802.11e EDCA Protocol Parameterization: A Modeling and ...

802.11e EDCA Protocol Parameterization: A Modeling and Optimization StudyIoannis KoukoutsidisFORTH-ICSP.O. Box 1385, 71110 Heraklion, Greecejkoukou@ics.forth.grVasilios A. SirisFORTH-ICS/University of CreteP.O. Box 1385, 71110 Heraklion, Greecevsiris@ics.forth.grAbstractThe IEEE 802.11e MAC protocol specifies an enhanceddistributed channel access (EDCA) mechanism with adjustableprotocol parameters, providing differentiated accessto wireless stations. The EDCA parameters are: CW minand CW max (minimum and maximum contention window),AIFS (arbitration interframe space), and TXOP (transmitopportunity). In this paper, we study the joint setting ofthese parameters in order to maximize capacity and optimizeperformance under QoS constraints. We first revisitthe analytical modeling in saturation and non-saturationconditions and provide more detailed approximations of themean channel access delay and throughput. Then, consideringtwo classes of wireless stations with higher andlower QoS demands, and optimizing with respect to averagemeasures and constraints, we provide Pareto optimal pairsfor the number of supported stations from the two classesfor different parameter set configurations and representativeload values. Further, we examine optimal parameterselection for a class of elastic traffic, in the presence of adelay-sensitive class whose parameters are fixed. Our findingsshow that drastic service differentiation can underminecapacity of a WLAN. They also demonstrate the optimalityof jointly setting high values for TXOP and AIFS in orderto maximize the throughput of the elastic traffic class whileguaranteeing delay of the delay-sensitive class. We also revealdifferent optimal settings for CW min for different loadconditions. We summarize our findings as guidelines for thesetting of 802.11e parameters in a scenario with data andreal-time service classes.1. IntroductionThe IEEE 802.11 series gives protocol specifications forthe interconnection of telecommunications equipment in aWLAN, using a CSMA/CA medium sharing mechanism[4]. In a heterogeneous environment with multiple trafficclasses having different service requirements, it is appropriateto provide service differentiation through the channelaccess mechanism. With this intent, in the IEEE 802.11eEDCA mechanism finalized in [5] a number of protocol parameterscan be set differently for each class of wirelessstations.For a given class i, adjustable EDCA parameters are: 1• CW min,i , CW max,i : The minimum and maximumcontention windows. Before each transmission attemptand in order to reduce the probability of a collision,a station enters a “backoff stage”, which consists ofwaiting a random number of time slots, wherein themedium is sensed idle. This number is initially selecteduniformly in a minimum “contention window”interval [0,CW min,i − 1]. In the event of a collision,a new backoff stage is entered and a larger contentionwindow is selected. The protocol suggestsdoubling the window until a maximum stage m i , forwhich 2 mi · CW min,i = CW max,i . The numberof backoff slots is in general chosen in the interval[0,2 (k∧mi) · CW min,i − 1], where k = 0...m i is thecurrent backoff stage.• AIFS i : The arbitration inter-frame space. It is theamount of time a station must sense the channel idlebefore decrementing its backoff counter, or attemptinga transmission. Assigning different values of AIFS todifferent classes can distribute contention for the channeland prioritize access. For two stations of classes kand j, with class k having a lower priority, the value(AIFS k − AIFS j ), yielding the AIFS separation inslots, is of practical significance.• TXOP i : The transmit opportunity. It is used topermit consecutive frame transmissions by a station.It is defined as the maximum interval of time duringwhich a station has the right to initiate a sequenceof frame transmissions uninterrupted by others, afterit has gained access to the channel through the contentionmechanism. It is a basic building block of the1 These parameters, when used as mathematical variables in this paper,are italicised.

This approximation becomes more accurate as the numberof stations increases. Practically, it works well even fora number of stations as low as 2 (see [1]).Since the collision probability is dependent on the attemptrate and vice-versa, appropriate expressions can constructa system of equations to solve for these values.Denote the collision and attempt probabilities of a stationin class i (i = 1,...,K) by c i , p i respectively. From astochastic analysis (either a Markovian analysis as in [1], ora renewal theory analysis as in [7]), the attempt rate can beexpressed as a function of the collision probability and thebackoff parameters CW min,i , m i . Assuming for simplicitythat there does not exist a limit on the number of retries tosend a packet (see also Remark 2.1), we have2(1 − 2c i )p i =(CW min,i − 1)(1 − 2c i ) + CW min,i c i (1 − (2c i ) mi )(1)Then, in the frame of the decoupling approximation,considering a population N i for each class i, we writec i = 1 − (1 − p i ) Ni−1 ∏ j≠i(1 − p j ) Nj . (2)For K classes, we end up with a system of 2K nonlinearequations, through which p i , c i can be derived numerically.Remark 2.1 In the single-class case, the parameter configurationwhich minimizes the average time between successfultransmissions also yields the highest expected numberof successes in any bounded interval (0,t], and hence is optimalin any limited or unlimited-retry case. For multipleclasses a minor influence can be expected, becoming negligibleas the retry-limit increases.2.2. Contention zonesEnhancing the idle sensing time of some stations by controllingthe AIFS parameter is a basic tool for setting priorities.Consider classes indexed according to “service privilege”order, i.e., AIFS 1 < AIFS 2 < · · · < AIFS K . Thiscreates similarly indexed “zones” of channel activity, wherein zone i only classes j ≤ i are allowed to contend.Denote by π i the stationary probability that the systemis in zone i. This can be easily derived by Markov chainanalysis (see e.g. [8] for the case of 2 classes). Then thecollision probability of a station of class i isc i =π i∑ Kj=i π (1 − (1 − p 1 ) N1 · · · (1 − p i ) Ni−1 ) + · · ·j+ π K∑ Kj=i π (1−(1 − p 1 ) N1· · ·(1 − p i ) Ni−1· · ·(1 − p K ) NK ),j(3)i.e. the sum of collision probabilities for class i in zonesj ≥ i, weighted by the probability of being in each zonewhen there is an attempt. Along with (1), we have again asystem of 2K nonlinear equations.3. Performance measuresThe major performance measures we are preoccupiedwith are the channel access delay and throughput, for eachclass station. The analysis follows previous works, mainly[3]. It also includes the use of TXOP, which has notbeen covered in many previous works on 802.11e (including[2,3,8,10]). We only consider basic channel access (i.e.,without the use of RTS/CTS [4]), without loss of generalityfor our results.The calculation of performance measures is confined tothe case of 2 service classes A and B, of which class A willbe favored by service differentiation. The following refinementsin the analytical model are introduced. We providea correction in the calculation of the mean channel accessdelay (and subsequently, throughput) in the case of AIFSdifferentiation, to include the whole delay a disadvantagedclass-B station faces until it is allowed to attempt or performbackoff. Additionally, we calculate the average throughputseen by a station rather than the one seen by the system,quantities which as we show may differ substantially, especiallyin non-saturation conditions.3.1. Channel access delayThe channel access delay is defined as the delay a frameexperiences from the time it arrives at the head of the transmissionqueue until it is transmitted successfully, and itstransmission is acknowledged. Thus it is (deliberately) setto be a little more than just the “access” time.We consider a station of class i (i = A,B) has a MACpacket size σ i and transmits at rate R i . Let also δ be thepropagation delay, T RxTx the time for the transceiver to turnaround, T PLCP the time to transmit the PLCP preamble andheader (adjoined by the physical layer, see [4]) and ack thesize of a MAC level acknowledgement. The T PLCP is fixedfor each physical layer configuration. Further, ACK packetsare always transmitted at a (lower) basic service rate R b . Inaddition, a SIFS (short inter-frame space) interval is usedbetween the transmission of a frame and the sending of anacknowledgement, to allow the MAC layer to receive thepacket and subsequently the transceiver to turn around.According to the protocol, the duration the medium isbusy because of a successful transmission of class i –including the reception of the acknowledgement – isT succi=AIFS i − T RxTx + δ + T PLCP + σ iR i+ δ + T PLCP + SIFS + ackR b.(4)

The time the medium is busy during a collision of class-istations isT colli= AIFS i − T RxTx + δ + T PLCP + σ iR i. (5)We first derive the mean channel access delay for a stationof the priority class A. Following the analysis in [3],for a station of class i = A the channel access delay can beexpressed as:D acci =∑A i U k∑k=1 j=1S k,ji+ (A i − 1)T colli+ T succi , (6)where A i is the number of channel attempts for the givenframe, and U k is a random variable uniformly distributedin [0,2 (k−1)∧mi CW min,i − 1]. Under the decoupling approximation,S k,ji are i.i.d random variables representingthe duration of each backoff decrement cycle as seen by thestation, where in such cycle a successful transmission orcollision may follow the idle period. This is referred to as ageneric slot duration.The number of transmission attempts follows a geometricdistribution with Pr{A i = k} = (1 − c i )c k−1i . Packetsizes and transmission rates are deterministic, however theduration of a collision depends on the type of stations implicated.Considering the mean number of backoffs and collisions,we have:Using thatj=1E[D acci∑U kE[ 1 {Uk ≥j}] =∑A i∑] =E[S i ]E[U kk=1 j=11 {U k ≥j}]+ c iE[Ticoll ] + Ti succ .1 − c i2 k−1 CW∑ min,i−1j=1= 2k−1 CW min,i − 12after some calculations we obtain:E[D acci ] =E[S i ]−[CWmin,i212(1 − c i )·]+ c iPr{U k ≥ j},(7)( 1 − (2ci ) mi1 − 2c i+ (2c i) mi1 − c i)E[Ticoll1 − c i] + T succi . (8)The expected duration of a backoff decrement cycle isE[S i ] = π A · E[S A i ] + π B · E[S B i ] , (9)where E[Si A], E[SB i ] are the expected generic slot durationsfor the class i = A station, when it is performing backoff,if it were in zone A or zone B, respectively. Also, the expectedduration of a collision is calculated by consideringthe max(TAcoll,T Bcoll ) if it is among a class-A and class-Bstation, or TAcoll collor TB, weighted by their respective probabilities.Starting from (6), we can approximately calculate thevariance of the channel access delay. We finally get for thesecond moment thatE[(D acci ) 2 ] ≈E[S 2 i ] · Ω i + Ω i (Ω i − 1)E 2 [S i ]+ c i(1 + c i )(1 − c i )collE[(T2 i) 2 ] + (T succi ) 2+2E[Ticoll ]E[S i ]Θ i + 2E[S i ]Ω i Tisucc+ 2c iE[Ticoll ]Ti succ ,1 − c i(10)where Ω i , Θ i are defined in (12), (13), respectively. Relation(10) is an approximation because we have considered inthe calculations that E[Ω 2 i ] = E2 [Ω i ]. Finally, the varianceis computed as Var[Diacc ] = E[(Diacc ) 2 ] − E 2 [Di acc ].We now extend the analysis to derive the mean channelaccess delay of class-B stations, when there is AIFS differentiation.In this case, after each busy medium end a stationof class B will go through a number of slots where it is notentitled to transmit.To include this period, we consider the AIFS separationl = AIFS B −AIFS A and the discrete-time Markov chainshown in Fig. 1, with probability q A = (1 − p A ) NA and anabsorbing state l. The state of the Markov chain representsthe number of idle slots that have elapsed since the last busymedium end, as indicated by the carrier sense mechanism ofa station.q Aq A1 − q A01 − q A1 2 l-1 l11 − q A1 − q AFigure 1. Discrete-time transitions in zone A.We are interested in the mean number of visits to states0,1,...,l − 1 prior to absorption in state l. Denote byP n = [p (n)ij ] (0 ≤ i,j ≤ l) the nth power of the transitionmatrix and its elements. Then, starting from state 0 themean number of visits to 0 is 2m 0 =∞∑q An=0q Aq Ap (n)00 , (11)2 For computations, m 0 and m 1,...,l−1 are found merely by inverting(I − Q), where Q is the restriction of P to the set of transient states{0, 1, . . . , l − 1} and I is an identity matrix with the same dimensions.−

∑A iΩ i E[∑U kk=1 j=1k=11 {Uk ≥j}] = CW min,i2∑A i∑Θ i E[ (A i − 1) 1 {Uk ≥j}] = (CW min,i − 1)c i2(1 − c i )U kj=1]2c i (1 − c i )(1 − (2c i ) mi−1 )(1 − 2c i ) 2 − c i + 2 mi−1 (c miiCW min,i( 1 − (2ci ) mi+ (2c )i) mi 1−1 − 2c i 1 − c i 2(1 − c i ) , (12)+ CW [min,i ci − [c i + (m i − 1)(1 − c i )](2c i ) mi+2(1 − c i ) 1 − 2c i− c mi+1i)(m i − m i c i + c i ) + c mi+1i (1 − c i )(1 − c i ) 3 − c i(1 + c i )2(1 − c i ) 2 .(13)while the mean number of visits to states 1,...,l − 1 ism 1,...,l−1 =∞∑n=0p (n)01 + p(n) 02 + · · · + p(n) 0 l−1 . (14)We know that a visit to one of states 1,...,l − 1 lastsone idle slot time, while that to state 0 lasts either the timeof a successful transmission or of a collision. Thereforethe mean channel access delay for a station of class B willbecomeE[DB acc ] = [ E[SB] B + T slot · m 1,...,l−1 + Tbusy zone slot A ]· m 0∑A B∑· E[ 1 {U ≥j}] + c BE[T k Bcoll1 − c BU kk=1 j=1] + T succB .(15)In the above expression, T slot is an idle slot time, whileTbusy zone slot A is the mean duration of a busy slot in zone A. Thelatter writes asTbusy zone slot A = N Ap A (1 − p A ) NA−1T succ1 − (1 − p A ) NA A+ 1 − N Ap A (1 − p A ) NA−1 − (1 − p A ) NA1 − (1 − p A ) NA T collA .(16)In the calculation of E[S B B ] above one must set AIFS B =AIFS A , since the AIFS separation is now accounted forwhen calculating the mean time to absorption.Finally, it is noted that in this case it is extremely difficultto compute the delay variance, since second moments of thenumber of visits to a state prior to absorption are unknown.3.1.1. Use of TXOPAs mentioned before, wireless stations can carry out multipleframe transmissions, taking advantage of advertisedTXOPs. Let a station of class i transmit η i frames successively(as derived from the TXOP i limit), where η i ∈ N.Transmissions are separated by a SIFS period, to allowtransceivers to turn around from ACK receptions [5]. Arandomly chosen frame of class i is found with probability1/η i to be at the head of the transmission queue priorto a TXOP grant, and (η i − 1)/η i to be one of the η i − 1following frames that will be transmitted successively. It isclear that the frame at the head of the queue will undergothe standard transmit procedure, and thus suffer a meanaccess delay obtainable from the previous analysis, which|η i = 1]; on the other hand, the remainingframes benefit by having a much smaller delay, equal tod ′ i = SIFS + δ + T PLCP + σ i /R i . The expected delay ofa class-i frame is thenwe call E[D acciE[Diacc ] = 1 E[Di acc |η i = 1] + η i − 1d ′ i . (17)η i η iFor the calculation of generic slot times, note that theduration of a successful transmission which includes theACK ( reception is now increased to AIFS i − T RxTx +ση i i R i+ 2δ + 2T PLCP + SIFS + ackR b)+(η i −1)·SIFS.On the other hand, a collision is supposed to occur on thefirst transmitted frame, and therefore the expression in (5)is unchanged.Finally, we can also employ (10) to calculate the delayvariance in the case where TXOP is used.3.2. ThroughputThe evaluated throughput is the rate of successfullytransmitted MAC-level information per unit of time. Denoteit by γ i for a station of class i. The usual way to derivethis (e.g., in [1, 3, 9]) is to consider each end of a genericslot as a renewal epoch and calculate the mean amount ofsuccessfully transmitted information over the mean genericslot duration,γ i =(π A σ A p A (1 − p A ) NA−1 + π B σ B p B (1 − p B ) NB−1(1 − p A ) NA )/(π A E[S A ] + π B E[S B ]) .(18)However, this can only be characterized as the individualthroughput seen by the system. To calculate the actual

throughput of a station we have to take the total channelaccess time as the renewal period, henceγ i =σ iE[D acci ] . (19)This further allows to include the corrected calculation ofclass-B access delay in case of AIFS differentiation.4. Non-Saturation conditionsIn constructing a model for non-saturation conditions,we would like to include the traffic arrival characteristics inits parameters, and simply extend the set of nonlinear equations.The key modeling assumption here is to consider aconstant busy station probability at each idle-sensed slot,equal to the load of the station envisaged as a single serverqueue, as shown in [3].Consider an arrival rate λ i for each station in class i, andthe queue load ̺i. The collision probability now isc i = 1 − (1 − ̺ip i ) Ni−1 ∏ j≠i(1 − ̺jp j ) Nj , (20)where the probability of an attempt by class i is conditionedon having a packet to transmit and hence given by the samefunction of c i as in the saturation case (1). Along with ̺i =], for K service classes we now have a system of3K nonlinear equations to solve for p i , c i , ̺i.The mean channel access delay is then calculated followingthe same approach, which yields a sufficiently good approximation[6]. To calculate the average throughput experiencedby a station, we would have to consider a sequenceof alternating ON/OFF periods, where the OFF period is geometricallydistributed with parameter ̺i (and may take thevalue 0). Treating this as a regenerative process, we wouldλ i · E[D acci] + (1 − ̺i)/̺i · E[S i ]). This turnsout to be extremely inaccurate, yielding throughput resultsof about 1 order of magnitude greater.To tackle this, we consider a more involved ON/OFFmodel where a station may send 1 or more frames successivelyin the ON period (Fig. 2).have γ i = σ i /(E[D acci000 111OFF00 11000 111001st collision 2nd collision success 1st collision1st frameONregeneration cycle2nd framesuccess0000 1111OFF00 11 −0000 111100Figure 2. Sample path evolution of the systemwith ON and OFF periods.Define ri ON : the probability of an empty station after aframe transmission and riOFF : the probability of an emptystation after a generic slot in the OFF period. We considerthese constant and approximate them for Poisson arrivals asr ONi=e −λiE[Dacc i ] , (21a)r OFFi =e −λiE[Si] . (21b)Eq. (21a) represents a low load approximation where consecutiveframe transmissions are less frequent; this is becausewe confine the probability of no arrival in [0, E[Di acc ])(for consecutive transmissions it should be greater).It is clear that this model describes a regenerative process,as the end of an OFF period is a regeneration epoch.The throughput for class i is calculated as the mean MAClevelinformation transmitted in a regeneration cycle, overthe duration of this cycle:Throughput (kbps)γ i =40035030025020015010050E[D acc,i ]/r ONiON/OFF model’Seen by system’Simulationλσσ i /r ONi+ E[S i ]/(1 − r OFFi ) . (22)010 100 1000λ (packets/sec)Figure 3. Comparison of different throughputapproximations in a 1-class case.Fig. 3 shows an example of this throughput approximationin a 1-class case with CW min = 32, m = 5 andN = 10 stations, in 802.11a at 6 Mbps, for different Poissonarrival rates until saturation. Results are compared against adiscrete-event simulator written in C++. It can also be seenthat the corresponding individual throughput “seen by thesystem” is largely inaccurate for non-saturation conditions(even if the ‘kbps’ throughput scale is a coarse scale whenprotocol timings are in µs). Also shown on the graph isthat the approximation by λ · σ is extremely accurate for avery large lange of loads, which reflects the simple fact thatin non-saturation conditions where collisions are fewer, thethroughput is almost equal to the information arrival rate.5. OptimizationWe examine two optimization problems in 802.11e. Wefirst assess the capacity of the network for different param-

eter settings, and secondly we attempt to jointly optimize AIFS B − AIFS A = 0. Subsequently we modify each parameterAn upper delay bound is set for class-A stations. For the3 Bear in mind that the majority of data packets sent over the Internetdata transmitting stations no constraints are imposed, yetare also of small size.A vector (NA ∗ , N B ∗ ) is said to be Pareto optimal iff any other vector we aim at maximizing their throughput. This formulation(N A , N B ) in the feasible set has N A ≤ NA ∗ or N B ≤ NB ∗ . is consistent with intrinsic QoS demands of delay-sensitiveparameters for the two classes A and B, transmitting delaysensitiveand elastic traffic, respectively. In the first problem,we consider delay and throughput constraints for bothclasses; in the second, a delay bound for class A, while forclass B a better-than-best-effort behavior, in terms of thebest achievable throughput.The results are based on the analytic evaluation of meanperformance measures in the previous sections. Results inall cases are for 802.11a MAC and PHY layer characteristics.separately – favoring class A – and derive Paretopairs. We say a capacity improvement exists in the changedparameter configuration if the Pareto pairs lie “above” thoseof the balanced case (i.e., in a vector inequality sense). Eachmodified parameter is shown in the title of each subgraph,and Pareto optimal pairs are depicted by ‘◦’ in the unbalancedcases, and by ‘+’ in the balanced ones.The general goal is to increase capacity of the systemby service differentiation in favor of class A, since class-BValues of related parameters used in our analyti-stations can tolerate lower quality. An overall capacity im-cal formulas are summarized in Table 1. The transceiverturnaround time and propagation delay are negligible andare omitted.provement can be seen in saturation conditions (Fig. 4(a))in cases where QoS deterioration for class B is more tolerable(cases where m B = 10 and AIFS B − AIFS A =2).However, a noteworthy observation is that a more drasticTable 1. 802.11a MAC and PHY parameters.service differentiation can have an adverse effect: when anumber of inferior-class stations transmits in the system andParameter Valuerequires a certain – even inferior – QoS, capacity of the favoredT slot 9 µsclass should largely decrease to accommodate theseSIFS 16 µsstations in the network. For instance in the case wheremin i AIFS i 34 µsCW min,B = 32, when no class-B stations exist in theT PLCP 20 µssystem, the maximum number of allowed class-A stationsack 14 bytesis 10. When at least 1 class-B station should be able totransmit, the capacity of class A drops to 6. These phenomenaare more likely to occur in a saturated network:We focus on EDCA parameter differentiation and do notintroduce other biases. In this sense we set physical transmissionrates equal, R A = R B = 6 Mbps. The basic ser-in non-saturation conditions constraints are easier satisfiedand service deterioration usually effects an overall increasevice rate is also chosen as R b = 6 Mbps. Moreover, the sizein capacity, even with the same constraints for both classesof MAC packets is set equal to 160 bytes for all stations. 3 (Fig. 4(b)).It is worth stressing that the influence of backoff protocolparameters on performance reflects also their influenceon capacity. Further results attest that in the protocol,5.1. Pareto optimal pairsCWWe seek the maximum number of stations from eachmin , AIFS and TXOP are more influential parametersthan CWclass that can be admitted in the system subject tomax , a parameter which may have no effect at allin non-saturation conditions (see (Fig. 4(b))). The smallerQoS constraints. Since we have contending stationsinfluence of CWwith contradicting performance objectives, we shall derivemax was also witnessed in [10].Pareto optimal pairs 4 . Different parameter settings{CW min,A ,CW min,B ,m A ,m B ,l,η A ,η B } are examined. 5.2. Optimal parameter selectionOptimal pairs are shown in Fig. 4 for some cases of saturationand non-saturation conditions. In the saturation case, Parameter design involves searching for performanceoptimizingparameters in a space of allowed values. Hereconstraints are set as follows: for delay, E[DA acc]E[DB acc]A ≥ 300 kbps, we confine ourselves to the finding of optimal parametersγ B ≥ 200 kbps. In the non-saturation case we consider for the class of elastic traffic, when the delay-sensitive classmore tight constraints, set to be the same for both classes has its parameters fixed. This simplifies the automatedi = A, B: E[Diacc ] ≤ 1 ms, and γ i ≥ 100 kbps.search and allows for clearer conclusions. Also, in a practicalWLAN scenario stations transmitting delay-sensitiveThe arrangement for this set of results is as follows.We take a “balanced” configuration where EDCA parametersare the same for both classes. These are CW min,A =CW min,B = 16, m A = m B = 5, η A = η B = 1, and alsotraffic are usually fewer in number and unsaturated, andhence little is to be gained further by optimizing their parameters.

10CW min,B =3210m B =10888106668N A N A N A N A 64444222200000 2 4 6 8 10 12 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12N BN BN BCW min,B =3210(a) Saturation conditionsAIFS B –AIFS A =2N A181818251616161414142012121210N1010158A N8A N8A10666444522200000 2 4 6 8 10 12N Bm B =100 2 4 6 8 10 12N BAIFS B –AIFS A =20 2 4 6 8 10 12N B(b) Non-saturation conditions, λ A = 10 2 , λ B = 2 · 10 2 packets/sec12η A =30 2 4 6 8 10 12N Bη A =30 2 4 6 8 10 12N BFigure 4. Pareto optimal pairs for various parameter sets.and elastic traffic. Depending on the number of class-A andclass-B stations, we shall find the optimal protocol parametersto set for class B.We must consider a limited space in our search. In theexample we solve, this is the Cartesian product of the valuesets that follow, for each parameter:CW min,B : {4,8,16,32,64,128,256}m B : {2,3,4,5,6,7,8,9,10}l : {0,1,2,3,4,5}η B : {1,2,3,4,5,6,7,8,9,10}Class-A parameters are fixed at values CW min,A = 16,m A = 5, and η A = 1. Results are presented in Table 2, fora case where both classes are saturated, as well as for a casewhere only class-B stations are saturated, a scenario likelyto be encountered in practice. The behavior, with regard tothe most influential parameters, is as follows.• For the case where only class-B stations are saturated,the situation resembles the one where only a singleclass exists (class-A queue utilization was about 30%in the results of Table 2(b)). Hence, as in the 1-classcase, there is an intermediate value of CW min,B whichis optimal. However, when both contending classesare saturated, CW min,B should be adjusted to muchsmaller values, in order to avoid successive channeloccupations by the contending class.• The number of successive transmissions η B assumesthe maximum value in all cases shown in the table.Hence the exploitation of transmit opportunities is crucialfor maximizing the throughput of data traffic.• Performance degradation of delay-sensitive traffic isat the same time counteracted by increasing the AIFSseparation. We see that this is adjusted to higher valuesfor stricter delay constraints (Table 2(a)) or when class-B stations increase in number, in order to prevent theaccess delay of class A from degenerating inappropriately.Hence in an optimal configuration, depending onload conditions and the tightness of constraints of thedelay sensitive class, setting high TXOP value shouldbe supplemented by appropriately increasing AIFS.The setting of CW max , on the other hand, shows no cleartrend, which can be expected since it has a smaller influenceon performance. Finally, a useful observation is thatthe aggregate throughput of elastic traffic increases (with adecreasing rate) as the number of stations increases.Additional results when also class-A parameters are optimallyselected in the same range showed the same trends forclass-B parameters, and only small improvements in class-B throughput. Finally, in cases where both classes are unsaturated,it is intuitive that the setting of higher TXOP isless important (since a station has fewer packets to send)and contention windows can be reduced, since there is lesscongestion in the network.6. Conclusions and guidelinesOverall the results in this paper have shown that while inthe single-class case, given a certain TXOP, an optimal se-

Table 2. Optimal parameter sets(a) Saturation conditionsNumbers of constraint x Optimal parameters for class B E[DA acc]max γ B max N B γ Bstations (E[DA acc]CW min,B m B l η B (ms) (kbps) (Mbps)N A = 5, N B = 1 5 8 3 2 10 4.760 2774.62 2.775N A = 5, N B = 10 5 4 10 3 10 4.933 333.17 3.332N A = 5, N B = 20 5 16 5 3 10 4.964 173.43 3.469N A = 5, N B = 30 5 8 10 3 10 4.981 117.38 3.521N A = 5, N B = 1 3 8 3 4 10 2.915 2074.26 2.074N A = 5, N B = 10 3 8 8 5 10 2.867 303.11 3.031N A = 5, N B = 20 3 8 8 5 10 2.946 163.25 3.265N A = 5, N B = 30 3 8 9 5 10 2.958 112.06 3.362(b) Class B: saturated, Class A: unsaturated, λ A = 10 2 packets/secN A = 5, N B = 1 3 16 2 3 10 2.629 3451.29 3.451N A = 5, N B = 5 3 32 10 5 10 2.493 724.57 3.623N A = 5, N B = 10 3 32 10 5 10 2.794 371.61 3.716N A = 5, N B = 20 3 128 2 4 10 2.871 188.05 3.777lection of CW min practically suffices to achieve best capacityand performance, in a multiple-class case with differentclass objectives additional settings are in order.In the most important scenario with an elastic and realtimeclass, the following general guidelines can be deduced:Throughput maximization of the elastic class canbe achieved by exploiting TXOPs, while delay constraintsof the real-time class can be met by increasing the AIFSseparation of the two classes. The CW min of the elastic trafficclass can be set to its respective 1-class optimal valueif it faces light real-time traffic, while for increased realtimetraffic it should be adjusted to smaller values. Specificvalues can be investigated for each problem configuration,based on the analytic modeling presented. Finally, CW maxis the least influential parameter and may be fixed at a constantvalue.The following critical issues should be considered: First,that increasing the number of frames sent successively viaTXOP increases delay variance, since the initial access delayof a frame is comparatively very large. A large transmissionvariance can result in losses due to retransmissiontimeouts, even in the presence of a higher-layer protocolwith dynamic flow control (e.g., the self-clocking mechanismof TCP). The use of TXOPs is more appropriate forthe transmission of larger upper-layer segments, that wouldanyway be fragmented by the 802.11 MAC and can nowbe transmitted successively. Secondly, as it was shown inSection 5.1, setting drastic service differentiations shouldbe avoided, since it may seriously undermine the overallcapacity of the network.References[1] G. Bianchi. Performance analysis of the IEEE 802.11 distributedcoordination function. IEEE J. Select. Areas Commun.,18(3):535–547, Mar. 2000.[2] P. Clifford, K. Duffy, J. Foy, D. Leith, and D. Malone. Modeling802.11e for data traffic parameter design. In Proc.IEEE WiOpt 2006, Boston, MA, USA, Apr. 2006.[3] N. Hegde, A. Proutière, and J. Roberts. Evaluating the voicecapacity of 802.11 WLAN under distributed control. InProc. IEEE LANMAN 2005, Chania, Greece, Sept. 2005.[4] IEEE Computer Society. ANSI/IEEE Std 802.11, 1999.[5] IEEE Computer Society. IEEE Std 802.11e-2005, 2005.[6] I. Koukoutsidis and V. Siris. Modeling approximations foran IEEE 802.11 WLAN under Poisson MAC-level arrivals.In Proc. IFIP Networking’07, Atlanta, GA, USA, May 2007.[7] A. Kumar, E. Altman, D. Miorandi, and M. Goyal. New insightsfrom a fixed-point analysis of single cell IEEE 802.11WLANs. In Proc. IEEE Infocom ’05, pages 1550–1561, Miami,FL, USA, Mar. 2005.[8] V. Ramaiyan, A. Kumar, and E. Altman. Fixed point analysisof single cell IEEE 802.11e WLANs: Uniqueness, multistability,and throughput differentiation. In Proc. ACM Sigmetrics’05, pages 109–120, Banff, Canada, June 2005.[9] J. Robinson and T. Randhawa. Saturation throughput analysisof IEEE 802.11e enhanced distributed coordination function.IEEE J. Select. Areas Commun., 22(5):917–928, June2004.[10] I. Tinnirello, G. Bianchi, and L. Scalia. Performance evaluationof differentiated access mechanisms effectiveness in802.11 networks. In Proc. IEEE Globecom ’04, volume 5,pages 3007–3011, Dallas, TX, USA, Nov. 2004.