Analysis of Burst Acknowledgement Mechanisms for IEEE e WLANs over Fading Wireless Channels

Transcription

1 Analysis o Burst Acknowledgement Mechanisms or IEEE e WLANs over Fading Wireless Channels Department o Computer Science and Inormation Engineering Providence University 200 Chung-Chi Rd., Shalu, Taichung Hsien, 433 Taiwan chhliu@pu.edu.tw Abstract: Transmission opportunity, or TXOP, is a channel control method introduced in the IEEE e wireless local area network (WLAN standard. The control method includes some new operations developed or improving channel eiciency. In this paper, we propose an analytical model to evaluate these TXOP operations under ading channels. With this model, we calculate the maximum achievable throughput or the IEEE DCF with RTS/CTS access mode. In addition, we quantiy in the experiments how these operations can aect the system eiciency or dierent environments. The experiment results well conirm the theoretical model that provides new insights on design criterion or a WLAN in the real world. Key Words: WLAN, TXOP, Burst Transmission, Acknowledgment Aggregation, Perormance Analysis. 1 Introduction With the increasing deployment o WLANs in customer premises, came the challenge o supporting diverse networked multimedia applications over a shared wireless medium. Facing the challenge, the IEEE Task Group E proposes an enhanced MAC layer standard, namely IEEE e [1], to provide service dierentiation among WLAN users and applications. The e MAC deines two medium access schemes: contention-based Enhanced Distributed Channel Access (EDCA and centrally controlled Hybrid Coordination Channel Access (HC- CA. However, many research works only ocus on EDCA because it is currently promoted by the majority o vendors. In particular, these works concentrate mainly on how to conigure the WLAN parameters so as to achieve better service dierentiation. The various proposals or realizing EDCA are conined to the assignment o Arbitrary Inter-rame Spacing (AIFS value and Backo periods to dierent traic classes. Additionally, IEEE also provides means or increasing throughput and reducing contention through a prioritized access scheme called Transmission Opportunity (TXOP. This scheme increases aggregate system throughput by allowing multiple consecutive rame exchanges to take place between a station and access-point (AP. More precisely, two new operations, namely data transmission bursting and aggregated acknowledgments that can eiciently eliminate communication overheads in the legacy DCF, are 383 standardized as part o the IEEE e MAC, which receives quite a lot o attentions. In this paper we consider these new operations perormed under an errorprone channel. A modiied Markov chain model o the back-o window is derived to account or both rame error probability and the maximal retransmission limit or each o the ollowing methods that involve the new operations. These methods are 1 the Normal Acknowledgement (NA method that involves only the transmission bursting, and 2 the Block Acknowledgement (BA method that involves both transmission bursting and aggregated acknowledgments. For these methods, we derive their maximum throughputs with dierent rame error probabilities, TXOP limits, and the other parameters involved. Finally, in the experiments, we quantiy the two methods by showing their eects on the system perormance in dierent environments. Their results are shown to be very consistent with those o the theoretical analysis. The paper is organized as ollows. In Section 2, we briely summarize the new operations o EDCA. In Sections 3 and 4, we calculate the maximum throughput or the NA method and the BA method, respectively. The theoretical results are examined in Section 5. The related works are summarized in Section 6, and inally, conclusions are drawn in Section 7. 2 IEEE e EDCA As known widely, the IEEE e deines Enhanced Distributed Channel Access (EDCA to provide d-

2 MH RTS MH RTS BREQ AP CTS ACK ACK ACK ACK AP CTS BACK TXOP Limt (a TXOP Limt (b Figure 1: Transmission with Normal ACK (NA and Block ACK (BA: (a the NA method, and (b the BA method. ierential services among contending stations [1]. Speciically, there are two major operations o EDCA designed to improve the system eiciency. The irst allows the probability o accessing the channel to be dierentiable among stations. The second deines the transmission unit based on the channel access time. Given these operations, we ocus on the innovative aspects o the burst transmission and the corresponding acknowledgment operations. That is, we ocus on the act that once a station succeeds in competing the channel, EDCA will give the station a TXOP or its data transmission and speciy an ACK mechanism to response it. For reerence, their characteristics are summarized as ollows. 2.1 Transmission Opportunity To enhance the system eiciency, EDCA allows a s- tation wining the medium contention to gain a TXOP, deined by the starting time and the maximum duration o a transmission, with that the station can send one or more MPDUs in a burst, separated by and limited by a threshold, namely TXOP limit, to complete its channel access. Given this mechanism, ragmentation is mandatory whenever the MSDU transmission duration exceeds the TXOP limit. 2.2 Block Acknowledgment To reduce the channel wastes caused by the ACK transmissions, EDCA also deines a new acknowledgment scheme that allows a block o MPDUs to be acknowledged by a inal aggregated ACK rame, called block ACK (BACK, and thus reducing the number o ACKs required by each data rame in a burst transmission. The block ACK contains inormation about the reception o the whole block o data rames through a bitmap. However, it will not be transmitted automatically ater a burst o data transmission. Instead, it only begins ater receiving an explicit transmission request, namely block ACK request, sent by the requester. 384 In addition, or quickly identiying collisions and reducing the possibility o other transmissions occurred during a TXOP, the head-o-burst (HOB rame o each new burst transmission requires to be protected with an immediate acknowledgement. The mechanism can be done with the RTS/CTS exchange. That is, ater successully receiving a CTS rame, other stations are orbidden on the channel access during the period o time speciied in the RTS/CTS duration ields. 2.3 NA and BA Methods When these operations combined, two corresponding methods or the WLAN could be resulted. As shown in Fig. 1 (a, the method without BACK, namely the Normal Acknowledgment (NA method, transmits its data rame once a time and waits an immediate ACK until reaching the TXOP limit. On the other hand, the method with BACK, namely Block Acknowledgement (BA method, sends multiple back-to-back data rames, each separated by a period o time, and then issues a block ACK request (BREQ to expect the receipt o the corresponding BACK, as shown in Fig. 1 (b. 3 Throughput Analysis or The NA Method In this section, we irst introduce a Markov chain model or the NA method, and then, based on this model, we calculate the method s maximum achievable throughput. 3.1 Markov Chain Model In this work, we adopt a Markov chain model with a representation similar to that o [2], and also, make a similar assumption that the network consists o N contending stations and each o them always has backlog packets to be transmitted. However, unlike that

3 (c ack i,-2n b 3 data i, -5 ack i, -4 data i, -3 cts i, -2 rts i, -1 (1- Pc (a i, 0 P ack P data P ack P data P cts P rts P c (b (b (b (b (b (b (b (c (a 1 W , 0 0, 1 0, 2 0, W 0 2 0, W0 1 (b W 1 (a i, 0 i, 1 i, 2 i, W i 2 i, W i 1 (a (b W 1 1 i 1 1 i+1, 0 i+1, 1 i+1, 2 i+ 1, W i+ 1 2 i+ 1, W i (b W m 1 1 m, 0 m, 1 m, 2 mw, m 2 mw, m 1 Figure 2: Markov chain model or the NA method work, our model takes into account not only the backo procedure, but also the new operations o EDCA (i.e., TXOP and block ACK, the rame error probability or each type o rame involved, and the maximal allowable number o retransmission attempts. In addition, due to our analysis involving the rame error probability, we consider that 1 only RT- S will suer both collisions and rame errors while the other rames suer only rame errors, and 2 i no response or a RTS/DATA/BREQ returns, the sender will timeout and invoke the binary exponential backo (BEB procedure. The irst is made because a control rame should be transmitted with the maximum BSS basic rate equal to or lower than the data rate. In our work, a control rame is transmitted with the lowest rate to reach the most distant station in the WLAN and thus to robustly prevent collisions in the network 1. The second is made because the BEB procedure will be invoked or the transmission ails, indicated by a ailure to receive a CTS in response to an RTS, a ailure to receive an ACK rame that was expected in response to a unicast MPDU, or ailure to receive a BACK or ACK rame in response to a BREQ rame 1 The same assumption is also adopted in [3]. 385 (reerring to [1]. In such cases, a timeout period is required beore invoking the BEB procedure. The Markov chain model or the NA method is given in Fig. 2, which involves two halves. The bottom hal represents the back-o procedure with the maximal allowable number o retransmission attempts o EDCA, m. When reaching this limit, a station will give up its current transmission and go to the irst stage or the next transmission with probability o 1. On the other hand, the upper hal represents the states ater reaching the zero back-o count that accounts or the NA method. It denotes the act that ater reaching the state o 0 ( i.e., reaching the zero back-o count, the model can not decide its next back-o stage only according to the collision probability P c. Instead, it should go through the states in the upper hal that represents the collision s status, the RTS/CTS transmissions status, and the multiple DATA/ACK transmissions status. Thus, i collisionree, the chain will go to (i; 1 (as shown by the arrow with a mark o (a, and then i RTS error-ree, it will go to (i; 2, and so on. Finally, i collisionree and error-ree or all the rames involved (RT- S/CTS/DATA/ACK, the burst is successully trans-

4 mitted, which leads the chain to the irst back-o stage as indicated by the arrow with a mark o (c. On the contrary, i there is any error occurred, the burst is terminated and the back-o procedure is restarted, which leads the chain to the next back-o stage as indicated by the arrow with a mark o (b Given this model, however, in what ollows we will instead use a simpliied model to obtain the transmission probability i, and with this probability, we can then obtain the maximum achievable throughput by means o the complete Markov chain model shown in Fig. 2. For the irst step, a simpliied Markov chain is made here by merging the states in the upper hal or each stage i and the state (i; 0 in the bottom hal as a virtual state (i 0 ; 0 0, and renaming the other states (i; js by(i 0 ;j 0 s. With the simpliied and equivalent model, we let b(t and s(t denote the stochastic processes representing the back-o timer and the backo stage, respectively, or a given station at slot time t. Then, the non-null probabilities involved can be represented by 8 >< WSEAS TRANSACTIONS on COMMUNICATIONS P i 0 ;k 0 ji 0 ; (k +1 0 g = 1; i k 0 2 (0 0 ; (W i 2 0 ; and i 0 2 (0 0 ;m 0 P 0 0 ;k 0 ji 0 ; 0 0 g = e 1 P W 0 ; i k 2 (0 0 ; (W ; and i 0 2 (0 0 ;m 0 P i 0 ;k 0 j(i 1 0 ; e 0 0 P g = W i ; i k 0 2 (0 0 ; (W i 1 0 ; and i 0 2 (1 0 ;m 0 P 0 >: 0 ;k 0 jm 0 ; 0 0 g = 1 W 0 ; i k 0 2 (0 0 ; (W m 1 0 (1 where P e = 1 PT, and P T denotes the probability leading the current state to the irst back-o stage. Clearly, the latter (P T involves the probability o collision-ree, that o RTS/CTS transmission successul, and that o multiple DATA/ACK transmission successul. That is, P T = (1 P c (1 P rts (1 P cts (1 P data (1 P ack Nb (2 where P c denotes the conditional probability o collision, and can be calculated by 1 (1 i N 1 given N completing stations in the network. N b is the maximum number rames transmitted in a TXOP limit. P rts, P cts, P data, and P ack represent the rame error probabilities o RTS/CTS/DATA/ACK rames, respectively, and can be obtained by 1 (1 P b l, with bit error rate o P b and rame size o l bits. With the above, and ater some algebra manipulations similar to that in [2], we can obtain the stationary 386 probability o state (0 0 ; 0 0 as where b 0 0 ;0 0 = i = 2(1 2 P e (1 P e 8 W 0 (1 (2 P e m+1 (1 P e + i = >< >: (1 2 e P (1 e P m+1 ; i m» m 0 W 0 (1 (2 e P m 0 +1 (1 e P + (1 2 P e (1 P e m+1 + W 0 2 e m0 P m 0 +1 (1 2 P e (1 P em m 0 ; i m>m 0 (3 In above, m 0 represents the largest contention window size. Finally, we can attain the probability i that a station transmits a rame in a randomly chosen slot time by mx i = b i 0 ;0 0 = i0 =0 mx i0 =0 e P m+1 b0 0 ;0 0 e = 1 P m+1 b 1 P e 0 0 ;0 0 (4 Now, it can be seen that the relationship between ep and i in act represents a non-linear system involving the parameters W 0, m, m 0, N, N b, and P b. That is, i = (W 0 ;m;m 0 ;N;N b ;P b, which can be solved with numerical methods. 3.2 Throughput Calculation In this work, we consider the NA method with the IEEE a PHY, which provides dierent modulation schemes with corresponding dierent data rates (namely, 6, 9, 12, 18, 24, 36, 48, and 54 Mbps. According to the standard, data rame and control rame are transmitted with dierent rates. Thus, we denote the rate or data rame by r and that or control rame by r Λ. Speciically, a control rame is transmitted with the lowest rate (6 Mbps in order to reach the most distant station in the a WLAN or robustly preventing collisions in the network, as mentioned previously. The channel occupancy time o RTS/CTS exchange, data rame and ACK, are denoted by RT S, CTS, DATA, and ACK, respectively. In above, a data rame with payload size o L should also include a MAC header. As a reerence, all the times involved are summarized in Table 1, which also includes that or the BA method. However, it does not show the details such as that each rame should include a common physical header, and its transmission time has to

5 Table 1: PHY payload and header transmission times RTS CTS ACK BREQ BACK DATA 160=r Λ 112=r Λ 112=r Λ 192=r 1216=r (MAC + P =r Table 2: Channel Occupancy Times T O A T O R T P NA RT S +2 + CTS 0 DATA +2 + ACK BA RT S +2 + CTS BREQ +2 + BACK DATA + be added to the PHY payload time, although our simulations involve all the details. For the throughput calculation, we consider that any block does not split among multiple TXOPs, and hence a data block corresponds to a single data burst. In addition, we consider also that the channel occupancy time is divided into three components. That is, 1 the overhead or channel access, TA O, 2 the time or data payload transmission, T P, and 3 the overhead or channel release, TR O. Speciically, a burst transmission is composed o a given number o unit times o T P because the latter only corresponds to the time or the transmission o a single data rame. Note that in these time components, denotes the short interrame space in the IEEE standard. For reerence, we summarize the values o these components in Table 2, including also that or the BA method. Given that, we can now ocus on the saturated throughput o the network represented by the data payload transmitted in a slot time divided by the average length o a slot time. That is, where S = E[m] E[T ] E[m] = P s P tr E[N s ] E[L] E[T ] = (1 P tr + P tr P s P succ T s + P tr (1 P s T c + P tr P s E[T e ] (5 In (5, E[L] is the average data payload size, and we assume that all rames have the same size, i.e., E[L] = L. E[N s ] is the average number o rames successully transmitted in a burst transmission. P tr is the probability that at least one station transmits in a time slot, and can be obtained by P tr =1 (1 i N. Thus, the probability o an empty slot can be derived by 1 P tr, which consumes an empty slot time. P s is the probability o a single successul transmission given at least one station is transmitting, i.e., 387 P s =(N i (1 i N 1 =P tr. Based on the above, we note that 1 the probability that all data rames in a burst are transmitted successully is given by P tr P s P succ, and 2 the unsuccessul transmission probability due to collisions is P tr (1 P s. The t- wo probabilities are accounted or the corresponding times, i.e., the average time the channel sensed busy due to a successul transmission or a collision, T s, and T c, respectively. And these times can be obtained by T s = TA O + N b T P + TA R + DIFS T c = RT S + DIFS (6 where DIFS denotes the distributed interrame space in the IEEE standard. In addition to that, with the new operations o EDCA, we should also take into account the average time the channel being sensed busy due to successul RTS/CTS exchange but incomplete multiple data rame transmissions in a burst. This is represented by P tr P s E[T e ]. Now, we reer to the complete Markov chain model in Fig. 2 in order to derive the parameters involved in above but not yet solved. At irst, the maximum number rames transmitted in a TXOP limit is obtained by N b = b TXOP T O A T O R + T P c (7 Here, a is involved due to its overlap between T O A and T P. Given this number, we can consider that a burst may be terminated on the i+1th data rame due to its rame error or the corresponding ACK s error. In this case, there are only the irst i rames successully transmitted. Thus, E[N s ] can be represented by E[N s ] = 0 N b i=2 (i 1 (P data (i +P ack 1 (i A + P succ N b (8

6 In above, the probability that a burst is terminated on the ith data rame includes the successul probability o RTS/CTS exchange, that o the irst i 1 data/ack transmissions, and the ailure probability o the ith data rame. That is, P data (i = (1 P rts (1 P cts (1 P data i 1 (1 P ack i 1 P data (9 Similarly, the probability that a burst is terminated on the ith ACK can be obtained by can be considered by taking into account the time required by the irst i data/ack transmissions and then T timeout. That is, T data (i =T ack (i =TA O +i T P +T timeout (15 4 Throughput Analysis o The BA Method P ack (i = (1 P rts (1 P cts (1 P data i (1 P ack i 1 P ack (10 On the contrary, i all data/ack rames in a burst are successully transmitted, the probability should be P succ = (1 P rts (1 P cts (1 P data (1 P ack Nb (11 Given these probabilities, we can now consider the corresponding times or the dierent cases. First, the average time spent or an incomplete burst transmission is obtained by inding the expectation o the times required by transmission ailures occurred at dierent points o time. That is, a burst may ail on RTS/CTS exchange or the ith data/ack transmission. Taking these into account, we can obtain the average time by E[T e ] = P rts T rts +(1 P rts P cts T cts + XN b i=1 P data (i T data (i + P ack (i T ack (i (12 Here, a ailure on RTS/CTS exchange will spend a period o time that ensures the corresponding CTS ailure, and a period o timeout beore the BEB procedure can be restarted. That is, T rts = T cts = T O A + T timeout (13 The last term in above, T timeout, is obtained by T timeout = EIFS DIFS + AIF SN [AC] + T T urnaroundt ime (14 according to [1]. For the timeout, we let AIF SN [AC] = 2 because it is the minimal setting allowed or an EDCA station, and we ignore T T urnaroundt ime when it is small as compared with the other components. Similarly, T data (i and T ack (i 388 In this section, we analyze the BA method or its throughput perormance. To this end, we consider its Markov chain model irst. As shown in Fig. 3, only the upper hal o this model is drawn here or the bottom hal has been given in Fig. 2. In this model, the upper hal similarly represents the states ater reaching the zero back-o count at stage i. However, unlike the NA method, only our states are involved here. That is, collision-ree leads the chain to (i; 1, and then RTS/CTS error-ree leads to (i; 2 and (i; 3, respectively. The irst three states are the same as those o the NA method. However, in the BA method, the multiple data rames in a burst transmission require no responses (ACKs. Thus, only BREQ and BACK should be considered with their rame errors. Hence, i RTS/CTS exchange is successul and BREQ is error-ree, the chain will go to (i; 4. Finally, i BACK is also error-ree, the burst is considered to be successully transmitted, leading the chain to a state in the irst back-o stage. Otherwise, the chain moves to the next back-o stage. With a similar simpliied Markov chain model as that or the NA method, we can obtain the transmission probability i or the BA method. Given this probability, we can obtain the method s maximum achievable throughput with the same equation o (5. O course, some parameters involved should be modiied to accommodate themselves to this method. The irst to be considered is that, instead o using a single ACK to response a data rame, in the BA method all data rames in a burst transmission is acknowledged with only one BACK. It implies that the RTS/CTS exchange and the BREQ/BACK exchange should be all successul. Otherwise, the sender can not conirm which rame is correctly received even though its multiple back-to-back data rames are all transmitted in a burst. Thus, P T in (2, which denotes the probability leading the current state to the irst back-o stage, should be replaced by P T = (1 P c (1 P rts (1 P cts (1 P breq (1 P back (16

7 (c back i, -4 breq i, -3 cts i, -2 rts i, -1 (1- Pc (a i, 0 P back P breq P cts P rts P c (b (b (b (b (b Figure 3: Markov chain model or the BA method. where P breq and P back denote the rame error probabilities o BREQ/BACK rames, respectively, and similar to those or the other rames, they can be also obtained by 1 (1 P b l with bit error rate o P b and rame size o l bits. Similarly, or the BA method, the successul probability in the denominator part o (5 should be rewritten as P succ =(1 P rts (1 P cts (1 P breq (1 P back (17 With this probability, a station can know which and how many rames are successully transmitted in a burst when the corresponding BACK is correctly received. In addition, although a transmission burst consists o N b rames, there may have only i rames located in dierent positions in the burst to be acknowledged. Taking these into account, we have E[N s ] or the BA method as E[N s ]=P succ XN b i=0 i ψ Nb i! (1 P data i (P data N b i (18 Similarly, a station can know its ailures on transmitting RTS, CTS, BREQ, and BACK rames, despite the unknown status o its multiple data transmissions that can only be solved with a BACK. Thereore, we can consider the average time spent on the ailure as E[T e ] = P rts T rts +(1 P rts P cts T cts + (1 P rts (1 P cts P breq T breq + (1 P rts (1 P cts (1 P breq P back T back (19 In above, the time or BREQ or BACK ailure consists o the whole period o time or a burst transmission 389 because a station should wait a period o time to conirm the BACK ailure, and then wait a T timeout period to restart the BEB procedure. Thus, we have T breq = T back = T O A +N b T P +T O R +T timeout (20 5 Perormance Evaluation In this section, we report on experiments made in order to veriy the perormance results derived previously. To this end, we design our experiments to ocus on the new methods in EDCA and ignore the other characteristics in the MAC. That is, we consider that each station carries a single traic low with the same access category (AC that provides only one set o parameters or each station. For example, we let r Λ be 6 Mbps, m 0 be 5, m be 7, CW min (the minimum contention window size be 31, CW max (the maximum contention window size be 1023, and L (the rame size be 1024, or each station. Speciically, we conduct our dierent sets o experiments to exhibit the dierent eects resulted rom the our major actors to be considered, which are bit error probability (P b, TXOP limit, number o stations, and data transmission rate. To ocus on the eects o a single actor, the our sets o experiments are so conducted to vary one o these actors while remaining the others ixed, as summarized in Table 3. For example, in the irst set, we let the data rate be 54 Mbps, the number o stations be 100, and the TXOP limit be 10 ms and 100 ms, respectively, while varying the bit error probability under consideration rom P b = 0 to P b = Given that, or each set we consider the normalized throughput, deined as the throughput divided by the data transmission rate adopted. The corresponding results are given in Fig. 4. The irst set s

8 Table 3: Experiments in the Perormance Evaluation Tag bit error probability (P b TXOP limit (ms number o station data transmission rate (Mbps a 0to and b 0 and to c 0 and to d 0 and to54 results are given in Fig. 4 (a, and the other results are given in the subigures (b, (c, and (d, respectively. As shown in Fig. 4 (a, the throughput decreases when P b increases, as expected. Another expected result is that the higher TXOP limit (100 ms provides higher throughput than that o the lower one (10 ms. However, it should be noted that although the higher limit is 10 times o the lower limit (100 ms/10 ms=10, its improvement on the throughput is much lower than the scale (10 times. This is also expected because the existed overheads in the MAC, e.g., the time required by the common physical header and the necessary spacing time such as, will inevitably consume the bandwidth. In addition, we also observe that the BA method provides higher throughput than that o the NA method. This is because the ormer e- liminates the ACK overhead or each data rame in a transmission burst. However, when P b is high (e.g., 10 3, the multiple rames spaced with only in a burst will not be correctly received with a high probability, and the BA method can only provide nearly the same throughput as the NA method. In Fig. 4 (b, we show more the throughput results that correspond to not only the TXOP limit o 10 ms and 100 ms but also that rom 2 ms to 100 ms, while ixing P b at 0 and 10 5, respectively. From this igure, it can be seen that the curves or the two new methods (NA and BA increase more steeply when the TXOP limit increases at the beginning rom 2 to 10 ms as compared with that ater 10 ms. On the contrary, the IEEE MAC remains the same lat curves because no TXOP limit is given in the MAC and only P b can aect its results. From this igure as well as Fig. 4 (a, we can clearly observe the marginal beneit to be obtained with the new methods when the TXOP limit increases, and its trend would persist despite P b. In Fig. 4 (c, we show the throughput results or each station in the network. As shown in this igure, the per-station throughput decreases as the number o stations increases. This is expected because the increase o the number o stations will increase the channel contention level, which eventually decreases the throughput. Finally, in Fig. 4 (d, it can be observed that the normalized throughput decreases as 390 the data rate increases. It s no surprise because even though the data rate could continuously increase, the control overhead can not be avoided and still remain constant. This overhead will occupy more bandwidths and thus reduce more throughputs as the data rate increases. 6 Related Works In the decade, many related works or WLANs, e.g., [2, 4 8], have been done or the legacy IEEE MAC. Most o them complete their analyses with the assumptions that 1 the network is saturated (i.e., every station always has a packet waiting to be transmitted, and 2 transmission error is a result o rame collision and is not caused by medium error. Although these assumptions provide a tractable basis or the analyses and give these related works remarkable accuracy in theory, such assumptions may not be valid in the real world. As a ollower o the legacy MAC, IEEE e uses the TXOP mechanism to increase system throughput. With the same aim, there are also some other works proposed to provide better throughput when the channel condition is good or multiple rames to be transmitted in a burst [3, 9 13]. These protocols have their own speciications and mechanisms, and thus, do not provide exactly the same two operations o IEEE e. Thereore, the results or those protocols can not be directly applied to the operations under consideration. Apart rom the above, only a ew results have been reported about the new operations under consideration. Currently, only theoretical maximum throughput, theoretical throughput upper limit, and/or theoretical delay lower limit have been proposed in literature [14 17]. None o the above involves a ading channel. On the other hand, although some eorts had been done or the perormance analysis under a ading channel, e,g., [18 21], these eorts mainly ocus on the legacy IEEE MAC and involve no the operations under consideration.

9 Normalized throughput theory simulation BA theory (TXOP = 10ms 0.2 BA simulation (TXOP = 10ms NA theory (TXOP = 10ms NA simulation (TXOP = 10ms BA theory (TXOP = 100ms 0.1 BA simulation (TXOP = 100ms NA theory (TXOP = 100ms NA simulation (TXOP = 100ms ^-7 10^-6 10^-5 10^-4 10^-3 Bit error probablity (Pb Normalized throughput theory (Pb = simulation (Pb =0 BA theory (Pb =0 BA simulation (Pb =0 NA theory (Pb=0 NA simulation (Pb= theory (Pb = simulation (Pb =10-5 BA theory (Pb =10-5 BA simulation (Pb =10-5 NA theory (Pb=10-5 NA simulation (Pb= TXOP limit (ms (a (b 0.08 Normalized throughput theory (Pb = simulation (Pb =0 BA theory (Pb =0 BA simulation (Pb =0 NA theory (Pb=0 NA simulation (Pb= theory (Pb = simulation (Pb =10-5 BA theory (Pb =10-5 BA simulation (Pb =10-5 NA theory (Pb=10-5 NA simulation (Pb= number o stations Normalized throughput theory (Pb = simulation (Pb =0 BA theory (Pb =0 BA simulation (Pb =0 NA theory (Pb=0 NA simulation (Pb= theory (Pb = simulation (Pb =10-5 BA theory (Pb =10-5 BA simulation (Pb =10-5 NA theory (Pb=10-5 NA simulation (Pb= Rate (Mbps (c (d Figure 4: Analysis and simulation results o throughput or the our major actors under consideration: (a the P b results with TXOP limit = 10 ms and 100 ms, (b the TXOP limit results with P b = 0 and 10 5, (c the results rom dierent numbers o stations with P b =0and 10 5 and (d the results rom dierent numbers o rates with P b =0and Conclusion 391 In this paper, we derive the maximum achievable throughput or the new methods o EDCA (NA and BA in an error-prone WLAN with a modiied Markov chain model that can take into account the channel error. Our experiments conirm the correctness o our derivation, and show their results to be very consistent with those o the theory. From both the theory and the experiments, we can see that the two methods outperorm the IEEE MAC rom the our aspects under consideration: bit error probability, TXOP limit, number o stations, and data transmission rate. In addition, we also ind that the BA method usually outperorms the NA method because the ormer requires only a BACK or a bulk o data transmissions and thus reduces the transmission overhead under most o the ading conditions. As a summary, it could be concluded that with the especial concern on the behavior o these methods under the error-prone channel, the perormance model can provide more insights on the design criteria or the IEEE based WLANs operated in the real world, beyond that or the networks under an ideal error-ree environment. Acknowledgement This work was supported by the National Science Council, Republic o China, under grant NSC E Reerences: [1] IEEE e. Part II: Wireless LAN Medium Access Control (MAC and Physical Layer (PHY Speciications. Amendment 8: Medium

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