and then we can obtain a bette esult. Note that we do not conside the queuing model and only assume one buffe at each station. The pefomance of OCW will get bette if we use a queue at each station. This is because it is moe possible fo the system to be in the satuation state when a queue is used. To apply the OCW scheme to the 82.11e EDCF, we let non eal-time packets use OCW as the contention window, and eal-time packets use R OCW as the contention window (we efe this optimal scheme as optimal-1). It is intuitive that high pioity packets with a smalle CW have a smalle backoff counte, and theefoe high pioity packets have a shote delay. In the simulation, we tied seveal sets of CW fo both eal-time and non eal-time packets. Hee we only give anothe pai of CW: we let non eal-time packets use OCW as the contention window, and ealtime packets use (R OCW)/2 as the contention window (we efe this optimal scheme as optimal-2). Thus, as we discussed in Section III, the CW fo ealtime packets is always R /2 of that fo non eal-time packets at each backoff so that the delay fo eal-time packets is always R /2 of that fo non eal-time packets. Since the smalle CW fo eal-time packets would cause moe collisions to the system, we can expect a wose aveage delay pefomance (among eal-time packets and non eal-time packets) fo optimal-2 scheme. Howeve, smalle CW can contibute a much shote delay fo eal-time packets. Theefoe, the aveage delay of optimal-2 should only slightly degade as compaed to optimal-1. The esults given in Figue 6 validate this expectation. To compae the pefomance between the EDCF with the OCW and 82.11e EDCF, we simulate the 82.11e by setting the minimum contention window of non eal-time packets be CW min and the minimum contention window of eal-time packets be R CW min. The 82.11e standad adopts exponential contention window scheme. Figue 7 compaes the pefomance of eal-time packets among diffeent schemes. We can see that the pefomance of optimal-2 is the best as to eal-time packets. Figue 8 shows the pefomance of non eal-

6 time packets. It can be seen that optimal-1 has the best pefomance fo non eal-time packets and at the same time dastically impove the pefomance of eal-time packets as compaed to the 82.11e. Fom the esults given in Figues 6, 7, and 8, we can conclude that ou OCW scheme woks vey well in 82.11e EDCF. It not only can impove the pefomance fo eal-time packets, but also can impove the oveall pefomance (i.e., the aveage delay). Futhemoe, we can adjust the contention window fo eal-time packets to get the desied pefomance accoding to the OCW fo non eal-time packets and at the same time impove the oveall pefomance. We need to point out that we cannot use an extemely small CW fo eal-time packets since the OCW scheme is a FCW and it cannot distibute the taffic sepaately enough if the CW is too small so that it can degade the pefomance. Fo example, when the numbe of eal-time packets is 1, we cannot use 2 as the CW fo eal-time packets. V. CONCLUSIONS In this pape, we have investigated the effect of CW on the pefomance of the IEEE MAC potocol. We used the fixed CW instead of the exponential inceased CW. Fist we analyzed the pefomance of the fixed CW scheme. Then based on the analysis, the optimal contention window OCW is deived. We cannot pove that the optimal CW in this pape is the optimal among all the CW schemes. But it definitely is the optimal fixed contention window scheme as discussed in Section III and the esults have shown that the poposed OCW scheme woks much bette than the exponential CW scheme. Futhemoe, we applied the OCW scheme to the 82.11e EDCF. The EDCF with OCW not only can impove the pefomance of eal-time packets, but also can impove the oveall pefomance as compaed to 82.11e EDCF. It is inteesting to note that the desied pefomance of eal-time packets can be easily obtained by adjusting the CW of eal-time packets accoding to the OCW of non eal-time packets. REFERENCES [1] IEEE Standad fo Wieless LAN Medium Access Contol (MAC) and Physical Laye (PHY) Specification, P82.11, Novembe [2] D. P. Agawal and Q-A Zeng. Intoduction to Wieless and Mobile Systems. Books/Cole Publishing, ISBN No , 438 pages, 23. [3] Y. Chen, Q-A Zeng, and D. P. Agawal, "Pefomance Analysis of IEEE 82.11e Enhanced Distibuted Coodination Function," Poceedings of IEEE Intenational Confeence on Netwoking, August 23. [4] M. Benveniste, G. Chesson, M. Hoeben, A. Singla, H. Teunissen, and M. Wentink, EDCF poposed daft text, IEEE woking document /1311, Mach 21. [5] H. S. Chhaya and S. Gupta. "Pefomance of Asynchonous Data Tansfe Methods of IEEE MAC Potocol," IEEE Pesonal Communications, Vol. 3 No. 5, pp. 8-15, [6] G. Bianchi, L. Fatta and M. Olivei. "Pefomance Evaluation and Enhancement of the CSMA/CA MAC Potocol fo Wieless LANs," Poceedings of PIMRC'96, Vol. 2, pp , [7] G. Bianchi. "Pefomance Analysis of the IEEE Distibuted Coodination Function," IEEE Jounal on Selected Aeas in Communications, Vol. 18, pp , 2. [8] Y. C. Tay and K. C. Chua. "A Capacity Analysis fo the IEEE MAC Potocol," ACM/Baltze Wieless Netwoks, Vol. 7, pp , 21. [9] H. Wu, Y. Peng, K. Long, S. Cheng and J. Ma. "Pefomance of Reliable Tanspot Potocol ove IEEE Wieless LAN: Analysis and Enhancement," Poceedings of INFOCOM 22, pp , Ma. 22. [1] M. Bay, A. T. Campbell, and A. Vees, "Distibuted Contol Algoithms fo Sevice Diffeentiation in Wieless Packet Netwoks," Poceedings of the IEEE INFOCOM 21, Anchoage, Alaska, pp , Apil 21. [11] J. Deng and R. S. Chang, "A Pioity Scheme fo IEEE DCF Access Method," IEICE Tansactions on Communications, Vol. E82-B, No.1 Januay [12] J. L. Sobinho, and A. S. Kishnakuma, "Real-Time Taffic ove the IEEE Medium Access Contol Laye," Bell Labs Technical Jounal, pp , Autumn [13] S. Mangold, S. Chio, P. May, O. Klein, G. Hietz, and L. Stibo, "IEEE 82.11e Wieless LAN fo Quality of Sevice," Poceedings of Euopean Wieless, Febuay 22. [14] Q. Qiang, L. Jacob, R. R. Pillai, and B. Pabhakaan, "MAC Potocol Enhancements fo QoS Guaantee and Fainess ove the IEEE Wieless LANs," Poceedings of Intenational Confeence on Compute Communications and Netwoks, Octobe 22. [15] S. Choi, J. D. Pado, S. Shanka, and S. Mangold, "IEEE 82.11e Contention-Based Channel Access (EDCF) Pefomance Evaluation," Poceedings of IEEE Intenational Confeence on Communications, May 23. [16] Y. Xiao, "Enhanced DCF of IEEE 82.11e to Suppot QoS," Poceedings of IEEE Wieless Communications and Netwoking Confeence, Mach,

7 [17] L. Romdhani, Q. Ni, and T. Tuletti, "Adaptive EDCF: Enhanced Sevice Diffeentiaion fo IEEE Wieless Ad-Hoc Netwoks," Poceedings of IEEE Wieless Communications and Netwoking Confeence, Mach, 23. [18] P. Gag, R. Doshi, R. Geene, M. Bake, M. Malek, and X. Cheng, "Using IEEE 82.11e MAC fo QoS ove Wieless," Poceedings of IEEE Intenational Pefomance, Computing, and Communications Confeence, Apil 23. [19] Y. Chen, Q-A Zeng and D. P. Agawal. "Pefomance Analysis and Enhancement of IEEE MAC Potocol," Poceedings of IEEE Intenational Confeence on Telecommunications, 23. [2] D. Qiao, and K. Shin, "UMAV: A Simple Ehancement to the IEEE DCF," Poceedings of the 36 th Hawaii Intenational Confeence on System Sciences (HICSS-36), Januay Optimal Offeed Load (G) Figue 4: Pefomance of optimal contention window fo non-satuation system with N= Numbe of nodes (N) Figue 2: Pefomance of optimal contention window Optimal Offeed Load (G) Figue 5: Pefomance of optimal contention window fo non-satuation system with N=5 Optimal Numbe of Nodes (N) Analytical Simulat ion Numbe of nodes (N) 82.11e optimal-1 optimal-2 Figue 3: Analytical VS simulation esults of optimal contention window Figue 6: Aveage delay 447

8 Numbe of nodes (N) Figue 7: Delay fo eal-time packets 82.11e optimal-1 optimal Numbe of nodes (N) Figue 8: Delay fo non eal-time packets 82.11e optimal-1 optimal-2 448