Modeling and Analysis of TCP Dynamics over IEEE WLAN

Transcription

1 Modeling and Analysis of TCP Dynamics over IEEE 8. WLAN Jeonggyun Yu and Sunghyun Choi School of Electrical Engineering and INMC Seoul National University, Seoul, Korea and Abstract Today, IEEE 8. Wireless LAN (WLAN) is a prevailing solution for the wireless Internet access while Transport Control Protocol (TCP) is the dominant transport protocol in the Internet. It is nown that, in the infrastructure WLAN with multiple long-lived TCP flow stations, the actual number of contending TCP stations is limited to a small number, and the aggregated TCP throughput is basically independent of the total number of TCP stations. It is due to the behavior of the TCP flow control in the infrastructure WLAN, where the downlin (i.e., Access Point-to-stations) is the bottlenec lin. In this paper, we develop an accurate and realistic analytical model of long-lived TCP over WLAN based on a well-nown p-persistent model of the 8.. We calculate the average number of the active TCP stations as well as the aggregated TCP throughput using our model for a given number of TCP stations and the maximum TCP receive window size. We verify our model via ns- simulations. Moreover, we find from our wor that the minimum contention window sizes of the standards (i.e., and for IEEE 8.b and 8.a, respectively) are not optimal in the sense of the TCP throughput maximization. I. INTRODUCTION In recent years, IEEE 8. WLAN has gained a prevailing position in the maret for the (indoor) broadband wireless access networing. IEEE 8. standard defines both the medium access control (MAC) layer and the physical (PHY) layer specifications []. The mandatory part of the 8. MAC is called the distributed coordination function (DCF), which is based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA). Many of the Internet applications run over the Transport Control Protocol (TCP). It is nown that in the infrastructure IEEE 8. WLAN with multiple long-lived TCP flow stations, the actual number of contending TCP stations at a given time is limited to a very small number, and the aggregated TCP throughput is almost independent of the total number of TCP stations [8], [9]. It is due to the behavior of the TCP flow control in the infrastructure WLAN where the downlin (i.e., the AP s transmission) is the bottlenec lin. In the long term, the DCF basically provides the contending stations an equal opportunity to access the shared wireless channel. Because the AP of a Basic Service Set (BSS) is just one of the stations in the MAC s perspective even if it should serve This wor was supported by the Korea Research Foundation Grant funded by Korean Government (MOEHRD) (R8---8-). An infrastructure BSS (or simply a BSS) is composed of an AP and a number of associated stations. multiple TCP flows, it asymptotically has the same channel access probability as a non-ap contending station. When the queue size of the AP is large enough, most of outstanding TCP pacets (in the form of either TCP ACK or TCP data) are accumulated at the AP. Therefore, for example, the source stations of file-upload TCP flows, where the corresponding long-lived TCP flows are in the congestion avoidance phase, can transmit a TCP data pacet only when they receive a TCP ACK pacet from the AP provided that a timeout does not occur. This maes only one or two stations actively contend for the channel on average irrespective of the number of the stations with TCP flows in a BSS. In this paper, we conduct a rigorous, comprehensive, theoretical analysis of the TCP dynamics over a DCF-based IEEE 8. WLAN discussed above based on a well-nown analytical model (i.e., p-persistent model) of the 8. DCF. Our model considers the maximum TCP receive window size larger than or equal to one (in terms of fixed-size pacets), different from a previous model [], which restricts the receive window size to a single pacet. We calculate the average number of the actively contending TCP stations as well as the aggregated TCP throughput using our analytical model. Then, we verify the analytical results by comparing with ns- simulation results. Moreover, we find from our study that the minimum contention window sizes of the current standards (i.e., and for IEEE 8.b and 8.a, respectively) are too large to maximize the TCP throughput. Finally, we obtain the optimal minimum contention window size to maximize the aggregated TCP throughput. There have been efforts to understand the TCP dynamics over the 8. WLAN [9] []. In [9], Choi et al. analyzed the number of active TCP stations using a Marov chain. However, they computed the state transition probabilities from simulations and experiments instead of mathematical analysis. In [], Kherani et al. mathematically analyzed the TCP performance in multihop 8. WLAN while our study focuses on the infrastructure WLAN. Burmeister et al. modeled the TCP over multi-rate WLAN []. However, they did not analyze TCP dynamics based on the characteristics of the contention-based MAC in detail, because they modeled the AP as an M/G//B queuing system. Bruno et al. mathematically In the 8. MAC terms, frame is a better word than pacet. However, we use the terms frame and pacet inter-changeably throughout this paper since we consider the issue across layers, i.e., TCP over WLAN.

2 Immediate access when medium is idle >= DIFS DIFS Fig.. Busy Medium PIFS SIFS Defer Access DIFS Contention Window Bacoff Window Slot Time Next Frame Select Slot and decrement bacoff as long as medium stays idle IEEE 8. DCF channel access scheme analyzed the TCP dynamics based on a p-persistent model of the DCF []. However, they assumed that no more than one TCP pacet is enqueued in the buffer of an active TCP station. This implies that each essful transmission of an AP always activates a TCP station. This assumption is not realistic. The number of outstanding pacets of a TCP flow in the congestion avoidance phase is equal to the maximum TCP receive window size (in pacets) in the real networ. Moreover, as discussed above, most of the outstanding TCP pacets are accumulated at the AP if its downlin transmission is the bottlenec lin. Therefore, each essful transmission of the AP may not always activate a new TCP station due to the multiple transmissions to the same station. Our model allows us to consider any TCP receive window sizes. Bruno s model is a subset of our model because his model is equal to our model with the TCP receive window size equal to a single pacet. The rest of the paper is organized as follows. In Section II, both IEEE 8. DCF and p-persistent model of the DCF are comparatively presented. Section III presents the analytical model that describes the characteristics of TCP over the 8.. In Section IV, our model is extensively validated via simulations. This model is used in Section V in order to find the optimal minimum contention window size to maximize the TCP throughput. We conclude the paper with the discussion of the future wor in Section VI. II. PRELIMINARIES A. IEEE 8. DCF IEEE 8. MAC [] defines two coordination functions, namely, the mandatory DCF based on CSMA/CA and the optional point coordination function (PCF) based on a polland-response mechanism. Most of today s 8. devices operate only in the DCF mode. We here briefly explain how the DCF wors as our model is for the DCF-based 8.. The CSMA/CA of the DCF wors as follows: when a pacet arrives at the head of a transmission queue, if the channel is busy, the MAC waits until the medium becomes idle, then defers for an extra time interval, called DCF Interframe Space (DIFS). If the channel stays idle during the DIFS deference, the MAC then starts the bacoff process by selecting a random bacoff counter. For each idle slot time interval, the bacoff counter is decremented. When the counter reaches zero, the Assuming that the delayed ACK option of TCP is not employed, a station with a TCP flow is activated or becomes active upon a reception of a TCP pacet from its AP when it does not have any pacet to transmit since it will then need to contend for the channel in order to transmit a corresponding response, e.g., a TCP ACK. pacet is transmitted. The timing of the DCF channel access is illustrated in Fig.. Each station maintains a contention window (CW), which is used to select the random bacoff counter. The bacoff counter is determined as a random integer drawn from a uniform distribution over the interval [, CW]. If the channel becomes busy during a bacoff process, the bacoff is suspended. When the channel becomes idle again, and stays idle for an extra DIFS time interval, the bacoff process resumes with the suspended bacoff counter value. For each essful reception of a pacet, the receiving station immediately acnowledges by sending an acnowledgement (ACK) pacet. The ACK pacet is transmitted after a short IFS (SIFS), which is shorter than DIFS. If an ACK pacet is not received after the data transmission, the pacet is retransmitted after another random bacoff. The CW size is initially assigned CWmin, and increases to (CW +) upon each transmission failure with an upper bound of CWmax. After each essful transmission, the CW value is reset to CWmin, and the transmission-completing station performs the DIFS deference and a random bacoff even if there is no other pending frame in the queue. This is often referred to as a post bacoff, as this bacoff is done after, not before, a transmission. This post bacoff ensures there is at least one bacoff interval between two consecutive MSDU transmissions. Moreover, when there is no on-going bacoff and channel is idle over a DIFS time, a frame can be transmitted immediately instead of starting a new bacoff. This is referred to as immediate access. B. p-persistent Model of IEEE 8. DCF Cali et al. [6] consider a p-persistent model of the DCF. Instead of using the binary exponential bacoff timer values, the p-persistent version determines its bacoff interval by sampling from a geometric distribution with parameter p. Thans to the memoryless property of this geometric distributed bacoff algorithm, it is more tractable to analyze the p- persistent model. From the geometric bacoff assumption, the processes that define the occupancy behavior of the channel (i.e., idle slots, collisions, and essful transmissions) are regenerative with the sequence of time instants corresponding to the completion of a essful transmission being the regenerative points. Using this regenerative property, Cali et al. define the j-th virtual slot time duration as the time interval between the j-th and (j +)-th essful transmissions. As shown in Fig., a virtual slot time consists of idle periods and collision periods preceding a essful transmission. That is, a virtual slot time is terminated by a essful transmission. An idle period is a time interval in which the channel is idle due to the fact that all the active stations are performing the bacoff without transmission attempts. A collision period is the interval in which two or more stations transmit simultaneously their frame and then their frames collide with one another. Statistically, the standard MAC and its p-persistent version wor the same when the stations are always active. That is,

3 Virtual Slots... μ j- μ j- μ j μ j+... Idle Collision (Tcol) DIFS Fig..... Idle Collision (Tcol) DIFS Idle Success SIFS ACK DIFS (TTCP DATA or TTCP ACK) Vitual slots in p-persistent version of DCF they always have a frame to transmit. However, in the longlived TCP over WLAN, TCP stations with the bottlenec downlin (i.e., the AP) can not always have a frame to transmit. They can have a TCP ACK (or TCP data) pacet to transmit only when they receive a TCP data (or TCP ACK) pacet from the AP in the congestion avoidance phase. As discussed above, a TCP station with the standard MAC which receives a TCP pacet from the AP can transmit the pacet without bacoff (i.e., via immediate access) or without starting a new bacoff when it is performing the post bacoff. This maes some difference from our p-persistent based analysis model. It is due mainly to the TCP processing delay which is the time interval between TCP ACK (or TCP data) pacet reception and TCP data (or TCP ACK) pacet transmission in a station. Therefore, we assume in the next section that there is no TCP processing delay. III. ANALYTICAL MODEL FOR TCP DYNAMICS OVER WLAN In this section, we mathematically analyze the average number of active TCP stations and the aggregated TCP throughput under the assumption of ideal channel conditions (i.e., no hidden terminals, no channel error, and no capture effect). A. Networ Model and Assumptions We consider a BSS with N STA long-lived TCP stations, which are associated with a single AP. TCP stations either download or upload data from or to the FTP server, which is co-located at the AP. We start our analysis with the following assumptions for the simplicity. () The queue size of the AP and stations is large enough not to incur any buffer overflow. () A essful transmission of each TCP data pacet is notified by the immediate TCP ACK instead of the delayed TCP ACK. () All TCP flows are under the congestion avoidance phase, and the congestion window of each TCP flow is larger than the TCP receive window. Then, the number of the outstanding pacets (including TCP data and TCP ACK) for a TCP flow is equal to the maximum TCP receive window size (in pacets). () There is no processing delay between a TCP data pacet reception and the corresponding TCP ACK pacet transmission. () A TCP data pacet has a fixed size. Even if TCP data pacet size is fixed, its transmission time depends on the Long-lived TCP flows often operate in the congestion avoidance phase during most of their lifetime. Term W M N STA N N i η P m, Q AP PSTA, P AP, P i AP, P i STA, TABLE I LIST OF NOTATIONS AND SYMBOLS Definition Maximum TCP receive window size (in pacets) Total number of states Total number of TCP stations in a BSS State- vector i-th element of the state- vector Number of active TCP stations in state State transition probability from state m to state Length of the AP queue in state Probability that a non-ap station eeds in a transmission attempt in state Probability that the AP eeds in a transmission attempt in state Probability that the AP eeds in transmitting a pacet to a class-i station in state. Probability that a class-i station eeds in transmitting a pacet in state transmission rate. In our analysis, we assume that the transmission rate is also fixed. However, one can easily extend our analysis to multi-rate WLAN. B. State Space A list of the notations and symbols used for the following analysis is found in Table I. Let N (t) = (N (t),n (t),n (t),...,n W (t)) be a (W +)- dimensional stochastic process representing the distribution of the numbers of stations with a particular number of TCP pacets in their queue at time t. That is, element N i (t) represents the number of stations with i TCP pacets in their queue at time t. Moreover, N (t) is the number of inactive stations without any TCP pacet to transmit in their queue. W is the maximum TCP receive window size (in pacets). A discrete integer time scale is adopted, i.e., t = j and t = j + correspond to the beginning of two consecutive virtual slots, µ j and µ j+ in Fig.. N (t) always satisfies the following condition. N STA = W N i (t). () i= N (t) can be modeled as a discrete-time Marov chain as depicted in Fig.. In this Marov chain, a number indicated above each state represents the index of the state. Let η be the number of active TCP stations including the AP in state, and can be defined as NSTA N η = +,NW <N STA, N STA N, () NW = N STA, where N i is the i-th element of the state vector, and hence N represents the number of inactive stations. N W = N STA means that the AP has no TCP pacet in its queue, and all the outstanding TCP pacets are in the active stations queues because the maximum number of pacets, which each station can have, is W. That is, all the stations in a BSS are active and each of them has W TCP pacets. The steady-state probability of the Marov chain π = lim t P N (t) = N }, [, M ], ()

4 Fig.. Marov chain model for the distribution vector of active and inactive TCP stations in a BSS where M is the total number of states. In the Marov chain, the state transition occurs only at the end of each virtual slot, which ends with a essful transmission. A transition from a left state to a right state in Fig. is due to a essful transmission of the AP, and an opposite transition occurs by a essful transmission of a station. For example, in state, the number of active stations including the AP is three. Each of the two non-ap stations has one TCP pacet in their queue. If one of the two stations finishes the current virtual slot with its essful transmission, the transition from state to state occurs. On the other hand, if the AP terminates the current virtual slot with its essful transmission, there can be two possible transitions. One is the case that the AP transmits a TCP pacet to one of (N STA ) inactive stations with no TCP pacet in their queue. In such a case, the number of the active stations increases by one, and hence the transition from state to state occurs. The other is the case that the AP transmits a TCP pacet to one of the two active stations, which already have one TCP pacet in their queue. In such a case, one of the two active stations comes to have two TCP pacets. As a result, the number of active TCP stations is not changed, but only the distribution of the active stations is changed (i.e., from state, (N STA,,,..., ), to state, (N STA,,,,..., )). Before we proceed further, we define the length Q AP of the AP queue in state as follows: Q AP = W N j j= (W j). () C. State Transition Probabilities Now, we derive the state transition probabilities of all the possible transitions. As discussed above, the values of only two elements in the two states, involved with a transition, change by one because the AP or a station transmits only a single pacet at a time. Therefore, the transition probability from state to state m is given by PSTA, i, if a unique i [, W ] such that Nm i = N i +,Ni+ m = N i+, P,m = PAP, i, if a unique i [, W ] such that N m i = N i, Ni+ m = N i+ +,, otherwise. () The first equation in Eq. () accounts for the fact that a station terminates the current virtual slot in state with its essful transmission. PSTA, i is the probability that a class-(i +) station eeds in transmitting its TCP pacet, where a class-i station is a station with i TCP pacets in its queue. The second equation accounts for the fact that the AP terminates the virtual slot with its essful transmission in state. PAP, i is the probability that the AP essfully transmits its TCP pacet to one of class-i stations. Note that a virtual slot is terminated only when a non-ap station or the AP eeds in transmitting a data frame in the p-persistent model. Therefore, the state transition probabilities in a given state depend on only the distribution of active stations but not transmission probability (i.e., contention window size) in our Marov chain model. We assume that both the AP and a station access a virtual slot with the attempt probability τ, where this value is derived in Section III-F. Then, the probability PAP, i is given by P i AP, AP (i) = PAP, P, (6) where the conditional ess probability PAP, of the AP s transmission at state assuming that a essful transmission occurs is given by PAP, /η, N = W <N STA,, N W (7) = N STA. AP (i) and the probability P that the AP transmits a pacet to a class-i station is given by AP (i) N i P = (W i) /Q AP, QAP >,, Q AP (8) =. Now, the probability PSTA, i is given by P i STA, = P STA, P STA(i+), (9) where the conditional ess probability PSTA, of a station s transmission at state assuming that a essful transmission occurs is given by P STA, = P AP,, () and the probability P STA(i) that a class-i station transmits a pacet to the AP is given by P STA(i) N i = /(η ), N <N STA,, N = N () STA.

5 D. Average Number of Active TCP Stations So far, we have assumed that the virtual slot length (i.e., the sojourn time) in each state is identical in order to model the TCP dynamics using the discrete Marov chain. However, the sojourn time in each state is dependent on the current state. Therefore, we need the long-term proportion of time spent by N (t) in each state in order to compute the average number of active stations as follows. ( M ) p = π µ / π jµ j, () j= where µ is the length of a virtual slot in state (i.e., the sojourn time in state ). Finally, we can determine the average number of active TCP stations excluding the AP as E [Num. of active STAs] = M (N STA N )p. = () Now, the sojourn time in state in the case of download TCP is given by µ = E [ NSTA, col ] T ac col + E [ NAP, col ] T data col + ( E [ N col ] )( [ ]) + DIFS + E T idle + E [ () T data ] + SIFS + ACK, [ ] where Tcol ac and E NSTA, col are the collision time and the average number of collisions due to collisions among only [ uplin ] TCP ACK pacets, respectively, and Tcol data and E NAP, col are the collision time and the average number of collisions due to the collisions between a downlin TCP data pacet and uplin TCP ACK pacets, respectively. Moreover, E [ ] T data, DIFS, SIFS, and ACK are the average TCP pacet transmission time, DIFS time, SIFS time, and MAC ACK frame transmission time, respectively. E [ ] N col and E [ ] T idle are the total number of collisions and the average idle time preceding a collision or a essful transmission, respectively. In Eq. (), the reason why we consider the two inds of collision times separately is that the collision times for both cases are different. On the other hand, in the case of the upload TCP, we use Tcol data instead of Tcol ac in Eq. () because at least one of colliding pacets is a TCP data pacet so that the collision time is always Tcol data. In the followings, we derive individual elements in Eq. (). The conditional essful transmission probability at state assuming that at least one station (possibly including the AP) transmits is P = P ( N tx = N tx ) = η τ ( τ) η ( τ) η, () where N tx denotes the number of transmitting stations including the AP immediately after an DIFS time in state. The conditional collision probability at state assuming that at least one station transmits is given by P col = P. Moreover, the conditional probability that AP s transmission fails assuming that at least one station including the AP transmits is given by τ( ( τ) η ) PAP, col = ( τ) η,n W <N STA, (6), N W = N STA. The probability that the total number of collisions is i and the probability that the number of collisions due to the AP s transmissions is j, bothinstate, are respectively given by P ( N col = i ) = ( ) P col i P ( ) ( P NAP, col = j = PAP, col ) j P., (7) Using Eq. (7), the average number of total collisions, the average number of collisions due to the AP s transmissions, and the average number of collisions due to only stations transmissions can be expressed as E [ ] N col = i= i P ( N col = i ) [ ], E NAP, col = ( j= j P NAP, ), col [ ] = j E NSTA, col = E [ ] [ ] (8) N col E NAP, col. The average idle time preceding a collision or a essful transmission in state can be calculated as E[T idle ]=aslott ime i P ( N tx > ) (P ( N tx = )) i i= ( τ AP )( τ STA ) η = aslott ime ( τ AP )( τ STA ) η. (9) In the case of the download, the average TCP pacet transmission time can be expressed as E [ T data ] = TTCP DATA PAP,+T TCP ACK PSTA,, () where T TCP DATA and T TCP ACK are TCP data and TCP ACK pacet transmission times, respectively. In the case of the upload, the positions of PAP, and PSTA, are exchanged in Eq. (). E. Aggregated TCP Throughput In the p-persistent CSMA/CA model [6], the aggregated throughput (in bits/s) is given by Average length of a data frame (bits) ρ = () Average duration of a virtual slot (sec) In our analysis, under the assumption that there exist a fixed number of active stations in a given state, the download TCP throughput in state is derived as ρ = L TCP DATA PAP,, () µ where L TCP DATA is the TCP data (i.e., segment) size (in bits). If we consider the upload TCP throughput, we use PSTA, instead of PAP, in the above equation. Finally, the average aggregated TCP throughput of a BSS can be determined as follows: ρ TCP = M ρ i p i. () i=

6 TABLE II ALGORITHM TO ESTIMATE τ FROM CW min IN EACH STATE In state Step : Initialize cw i =min ( CW max, i (CW min +) ), for i =,..., n r CW = CW min Step : Calculate the probability τ, and then store the current average value of CW τ =, α = CW CW+ Step : Calculate the average CW size with given η and p ( )( ) i, P (CW = cw i )=p pcol, pcol, for i =,..., n r CW = n r i= cw ip (CW = cw i ) Step : Determine whether the iteration is terminated or not If CW α <ε, then τ =, return τ CW+ Otherwise, go to Step F. Estimation of τ from CW min in Each State We now extend the Average Contention Window Estimation algorithm of [6] by considering different CW min sizes of the AP and stations in order to obtain the slot access probability τ. We can assume that τ is /(B +)) where B( is the average ) number of bacoff slots, and is equal to CW + [6]. Because the average contention window size CW is determined by CW min and the number of active stations in a given state, we can estimate τ from CW min in each state using the iterative algorithm of Table II. In Table II, n r is the retry limit for retransmissions of both the AP and a station. In state, the algorithm determines the average contention window size iteratively. In Step, p col, is the probability that a transmission of the AP or a station collides, and is given by p col, = ( τ) η. () p is the normalization factor, and can be obtained from the fact that n r i= P (CW = cw i)=. At the end of each iteration, if the difference between the current average contention window size (CW) and the previous average contention window size (α) is less than ε, the algorithm is terminated by returning the obtained τ value. IV. ANALYTICAL AND SIMULATION STUDIES In this section, we validate our model via ns- simulations. We mathematically analyze the aggregated TCP throughput as well as the average number of active TCP stations with IEEE 8.b/a PHYs and compare the analytical results with simulation results. Parameters for both calculation and simulations are shown in Table III. We consider the networ topology in which N STA TCP stations either download or upload data from or to the FTP server co-located at the AP. A. Number of Active TCP Stations Figs. 6 show the average number of active TCP stations except the AP from our analysis and ns- simulations with 8.b/a PHYs. We first observe that the average number of active stations remains very small, i.e., around one, across all TABLE III PARAMETERS Parameters 8.b 8.a aslottime µs 9 µs SIFS, DIFS µs, µs 6 µs, µs CW min, CW max,, Data, ACK Rates Mb/s, Mb/s Mb/s, Mb/s PHY Overhead 9 µs µs MAC ACK Length bytes MAC Overhead 8 bytes TCP data frame Data (6 bytes) + TCP/IP headers ( bytes) +SNAP * header (8 bytes) + MAC/PHY overheads TCP ACK frame TCP/IP headers ( bytes) + SNAP header (8 bytes) + MAC/PHY overheads * When an IP datagram is transferred over the 8. WLAN, it is typically encapsulated by an IEEE 8. Sub-Networ Access Protocol (SNAP) header. the considered cases while both the analytical and simulation results very well match. Moreover, the results are almost the same as the results of [9] where the number of active stations including the AP is evaluated via simulations and experiments but not mathematical analysis. The average number of the active stations remains flat beginning about three stations regardless of the maximum TCP receive window size for both upload and download cases with 8.b/a PHYs. When the maximum TCP receive window size is equal to one (i.e., W =) and the number of TCP stations is equal to one (i.e., N STA =), the average number of the active stations is much smaller than one. In this case, a station or AP does not contend with the AP or a station, respectively, because the number of outstanding TCP pacet is just one, and hence, only the AP or station, which has a pacet, can access the channel. As a result, the idle bacoff time occupies a considerable portion of the channel time, and hence the number of active stations becomes much smaller than one. On the other hand, when the maximum TCP receive window size is equal to one (i.e., W =) and the number of TCP stations is larger than one (i.e., N STA > ), a essful transmission of the AP always activates an inactive station, thus increasing the number of active TCP stations. Therefore, we can see that the average number of active stations in case of one-pacet TCP receive window is slightly larger than the other cases. Because this case (i.e., W =) is analyzed mathematically in [], and it is a particular case of our analysis, our model is a superset of the model in []. We observe that the average number of active stations in the case of the upload is slightly larger than the download in Figs. and. It is due to the fact that the transmission time of a station (i.e., TCP data pacet transmission time by a station) is larger than the download case (i.e., TCP ACK pacet transmission time by a station), and hence the time duration when stations have pacets is larger than that of the download case due to longer collision and transmission times. Actually, typical TCP configurations of commercial operating systems use a -pacet (or 7-byte) receive window in the case of MS Windows XP. However, we consider smaller receive window size in order to reduce the calculation overhead because similar trends are observed irrespective of the receive window size.

7 8.b PHY STAs STAs STAs 7 STAs Sim - STA Sim - STAs Sim - STAs Sim - 7 STAs TCP window size (a) Download TCP 8.b PHY STAs STAs STAs 7 STAs Sim - STA Sim - STAs Sim - STAs Sim - 7 STAs TCP window size (b) Upload TCP Fig.. The average number of active stations vs. TCP receive window size: 8.b 8.b PHY Window Window Window Sim - Window Sim - Window Sim - Window Sim - Sim The number of STAs (a) Download TCP 8.b PHY Window Window Window Sim - Window Sim - Window Sim - Window Sim - Sim the number of STAs (b) Upload TCP Fig.. The average number of active stations vs. the number of TCP stations: 8.b 8.a PHY STA STAs STAs 7 STAs Sim - STA Sim - STAs Sim - STAs Sim - 7 STAs TCP window size (a) The effect of TCP Window size 8.a PHY Window Window Window Sim - Window Sim - Window Sim - Window Sim - Sim the number of STAs (b) The effect of the number of TCP stations Fig. 6. The average number of active STAs vs. (a) TCP receive window size and (b) the number of TCP stations: 8.a, download TCP B. Aggregated TCP Throughput from Section IV-B. What happens if we use a CW min value different from that specified in the standards? In Fig. 8, we plot the relation between the aggregated TCP throughput and CW min value from the numerical analysis and simulations. The value of CW max is fixed to in all the cases. Note that the CW min values are and for the 8.b and the 8.a, respectively, as shown in Table III. In Fig. 8, we observe that the CW min values are too large to maximize the aggregated TCP throughput. Fig. 7 shows the aggregated download TCP throughput with IEEE 8.b/a PHYs. First of all, we can observe that the numerical results are almost the same as the simulation results in both cases. In Fig. 7, the aggregated TCP throughput is almost independent of the number of TCP stations (i.e., N STA ) in a BSS and the maximum TCP receive window size. This is due to the fact that the average number of active TCP stations remains flat irrespective of the number of TCP stations or the maximum TCP receive window size as shown in Figs. 6. When the number of station is one (i.e., N STA = ), throughput is slightly low. This is related to the fact that in Fig. (a) and 6(b) the number of active stations is very small. That is, the lower throughput means that the portion of idle bacoff time in the channel is larger than the other cases (i.e., N STA > ) due to a small number of active stations. V. CWMIN VALUE FOR THE MAXIMUM TCP THROUGHPUT We now now that the aggregated TCP throughput is almost independent of the number of TCP stations (i.e., N STA ) From our numerical and simulation results in Fig. 8, the optimal CW min values are summarized in Table IV. Here, we assume that there exist only download TCP stations. However, the optimal values of CW min in the case of upload can be also found via the similar method. We observe in Table IV that the optimal CW min values for 8.b and 8.a are about 7 and in the case of 6-byte TCP segment, respectively, and the standard values (i.e., CW min =for 8.b and CW min = for 8.a) are too large to maximize the aggregated TCP throughput. Moreover, when the size of TCP data segment is small (i.e., 6 bytes), we observe that even

8 b PHY Window Window Window Sim window Sim window Sim window Sim window 7 Sim window 9 8.a PHY Window Window Window Sim window Sim window Sim window Sim window 7 Sim window The number of STAs 6 7 The number of STAs (a) 8.b (b) 8.a Fig. 7. Aggregated throughput: download 8.b PHY, TCP segment = 6 bytes... TCP STAs TCP STAs 7 TCP STAs Sim - TCP STAs Sim - TCP STAs Sim - 7 TCP STAs. CWmin (a) 8.b - 6 bytes 8.a PHY, TCP segment = 6 bytes 8 6 TCP STAs TCP STAs 7 TCP STAs Sim - TCP STAs 8 Sim - TCP STAs Sim - 7 TCP STAs 6 CWmin (c) 8.a - 6 bytes 8.b PHY, TCP segment = 6 bytes TCP STAs TCP STAs. 7 TCP STAs Sim - TCP STAs Sim - TCP STAs Sim - 7 TCP STAs... CWmin (b) 8.b - 6 bytes 8.a PHY, TCP segment = 6 bytes TCP STAs TCP STAs 7 TCP STAs Sim - TCP STAs Sim - TCP STAs 8 Sim - 7 TCP STAs CWmin (d) 8.a - 6 bytes Fig. 8. Optimal CWmin value for maximum throughput TABLE IV OPTIMAL CW min VALUES WITH DIFFERENT DATA SIZES 8.b 8.a N STA analysis simulation analysis simulation TCP data segment: 6 bytes TCP data segment: 6 bytes smaller values of CW min (i.e., the optimal CW min for 8.b and 6 for 8.a) are desired. This is due to the fact that the collision overhead decreases as the size of TCP data segment decreases. Unfortunately, adapting the CW min value is not allowed in the current 8.. However, the emerging IEEE 8.e allows to control channel access parameters including the CW min value []. Therefore, our wor can be applied to the emerging 8.e WLAN in order to optimize the TCP performance. VI. CONCLUSIONS In this paper, we developed an accurate and realistic analytical model of TCP over Wireless LAN dynamics based on the analytical model (i.e., p-persistent model of IEEE 8. DCF) developed Cali et al.. Our model considers the maximum TCP receive window size. We calculate the average number of the active TCP stations as well as the aggregated TCP throughput by using our model. Moreover, we find from our analysis that the minimum contention window sizes, defined in the standards, are too large to maximize the TCP throughput for both IEEE 8.b and 8.a. We are currently extending our wor considering IEEE 8.e Enhance Distributed Channel Access (EDCA) and multi-rate WLAN []. IEEE 8.e EDCA has new features such as Transmission opportunity (TXOP) and the usage of different channel access parameter values between the AP and stations. The TCP dynamics in IEEE 8.e EDCA based networ can be different from that of the legacy DCF, which we present in this paper. REFERENCES [] IEEE, Part : Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications, IEEE Std , 999. [] IEEE, Supplement to Part : Higher-speed Physical Layer Extension in the. GHz Band, IEEE Std. 8.b-999, 999. [] IEEE, Supplement to Part : Higher-speed Physical Layer Extension in the GHz Band, IEEE Std. 8.a-999, 999. [] IEEE, Supplement to Part : Medium Access Control (MAC) Enhancements for Quality of Service (QoS), IEEE Std 8.e, Nov.. [] G. Bianchi, Performance analysis of the IEEE 8. distributed coordination function, IEEE J. Sel. Areas Commun., Mar.. [6] F. Cali, M. Conti, and E. Gregori, Dynamic Tuning of the IEEE 8. Protocol, IEEE/ACM Trans. Networing, Vol. 8, No. 6, Dec.. [7] I. Aad and C. Castelluccia, Differentiation mechanisms for IEEE 8., in Proc. IEEE INFOCOM, March. [8] J. Yu, S. Choi, and J. Lee, Enhancement of VoIP over IEEE 8. WLAN via Dual Queue Strategy, in Proc. IEEE ICC, June. [9] S. Choi, K. Par and C. Kim, Performance Impact of Interlayer Dependence in Infrastructure WLANs, IEEE Trans. Mobile Computing, Vol., No. 7, July 6. [] R. Bruno, M. Conti, and E. Gregori, Analytical Modeling of TCP Clients in Wi-Fi Hot Spot Networs, in Proc. IFIP Networing, May. [] A. A. Kherani and R. Shorey, Modelling TCP Performance in Multihop 8. Networs with Randomly Varying Channel, in Proc. WILLOPAN 6, Jan. 6. [] C. Burmeister and U. Killat, TCP over Rate-Adaptive WLAN An Analytical Model and its Simulative Verification, in Proc. IEEE WoWMoM 6, June 6. [] The Networ Simulator - ns-. online lin.