Mobile Netw ApplDOI 10.1007/s11036-008-0111-z

Analytical Study of TCP Performanceover IEEE 802.11e WLANs

Jeonggyun Yu · Sunghyun Choi · Daji Qiao

© Springer Science + Business Media, LLC 2008

Abstract IEEE 802.11 Wireless LAN (WLAN) hasbecome a prevailing solution for broadband wirelessInternet access while the Transport Control Protocol(TCP) is the dominant transport-layer protocol in theInternet. Therefore, it is critical to have a good under-standing of the TCP dynamics over WLANs. In this pa-per, we conduct rigorous and comprehensive modelingand analysis of the TCP performance over the emerging802.11e WLANs, or more specifically, the 802.11e En-hanced Distributed Channel Access (EDCA) WLANs.We investigate the effects of minimum contention win-dow sizes and transmission opportunity (TXOP) limits(of both the AP and stations) on the aggregate TCPthroughput via analytical and simulation studies. Weshow that the best aggregate TCP throughput perfor-mance can be achieved via AP’s contention-free ac-cess for downlink packet transmissions and the TXOPmechanism. We also study the effects of some simpli-fying assumptions used in our analytical model, andsimulation results show that our model is reasonablyaccurate, particularly, when the wireline delay is smalland/or the packet loss rate is low.

J. Yu · S. Choi (B)School of Electrical Engineering and INMC,Seoul National University, Seoul, 151-744, Koreae-mail: schoi@snu.ac.kr

J. Yue-mail: jgyu@mwnl.snu.ac.kr

D. QiaoDepartment of Electrical and Computer Engineering,Iowa State University, Ames, IA 50011, USAe-mail: daji@iastate.edu

Keywords TCP · IEEE 802.11e WLAN · EDCA ·TXOP · PIFS access

1 Introduction

In recent years, IEEE 802.11 WLAN has becomethe dominant technology for indoor broadband wire-less networking, where the mandatory protocol of the802.11 MAC is the Distributed Coordination Function(DCF) [8]. On the other hand, more than 90% ofthe Internet traffic is carried by the Transport ControlProtocol (TCP) [10]. Consequently, most of the datatraffic over the 802.11 WLAN is TCP traffic. Therefore,it is critical to have a good understanding of the TCPdynamics over WLANs.

It has been shown in [6, 17] that, with multiplestations carrying long-lived TCP flows in an 802.11WLAN, the number of stations that are actively con-tending remains very small. Hence, the aggregate TCPthroughput is almost independent of the total num-ber of stations in the network. This interesting phe-nomenon is due to (i) the closed-loop nature of TCPflow control and (ii) the bottleneck downlink (i.e., AP-to-station) transmissions. More specifically, since along-lived upload TCP flow usually operates in thecongestion avoidance phase, the source station can onlytransmit a TCP Data after it receives a TCP Ack fromthe AP; meanwhile, each client station of a downloadTCP flow only replies with a TCP Ack upon recep-tion of a TCP Data from the AP. On the other hand,the 802.11 DCF guarantees long-term equal channelaccess probabilities among contending stations, regard-less whether it is an AP or a station. As a result, mostof the outstanding TCP packets (in the form of either

Mobile Netw Appl

TCP Ack for upload or TCP Data for download) areaccumulated at the AP, and hence most of the stationsremain inactive waiting for their turns to transmit.

The above observations do not always hold in theemerging IEEE 802.11e WLANs, because the 802.11eMAC supports service differentiation. With the 802.11eEDCA [9], the AP can perform service differentiationbetween itself and stations as well as among stationswith different classes of traffic, thanks to its capabilityof setting flexible channel access parameters and trans-mission opportunity (TXOP) durations. For example,if the AP uses a smaller minimum contention windowsize or a longer TXOP duration than stations, the afore-mentioned TCP packet accumulation at the AP may bealleviated.

There have been efforts to understand the TCPdynamics over legacy 802.11 WLANs [3, 4, 6, 11, 16].However, none of them analyzed the TCP dynamicsover 802.11e WLANs. In [6], Choi et al. analyzed thenumber of active stations using a Markov chain model,but simply computed the state transition probabilitiesbased on empirical results. In [11], Kherani et al. con-ducted a theoretical analysis on the TCP performanceover multi-hop 802.11 WLANs; in contrast, our studyfocuses on infrastructure-based WLANs. Burmeisteret al. analyzed the TCP over multi-rate WLANs [4].However, they approximated the AP behavior as anM/G/1/B queuing system, and did not study the effectsof contention-based MAC on TCP dynamics in detail.Bruno et al. addressed this problem using a p-persistentDCF model [3] under a critical assumption that nomore than one TCP packet is enqueued in the bufferof an active station. This implies that a station becomesinactive after transmitting its packet successfully whileeach successful transmission from the AP always acti-vates a different station, which is not true in practice.In a real network, the number of outstanding packetsin a long-lived TCP flow is usually larger than one.Moreover, each successful transmission from the APmay not always activate a different station, because theAP could transmit a packet to an already active station.Yu et al. analyzed the TCP dynamics over legacy 802.11DCF-based WLANs using Markov chain model [16],which is the basis of the approach employed in thispaper.

In this paper, we conduct rigorous and comprehen-sive modeling and analysis of the TCP performanceover EDCA-based IEEE 802.11e WLANs. Our ana-lytical model is based on the p-persistent model de-veloped by Cali et al. [5]. We study the effects of theminimum contention window sizes (CWmin), arbitra-tion interframe space (AIFS) sizes, and the TXOPdurations of both the AP and stations on the aggregate

TCP throughput, and verify them using simulation re-sults. We show that (i) the aggregate TCP throughputcan be enhanced via a proper combination of CWminvalues for the AP and stations, and (ii) the best ag-gregate TCP throughput performance can be achievedvia AP’s contention-free access for downlink packettransmissions and the TXOP mechanism.

The rest of the paper is organized as follows.Section 2 briefly introduces the IEEE 802.11e EDCA,the TXOP mechanism, the p-persistent CSMA/CAmodel, and the dynamics of long-lived TCP flows.Section 3 describes our analytical model for TCP overthe 802.11e EDCA. Section 4 extends the analysisin Section 3 to consider the TXOP mechanism. AP’scontention-free access for downlink TCP packet trans-missions is presented in Section 5. In Section 6, ouranalytical models are evaluated via simulation, and theeffects of AP/station access parameters and TXOP du-rations on the aggregate TCP throughput are studied.We also discuss briefly the effects of various assump-tions on the accuracy of our models. We conclude thepaper in Section 7.

2 Preliminaries

2.1 IEEE 802.11e EDCA and TXOP

The 802.11 DCF [8] does not support service differ-entiation. Basically, the DCF provides long-term fairchannel access to contending stations with equal op-portunities. In contrast, the 802.11e EDCA [9] providesfour access categories (ACs) and the channel accessfunction of each AC is an enhanced variant of the DCF.Specifically, each EDCA channel access function usesAIFS[AC], CWmin[AC], and CWmax[AC] instead ofDIFS, CWmin, and CWmax as in the DCF. AIFS[AC]is determined by

AIFS[AC] = SIFS + AIFSN[AC] · σ, (1)

where AIFSN[AC] is an integer greater than 1 forstations and an integer greater than 0 for the AP, and σ

is a backoff slot time. The backoff counter is selectedrandomly from [0, CW[AC]]. Basically, if an EDCAchannel access function uses smaller AIFSN[AC] andCWmin[AC], it contends for the channel more aggres-sively. Hence, it may use more bandwidth than otherACs which use larger AIFSN[AC] and CWmin[AC].

In an 802.11e EDCA WLAN, after a station trans-mits a packet successfully, it resets its CW value toCWmin, and performs AIFS deference and randombackoff. This is often referred to as post backoff sincethis backoff is done after, not before, a transmission.

Mobile Netw Appl

SIFS SIFSSIFS

Source Data

ACK

Data

ACKDestination SIFS

Data

ACK

. . .

. . .

AIFS[AC]+Backoff

AIFS[AC]+Post Backoff

TXOPLimit[AC]Time gap >= 0

Figure 1 Illustration of transmission opportunity (TXOP)operation

Post backoff ensures that there is at least one backoffinterval between two consecutive frame transmissions.On the other hand, when there is no on-going backoffand when the channel has been idle for longer thanAIFS time, a frame can be transmitted immediatelywithout additional backoff. This is referred to as imme-diate access.

TXOP (transmission opportunity) is a new conceptintroduced in the 802.11e. A TXOP is a time intervalduring which a particular station is allowed to transmit.As shown in Fig. 1, a station may transmit multiplepackets (separated by SIFS) during a TXOP, whichenhances the communication efficiency by reducing un-necessary backoffs [13]. A TXOP can be obtained by asuccessful EDCA contention. The maximum durationof a TXOP (called TXOPLimit) can be differently con-figured for different ACs. With a larger TXOPLimit, anAC can use more bandwidth than the others.

The values of AIFSN[AC], CWmin[AC], CWmax[AC], and TXOPLimit[AC], which are referred to asthe EDCA parameter set, are determined and adver-tised to stations by the AP via Beacons and ProbeResponse frames. Stations should use the announcedvalues for their channel access and transmissions whilethe AP can use the different values from those an-nounced to stations. In this paper, we study how theaggregate TCP throughput performance may be en-hanced by using different EDCA parameter sets for theAP and stations. Service differentiation among differ-ent traffic priorities (i.e., ACs) is not the focus of thispaper. Accordingly, only a single AC, i.e., best effortAC, is considered.

2.2 p-persistent CSMA/CA model

Cali et al. [5] studied the DCF behavior with a p-persistent model. Instead of using the binary expo-nential backoff, the p-persistent model determines thebackoff interval by sampling from a geometric dis-tribution with parameter p. Thanks to the memory-less property of the geometric distribution, it is moretractable to analyze the p-persistent model. Based onthe geometric backoff assumption, the processes thatdefine the occupancy behavior of the channel (i.e., idle

. . . . . .

v-2 v-1 v v+1

Collision AIFSIdle

slotsCollision AIFS

Idle

slotsv-th Success AIFS

Idle

slotsSIFS ACK. . .

Figure 2 Illustration of virtual slots (μ) in the p-persistent model

slots, collisions, and successful transmissions) are re-generative, where the regenerative points correspondto completions of successful transmissions. The timeinterval between two consecutive successful transmis-sions is defined as a virtual slot. As shown in Fig. 2,the v-th virtual slot, denoted by μv , consists of thev-th successful transmission, as well as the precedingidle periods and collision periods. An idle period is atime interval during which all the backlogged stationsare performing backoff without transmission attempts.A collision period is the time interval during which twoor more stations transmit simultaneously and collidewith each other.

Statistically, standard DCF/EDCA operations andtheir p-persistent models are equivalent when the sta-tions are always active (i.e., when they always have aframe to transmit). However, when a station carrieslong-lived TCP flows, it may not always have a frame totransmit; for example, during the congestion avoidancephase, such station is allowed to transmit an addi-tional TCP Data only when it receives a TCP Ack forone of its outstanding TCP Data packets. Therefore,when analyzing the TCP dynamics over WLANs, thereare slight differences between standard DCF/EDCAoperations and their corresponding p-persistent mod-els. Nevertheless, our analysis is based on p-persistentmodels for simplicity, and the accuracy of the analysiswill be evaluated in Section 6.

2.3 Dynamics of long-lived TCP flows

Though there are different versions of TCP protocols,a TCP flow always operates in either slow-start or con-gestion avoidance phase regardless of the TCP version.The slow-start phase occurs during startup as well aswhen a timeout occurs at the sender due to packet loss.In this paper, we consider long-lived TCP flows so thatwe may ignore the effects of slow start since its fractionin the flow lifetime is very small.

In an early version of TCP, i.e., TCP Tahoe, thesender resets its congestion window to one MaximumSegment Size (MSS) and enters the slow start phaseafter each packet loss. This deficiency was remediedin later TCP versions such as TCP NewReno, whichhas been implemented in Microsoft Windows XP. Thekey difference between TCP NewReno and TCP Tahoe

Mobile Netw Appl

is the addition of Fast Retransmit and Fast Recoverymechanisms [12]. Fast Retransmit prevents the timeoutby retransmitting a packet when three duplicate ACKsare received at the sender. Fast Recovery cancels theslow start phase by setting the congestion window toapproximately half of its current value and keepingthe connection in the congestion avoidance phase. Al-though bursts of packet losses may still cause timeoutsat the sender and then force slow start to be invoked,TCP NewReno recovers from slow start much fasterthan earlier versions of TCP [7].

Because the current 802.11 WLAN has a smallerbandwidth than the wireline network, WLAN is verylikely to be the bottleneck in the round trip path of TCPtraffic. Therefore, most of the outstanding TCP packetsstay in the WLAN for most of their life time. Moreover,in the absence of frequent or bursty packet losses in thewireline network, the TCP send window may grow upto the maximum window size allowed by the receiver,i.e., the maximum TCP receive window size.

3 Analytical model for TCP dynamicsover the 802.11e EDCA without TXOP

In this section, we analyze the average number of ac-tive stations and the aggregate TCP throughput in an802.11e EDCA WLAN when the TXOP mechanismis not used. Then, we extend the analysis to take intoconsideration the TXOP mechanism in Section 4.

3.1 Network model and assumptions

We consider an infrastructure-based 802.11e WLANwith a single AP and NSTA stations; each station carrieslong-lived TCP flows. Stations either upload or down-load data from remote FTP servers. We conduct ouranalysis with the following assumptions for simplicityand the effects of some of the assumptions will bestudied in Section 6.

A1. The queue sizes of the AP and stations are largeenough to avoid buffer overflow.

A2. The successful transmission of each TCP Datapacket is notified by an immediate TCP Ackinstead of a delayed TCP Ack.

A3. As mentioned in Section 2.3, long-lived TCPflows usually operate in the congestion avoidancephase during most of their lifetime, as long aspacket loss does not occur in bursts frequently. Inour model, we assume ideal channel conditions(i.e., no hidden terminals, no channel error, andno capture effect). We will study the effects of

packet loss on the aggregate TCP throughput inSection 6.5.

A4. In practice, the TCP receive window size is asmall number, typically smaller than the TCPcongestion window size during the congestionavoidance phase. We also know that the numberof outstanding packets is determined by the mini-mum of the TCP congestion window size and theTCP receive window size. Based on this obser-vation and assumption A3, we assume that thenumber of outstanding packets (including TCPData and TCP Ack) for a TCP flow is equal to themaximum TCP receive window size (in packets).1

A5. There is no TCP Ack processing delay between aTCP Data reception and the corresponding TCPAck transmission. We will study the effect ofTCP Ack processing delay on the aggregate TCPthroughput in Section 6.4.

3.2 State space

Table 1 lists the notations and symbols used in ouranalysis. We use a discrete-time Markov chain to modelthe distribution of the numbers of stations carryingdifferent numbers of TCP packets in their queues atthe end of the v-th virtual slot in the p-persistentCSMA/CA model.−→

N (v) = (N0(v), N1(v), · · · , NW(v)) is the state vec-tor, where Ni(v) represents the number of stations,each of which carries i TCP packets in its queue at theend of the v-th virtual slot. We refer to such stationsas class-i stations. Therefore, N0(v) is the number ofstations without TCP packets in their queues. In otherwords, N0(v) is the number of inactive stations. W is themaximum TCP receive window size, or equivalently,the maximum number of outstanding TCP packets un-der assumption A4. For a class-i station, i packets residein its queue while the remaining (W − i) outstandingpackets reside in the AP queue.

Our Markov chain is shown in Fig. 3 with the indexof each state shown as the number above it. At State k,the following equation always holds:

NSTA =W∑

i=0

Nik, (2)

1The TCP window sizes are actually maintained in bytes. In ourmodel, for simplicity, we assume that the TCP Data packets havea fixed size and are transmitted at a fixed rate. Hence, the TCPwindow sizes can be measured in packets. Similar analysis couldbe done for variable packet sizes and multi-rate WLANs, whichis omitted due to space limitation.

Mobile Netw Appl

Table 1 List of notations and symbols

Term Definition

W Maximum TCP receive window size (in packets)M Total number of statesNSTA Total number of TCP stations in the WLAN

(excluding the AP)−→N k State k vectorNi

k i-th element of the State k vectorηk Number of active TCP stations in State kσ A backoff slot timePm,k State transition probability from State m to State kQAP

k Length of the AP queue in State k

PsuccSTA,k Probability that a non-AP station succeeds in

a transmission attempt in State kPsucc

AP,k Probability that the AP succeeds ina transmission attempt in State k

PiAP,k Probability that the AP succeeds in transmitting

a packet to a class-i station in State k.Pi

STA,k Probability that a class-i station succeeds intransmitting a packet in State k

where Nik is the i-th element of the State k vector, or

equivalently, the number of class-i stations at State k.Hence, N0

k is the number of inactive stations at State k.Consequently, the length of the AP queue (QAP

k ) andthe number of active TCP stations (ηk) at State k can becalculated by⎧⎨

⎩QAP

k =W∑j=0

N jk · (W − j),

ηk = NSTA − N0k.

(3)

Let M be the total number of states. The steady-stateprobability of the Markov chain is

πk = limv→∞ P

{−→N (v) = −→

N k

}, for each k ∈ [0, M − 1].

(4)

In this Markov chain, the state transition occursonly at the end of each virtual slot, which ends with asuccessful transmission. A transition from a right stateto a left state in Fig. 3 is caused by a station’s successful

transmission, and a transition from a left state to aright state is caused by a successful transmission bythe AP. For example, at State 2, the number of activestations (including the AP) is three. Each of the twonon-AP stations has exactly one TCP packet in itsqueue. If one of them ends the current virtual slot witha successful transmission, the transition from State 2to State 1 occurs. On the other hand, if the AP endsthe current virtual slot with its successful transmission,there are two possible cases. The first case is that theAP transmits a TCP packet to one of the (NSTA − 2)

inactive stations. In this case, the number of activestations becomes 2 + 1 = 3, hence the transition fromState 2 to State 4 occurs. The second case is that theAP transmits a TCP packet to one of the two activestations, each of which already has one TCP packet inits queue. As a result, the number of active stationsremains the same, while the station that just receivedthe TCP packet from the AP is allowed to add one morepacket to its queue. This means that the transition fromState 2 to State 5 has occurred.

3.3 State transition probabilities

We now derive the state transition probabilities. Asdiscussed above, during each transition, only two ele-ments of the state vector change their values and eachof them changes by one. This is because state transitionsare triggered by a single successful transmission fromeither the AP or a station. Therefore, the transitionprobability from State k to State m is given by

Pk,m =

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

PiAP,k, if ∃ a unique i ∈ [0, W − 1] such that

Nim = Ni

k − 1, Ni+1m = Ni+1

k + 1,

PiSTA,k, if ∃ a unique i ∈ [0, W − 1] such that

Nim = Ni

k + 1, Ni+1m = Ni+1

k − 1,

0, otherwise.

(5)

NSTA, 0, ··· NSTA-1,1, ··· NSTA-1,0,1, ··· NSTA-1,0,0,1 ··· NSTA-1,0,0,0,1, ···

NSTA-2,2, ··· NSTA-2,1,1 ···

NSTA-3,3, ···

NSTA-2,0,2, ···

NSTA-3,2,1, ···

NSTA-4,4, ···

NSTA-2,1,0,1, ···

···,0, NSTA···,1,NSTA-1···,1,0,NSTA-1

···,2,NSTA-2

. . .

. . .

. . .. . .

0 1 3

2

4

5

6

7

8

9

10

11 M-1M-2M-3

M-4

Figure 3 Our markov chain model to study TCP dynamics in WLANs

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The first equation in Eq. 5 accounts for the fact thatthe AP ends the current virtual slot with its success-ful transmission. Pi

AP,k is the probability that the APsuccessfully transmits its TCP packet to one of theclass-i stations. The second equation accounts for thefact that a station ends the current virtual slot with itssuccessful transmission. Pi

STA,k is the probability thata class-(i + 1) station succeeds in transmitting its TCPpacket.

We assume that the AP and a station access themedium with attempt probabilities τAP and τSTA, re-spectively, whose values will be derived in Section 3.6.Then, the probability Pi

AP,k is given by

PiAP,k = Psucc

AP,k · PAP(i)k , (6)

where

PsuccAP,k = P

(AP’s success

∣∣ a tx success at State k)

=

⎧⎪⎨

⎪⎩

τAP(1−τSTA)ηk

τAP(1−τSTA)ηk +ηkτSTA(1−τSTA)ηk−1(1−τAP),

NWk < NSTA,

0, NWk = NSTA,

(7)

and

PAP(i)k = P

(AP xmit to a class-i STA

∣∣ AP’s success)

={

Nik(W−i)QAP

k, QAP

k > 0,

0, QAPk = 0.

(8)

Similarly, the probability PiSTA,k is given by

PiSTA,k = Psucc

STA,k PSTA(i+1)

k , (9)

where

PsuccSTA,k = P

(STA’s success

∣∣ a tx success at State k)

= 1 − PsuccAP,k,

and

PSTA(i+1)

k = P(it is a class-(i + 1) STA

∣∣ STA’s success)

={

Ni+1k

NSTA−N0k, N0

k < NSTA,

0, N0k = NSTA.

(10)

3.4 Average number of active stations

Since the length of the virtual slot (i.e., the sojourntime) in each state varies, the average number of activestations (excluding the AP) is

E[Nactive] =M−1∑

k=0

ηk pk, (11)

where

pk = πkμk∑M−1j=0 π jμ j

, (12)

where μk is the sojourn time at State k. In the case ofdownload TCP flows, μk is given by

μk = E[Ncol

STA,k

]Tack

col + E[Ncol

AP,k

]Tdata

col

+ (E

[Ncol

k

] + 1) (

AIFS + E[T idle

k

])

+E[Tdata

k

] + SIFS + TACK. (13)

Here, Tackcol and E

[Ncol

STA,k

]are, respectively, the col-

lision time and the average number of collisions dueto contention among uplink TCP Acks. Tdata

col andE

[Ncol

AP,k

]are, respectively, the collision time and the

average number of collisions due to contention be-tween a downlink TCP Data and uplink TCP Acks.Moreover, E

[Tdata

k

]and TACK are the average TCP

packet transmission time and the MAC-layer ACKframe transmission time, respectively. E

[Ncol

k

]and

E[T idle

k

]are the average number of collisions and the

average idle time preceding a collision or a successfultransmission, respectively. On the other hand, in thecase of upload TCP, μk can be calculated by replacingTack

col with Tdatacol in Eq. 13, because at least one of the

colliding packets is a TCP Data, and hence the collisiontime is always Tdata

col .In the following, we derive individual elements used

in Eq. 13. E[Ncol

k

], E

[Ncol

AP,k

]and E

[Ncol

STA,k

]can be

expressed by⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

E[Ncol

k

] =∞∑

i=0i · P

(Ncol

k = i),

E[Ncol

AP,k

] =∞∑

i=0j · P

(Ncol

AP,k = j),

E[Ncol

STA,k

] = E[Ncol

k

] − E[Ncol

AP,k

],

(14)

where P(Ncol

k = i)

and P(Ncol

AP,k = j)

are the proba-bility that the total number of collisions is i and theprobability that the number of collisions due to theAP’s transmissions is j, respectively, which are given by{

P(Ncol

k = i) = (

Pcolk

)iPsucc

k ,

P(Ncol

AP,k = j) = (

PcolAP,k

) jPsucc

k .(15)

Psucck is the conditional successful transmission proba-

bility at State k given that at least one station (includingthe AP) transmits, which can be calculated by

Psucck = P

(Ntx

k = 1∣∣Ntx

k � 1)

=

⎧⎪⎪⎨

⎪⎪⎩

τAP(1−τSTA)ηk +ηkτSTA(1−τSTA)ηk−1(1−τAP)

1−(1−τAP)(1−τSTA)ηk ,

NWk < NSTA,

ηk·τSTA(1−τSTA)ηk−1

1−(1−τSTA)ηk , NWk = NSTA.

(16)

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Here, Ntxk denotes the number of transmitting stations

at State k. Pcolk is the conditional collision probability

given that at least one station transmits, which is Pcolk =

1 − Psucck . Moreover, Pcol

AP,k is the conditional probabil-ity that AP’s transmission fails given that at least onestation (including the AP) transmits, which is

PcolAP,k =

{τAP(1−(1−τSTA)ηk )

1−(1−τAP)(1−τSTA)ηk , NWk < NSTA,

0, NWk = NSTA.

(17)

The average idle time preceding a collision or asuccessful transmission in State k can be calculated as

E[T idle

k

] = σ

∞∑

i=0

iP(Ntx

k > 0) (

P(Ntx

k = 0))i

= σ(1 − τAP) (1 − τSTA)ηk

1 − (1 − τAP) (1 − τSTA)ηk. (18)

In the case of download TCP, the average TCP packettransmission time can be expressed as

E[Tdata

k

] = TTCP DATA PsuccAP,k + TTCP ACK Psucc

STA,k, (19)

where TTCP DATA and TTCP ACK are TCP Data and TCPAck transmission durations, respectively. In the caseof upload TCP, the positions of Psucc

AP,k and PsuccSTA,k are

exchanged in Eq. 19.

3.5 Aggregate TCP throughput

In the p-persistent CSMA/CA model [5], the aggregateTCP throughput (in bits/second) is given by

ρ = average length of a TCP Data (bits)average length of a virtual slot (seconds)

. (20)

In our analysis, with the assumption that there exista fixed number of active stations in a given state, thedownload TCP throughput at State k can be derived as

ρk = LTCP DATA PsuccAP,k

μk, (21)

where LTCP DATA is the TCP Data size and μk is thesojourn time at State k. Finally, the average aggregateTCP throughput can be calculated by

ρTCP =M−1∑

i=0

ρi pi. (22)

For the upload TCP throughput, PsuccAP,k is replaced by

PsuccSTA,k in Eq. 21. For the mixed case of upload and

download, we can calculate the TCP throughput by

modifying Eqs. 13 and 21, and details are omitted dueto space limitation.

3.6 Estimation of τ from CWmin at each state

In order to obtain the medium access probabilities τAP

and τSTA, we extend the Average Contention WindowEstimation algorithm in [5] by considering differentCWmin sizes for the AP and stations. We assume thatτ = 1/(B + 1) where B is the average number of back-off slots, and is equal to (CW + 1)/2 [5]. Because theaverage contention window size CW is determined byCWmin and the number of active stations in a givenstate, we can estimate τ from CWmin in each stateusing an iterative algorithm. The algorithm used inthis work is based on and improves upon the one weproposed in [16] by considering different CWmin sizesfor the AP and stations.

4 Analytical model for TCP dynamicsover the 802.11e EDCA with TXOP

In this section, we extend the analysis in Section 3to consider the TXOP mechanism. For simplicity, werepresent TXOPLimit as the maximum number of datapackets which the AP or a station can transmit withoutadditional backoff when it grabs the channel. Let ξAP

and ξSTA denote TXOPLimits (in packets) of the APand a station, respectively.

The number of active stations and the aggregate TCPthroughput depend on the distribution of TCP packetsin the AP queue. That is, when the packets directed todifferent stations are uniformly distributed in the APqueue, a TXOP burst from the AP may activate manyinactive stations. On the other hand, when the packetsdirected to the same station are grouped in the APqueue, a TXOP burst from the AP may activate lessnumber of inactive stations. In our analysis, we assumethat the packets in the AP queue are uniformly distrib-uted. This is reasonable since all the TCP sessions startfrom the slow start phase and each station randomlyaccesses the channel.

4.1 State transition probabilities

With the TXOP mechanism, though the state space ofthe Markov chain remains the same, the state transitionpatterns are different and the transition probabilitiesneed to be re-derived. The probability that the transi-tion from State k to State m occurs can be derived asfollows.

Mobile Netw Appl

4.1.1 Transitions caused by TXOP of the AP (k < m)

With TXOP, the AP may transmit multiple TCP pack-ets after a contention success. Hence, multi-hop statetransitions may occur in the Markov chain. Recallthat only single-hop transitions between linked statesare possible when TXOP is not used. Moreover, withTXOP, the state transition probability from State k toState m is equal to the sum of the probabilities of allpossible paths (in the increasing order of the state indexalong each path) from State k to State m in Fig. 3. Thepossible paths are determined by the order of packettransmissions in a TXOP. For example, there are twopossible paths from State 1 to State 5 in Fig. 3, which are1→2→5 and 1→3→5. The probability that the statetransition occurs following a particular path from Statek to State m is the product of the transition probabilitiesbetween each pair of neighboring states along the path.Let State i and State j (i < j) be a pair of neighboringstates along a path from State k to State m. Then fromEqs. 5 and 6, the transition probability from State ito State j given that the AP succeeds in accessing thechannel at State i is

P′i, j =

{Pi, j

PsuccAP,i

, i < j,

0, otherwise.(23)

Using Eq. 23, we construct an M × M matrix A,where the element corresponding to row i and columnj is P

′i, j. The diagonal and below-diagonal elements of

A are zeros according to Eq. 23. Each above-diagonalelement of A represents the transition probability fromthe corresponding row state to column state, assumingthat the AP succeeds in accessing the channel at the rowstate; therefore, if the row and column states are notneighboring states in Fig. 3, the corresponding elementof A is zero. Accordingly, if QAP

m − QAPk = n, i.e., if the

state transition from State k to State m is caused by nTCP packet transmissions by the AP, the probabilitythat the transition from State k to State m occurs giventhat the AP wins a TXOP at State k is the element ofthe matrix A

n that corresponds to row k and column m.More generally, when the AP succeeds in obtaining aTXOP at State k, the probability matrix that representsall the transition probabilities from State k to otherstates can be expressed as

Xk =⎧⎨

⎩

AξAP , QAP

k � ξAP,

AQAP

k , 0 < QAPk < ξAP,

0, otherwise,

(24)

where ξAP is the TXOPLimit (in packets) for the AP.Finally, we can derive the transition probabilities fromState k to State m (k < m) as

Pk,m = PsuccAP,k Xk(k, m), (25)

where Xk(k, m) is the element of the matrix Xk corre-sponding to row k and column m, and is the conditionaltransition probability from State k to State m given thatthe AP succeeds in obtaining a TXOP at State k.

4.1.2 Transitions caused by TXOP of a station (k > m)

In the case of state transition caused by a station’sTXOP, there exists only one possible path from State kto State m (k > m) because a station only transmits itspackets to the AP. This is different from the multiplepossible paths in the case of state transition caused bythe AP’s TXOP.

If there exists an i ∈ [1, W] such that Nim = Ni

k − 1,the transition probability from State k to State m, assum-ing that a station succeeds in getting a TXOP at State k,can be expressed as

P′′k,m =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

Nik

NSTA−N0k, i > ξSTA,

Ni−ξSTAm = Ni−ξSTA

k + 1,

Nlm = Nl

k, l �= i, l �= i − ξSTA,Ni

k

NSTA−N0k, i ≤ ξSTA,

N0m = N0

k + 1,

Nlm = Nl

k, l �= i, l �= 0,

0, otherwise,

(26)

where l ∈ [0, W]. Otherwise, P′′k,m is always zero. Fi-

nally, the transition probability from State k to State m(k > m) is given by

Pk,m = PsuccSTA,k P

′′k,m. (27)

4.2 Average number of active stations and aggregateTCP throughput

The sojourn time at State k in the case of download TCPflows is given by

μk = E[Ncol

STA,k

]Tack

col + E[Ncol

AP,k

]Tdata

col

+ (E

[Ncol

k

] + 1) (

AIFS + E[T idle

k

])

+E[TTXOP

k

], (28)

where E[Ncol

k

], E

[Ncol

AP,k

], E

[Ncol

STA,k

], and E

[T idle

k

]

can be calculated using Eqs. 14 and 18 because

Mobile Netw Appl

using TXOP does not affect the channel contention.E

[TTXOP

k

]is the average TXOP duration used in

State k:

E[TTXOP

k

] = E[TTXOP

AP,k

]Psucc

AP,k + E[TTXOP

STA,k

]Psucc

STA,k,

(29)

where E[TTXOP

AP,k

]and E

[TTXOP

STA,k

]are the average

TXOP durations which the AP and one of the activestations use for multiple TCP packet transmissions atState k, respectively, and are given by

E[TTXOP

AP,k

] =

⎧⎪⎪⎨

⎪⎪⎩

min(QAP

k , ξAP)

· (TTCP DATA + 2SIFS + TACK)

−SIFS, QAPk > 0,

0, otherwise,

(30)

E[TTXOP

STA,k

] =

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(W∑

i=1PSTA(i)

k min (i, ξSTA)

)

· (TTCP ACK + 2SIFS + TACK)

−SIFS, ηk > 0,

0, otherwise,

(31)

where PSTA(i)k is the conditional probability that a class-

i station succeeds in accessing the channel given that astation wins the channel access at State k as in Eq. 10.On the other hand, in the case of upload TCP, μk canbe calculated by replacing Tack

col with Tdatacol in Eq. 28,

TTCP DATA with TTCP ACK in Eq. 30, and TTCP ACK withTTCP DATA in Eq. (31).

Using Eqs. 11, 25, 27, and 28, we can calculate theaverage number of the active stations (excluding theAP). Moreover, the download TCP throughput at Statek can be derived as

ρk = min(QAPk , ξAP)LTCP DATA Psucc

AP,k

μk. (32)

In the case of upload TCP, the TCP throughput atState k is given by

ρk =

(W∑

i=1PSTA(i)

k min (i, ξSTA)

)LTCP DATA Psucc

STA,k

μk.

(33)

Finally, the average aggregate TCP throughput can becalculated using Eq. 22.

5 AP PIFS access

5.1 AP PIFS access without TXOP

As described in Section 2.1, AIFSN[AC] is an integergreater than 1 for stations and an integer greater than 0for the AP. Moreover, the values of CWmin[AC] andCWmax[AC] may be set to zero. Therefore, for theAP, we can use the smallest access parameter valuesof AIFSN[AC] = 1, CWmin[AC] = 0, and CWmax[AC] = 0 for downlink TCP packet transmissions. Thisallows the AP to transmit the pending TCP packetsafter a PIFS idle time without backoff. This schemeis referred to as PIFS Access in the rest of this paper.In [15], we have shown that, PIFS Access by the APcan improve the VoWLAN (Voice over WLAN) per-formance significantly.

When the AP does PIFS Access for TCP packettransmissions, all the outstanding TCP packets reside inthe queues of stations. As a result, the number of activestations is the same as the number of stations in theWLAN, and hence the behavior of stations is identicalto that of saturated UDP stations. The AP sends a TCPData (or TCP Ack) at PIFS time after it receives a TCPAck (or TCP Data) from one of the stations. That is, inFig. 3, the state transitions only occur between State (M-1) and State (M-2). When there are only download TCPflows, the aggregate TCP throughput with AP PIFSAccess can be calculated by

ρPIFS = LTCP DATA

μM−1 + PIFS + TTCP DATA + SIFS + TACK,

(34)

where μM−1 is the sojourn time at State (M-1) in Fig. 3.In the case of upload TCP, TTCP DATA in the denomina-tor of Eq. 34 is replaced by TTCP ACK.

5.2 AP PIFS access with TXOP

Employment of the TXOP mechanism does not af-fect the contention behaviors of the AP and stations.That is, the AP is assigned TXOP(s) to transmit thepending TCP packets after a PIFS idle time, and allthe outstanding TCP packets reside in the queues ofstations. Recall that ξAP and ξSTA are the TXOPLimits(in packets) of the AP and stations, respectively. There-fore, when there are only download TCP flows, we cancalculate the aggregate TCP throughput with AP PIFSAccess and TXOP by revising Eq. 34 as follows:

ρPIFS = ξSTA LTCP DATA

μM−1 + TPIFS, (35)

Mobile Netw Appl

Internet

FTP servers WLAN STAs(FTP Clients)

AP

Round trip time in wireline network (wireline delay)

Figure 4 The simulated network topology

where TPIFS is the time used to transmit TCP Datapackets by the AP after receiving TCP Ack packetsform a station, which is given by

TPIFS = PIFS⌈

ξSTA

ξAP

⌉− SIFS

⌈ξSTA

ξAP

⌉

+ ξSTA (TTCP DATA + 2SIFS + TACK) .

(36)

6 Simulation studies

In this section, we validate our model via ns-2 simula-tion [1]. We consider an IEEE 802.11b WLAN with asingle AP and seven stations that either download orupload large data files to remote FTP servers. Figure 4shows the network topology. As shown in the figure,the Round Trip Time (RTT) of TCP packets in thewireline network is referred to as the wireline delay.TCP NewReno is used for our simulation. Unless statedotherwise, we assume that the maximum TCP receivewindow size is W = 4 packets.2 Parameters used toproduce analytical and simulation results are summa-rized in Table 2. The considered values for CWmin are{2n − 1 |2 � n � 8}.

We first study how the TCP throughput performanceis affected by the CWmin and TXOPLimit values, as-suming no TCP Ack processing delay,3 no packet loss,and no wireline delay. Then, we show the effects ofthese parameters on the aggregate TCP throughput inSections 6.4 and 6.5.

2Actually, typical TCP configurations of commercial operatingsystems use a larger receive window size, e.g., the 12-packet(or 17520-byte) window used in MS Windows XP. We basicallyconsider the 4-packet receive window size in order to reduce thecalculation overhead; similar trends can be observed for otherreceive window sizes.3In this paper, TCP Ack processing delay is defined as timeduration between a TCP Data reception and the correspondingTCP Ack arrival at the MAC Service Access Point (SAP).

Table 2 Parameters used to produce analysis and simulationresults

Parameters Values

SlotTime 20 μsSIFS, PIFS, AIFS 10 μs, 30 μs, 50 μsCWmax 1023TXOPLimit VariableData, ACK Rates 11 Mbps, 2 MbpsPHY Overhead 192 μsACK length 14 bytesMAC Overhead 30 bytesTCP data frame Data (1460) + TCP/IP headers (40)

+ SNAP header (8)∗+ MAC/PHY overheads = 1538 bytes

TCP Ack frame TCP/IP headers (40) + SNAP header (8)+ MAC/PHY overheads = 78 bytes

∗When an IP datagram is transferred over 802.11 WLANs, itis usually encapsulated in an IEEE 802.2 Sub-Network AccessProtocol (SNAP) packet.

6.1 Effects of CWmin sizes

In this section, we study the effects of CWmin sizes ofthe AP and stations when the TXOP mechanism is notused.

6.1.1 When the AP and stations use the same accessparameters (including CWmin)

Figure 5 plots (a) the aggregate TCP throughput, (b)the collision rates experienced by the AP and a sta-tion, and (c) the average number of active stations(excluding the AP), for both download and uploadcases. We observe that analytical and simulation re-sults match very well for all simulated scenarios. InFig. 5a, in the case of download, the aggregate TCPthroughput of the 802.11 DCF (similar to EDCA withCWmin = 31) is about 4.46 Mbps while the maximumdownload throughput of about 4.56 Mbps is achievedwhen CWmin = 15. From this result, one may concludethat TCP over DCF is operating near the optimalthroughput point. Although this is true when the APand stations are required to use the same access para-meters, we will show in the subsequent subsection thatthe aggregate TCP throughput can be enhanced furtherby using different access parameters for the AP andstations.

The collision rate of a station is higher than that ofthe AP when CWmin is small. This is due to the factthat an active station contends with at least one station,i.e., the AP, because the AP is always active in thisscenario. Moreover, note that a station transmits longTCP Data and short TCP Ack for upload and downloadcases, respectively. Therefore, as CWmin decreases, the

Mobile Netw Appl

3 7 15 31 63 127 2552

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5

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Analysis, DownloadSimulation, DownloadAnalysis, UploadSimulation, Upload

(a) Aggregate throughput

3 7 15 31 63 127 2550

0.2

0.4

0.6

0.8

1

CWmin

Col

lisio

n ra

te

7 STAs, W = 4

AP collision rate, DownloadSTA collision rate, DownloadAP collision rate, UploadSTA collision rate, Upload

(b) Collision rate

3 7 15 31 63 127 2550

1

2

3

4

5

6

7

8

CWmin

Ave

rage

num

ber

of a

ctiv

e S

TA

s

7 STAs, W = 4

Analysis, DownloadSimulation, DownloadAnalysis, UploadSimulation, Upload

(c) Average number of active stations (ex-cluding AP)

Figure 5 TCP performance when the AP and stations use the same access parameters (including CWmin)

throughput in the upload case decreases more quicklythan the download case because the wasted time due tocollisions is more severe.

As shown in Fig. 5c, the average number of activestations remains small regardless of the CWmin size.This is due to (i) the closed-loop nature of TCP flowcontrol and (ii) the bottleneck downlink (i.e., AP-to-station transmissions) in the infrastructure-basedWLAN, as we have discussed in Section 1. Under suchscenario, the AP is the bottleneck because it uses thesame CWmin as stations but needs to serve multipleTCP flows.

6.1.2 When the AP and stations use different accessparameters

We study the aggregate TCP throughput performancewith various combinations of the CWmin sizes used by

the AP and stations. Figure 6 plots (a) the aggregateTCP throughput, (b) the collision rates experienced bythe AP and a station, and (c) the average number ofactive stations (excluding the AP), for the downloadcase. Similar results have also been observed for theupload case, which are omitted due to space limitation.

We have two sets of observations. First, whenCWminAP � CWminSTA, the AP’s downlink becomesa more severe bottleneck. The network is in a non-saturated state. As shown in Fig. 6c, the average num-ber of active stations (excluding the AP) is less thanor equal to one. As the gap between CWminAP andCWminSTA increases, the average number of active sta-tions decreases. This is due to the fact that most stationsspend more time idle, waiting for a TCP Data from theAP. On the other hand, it is interesting to see that theaggregate throughput does not increase monotonicallyas the gap decreases. For example, the combination

3 7 15 31 63 127 2552

2.5

3

3.5

4

4.5

5

STA CWmin

Agg

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(M

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7 STAs, W = 4

Analysis,Analysis,Analysis,Analysis,Analysis,

Simulation, ( AP CWmin = 3)Simulation, ( AP CWmin = 15)Simulation, ( AP CWmin = 31)Simulation, ( AP CWmin = 63)Simulation, ( AP CWmin = 127)

(a) Aggregate throughput

3 7 15 31 63 127 2550

0.1

0.2

0.3

0.4

0.5

STA CWmin

Col

lsio

n ra

te

7 STAs, W = 4

AP collision rate,AP collision rate,AP collision rate,AP collision rate,

STA collision rate, ( AP CWmin = 3)STA collision rate, ( AP CWmin = 15)STA collision rate, ( AP CWmin = 31)STA collision rate, ( AP CWmin = 63)

(b) Collision rate

3 7 15 31 63 127 2550

1

2

3

4

5

6

7

8

STA CWmin

Ave

rage

num

ber

of a

ctiv

e S

TA

s

7 STAs, W = 4

Analysis,Analysis,Analysis,Analysis,Analysis,

Simulation, ( AP CWmin = 3)Simulation, ( AP CWmin = 15)Simulation, ( AP CWmin = 31)Simulation, ( AP CWmin = 63)Simulation, ( AP CWmin = 127)

(c) Average number of active stations (ex-

cluding AP)

Figure 6 Download TCP performance when the AP and stations use different CWmin

Mobile Netw Appl

of CWminAP = 31 and CWminSTA = 7 yields a higherthroughput than the combination of CWminAP = 3 andCWminSTA = 3. This is because, the collision rates (es-pecially, the AP collision rate) increase as the gap de-creases, which may offset the effects of smaller numberof active stations under certain situations.

Secondly, when CWminAP < CWminSTA, packetcongestion at the AP bottleneck is alleviated. As thegap between CWminAP and CWminSTA increases, theaverage number of active stations increases, and iseventually saturated to 7 (i.e., all the stations are ac-tively contending). On the other hand, as shown inFig. 6b, the collision rates initially increase and thendecrease eventually. The reason is as follows. For agiven CWminAP, the number of active stations keepsincreasing until CWminSTA reaches a certain threshold;when CWminSTA becomes larger than this threshold,the number of active stations is saturated to 7 but theidle backoff time continues to increase. For example,when CWminAP is 3, such threshold for CWminSTA

is 31, which is shown in Fig 6c. In general, this thresh-old for CWminSTA varies with CWminAP, and a largerCWminAP corresponds to a larger threshold. Accord-ingly, we can clearly observe from the figure that, forsmall CWminAP values, the aggregate throughput firstdecreases (due to the increasing collision rate), thenincreases (due to the decreasing collision rate), andeventually decreases (due to the increasing idle backofftime). The reason that we do not observe similar behav-iors in the figure for larger CWminAP values is becausethe corresponding thresholds for CWminSTA are verylarge, beyond the x-axis range of the figure.

Comparing Fig. 6a with Fig. 5a, we can see that themaximum aggregate throughput in Fig. 6a is larger thanthat in Fig. 5a. It means that there exists at least oneoptimal combination of CWminAP and CWminSTA tomaximize the aggregate throughput. This fact is notsurprising since a similar fact has been well known forthe saturation throughput maximization in 802.11 DCFWLANs. According to [2, 5], there exists an optimalCWmin value that maximizes the saturation throughputfor a given number of stations. Unfortunately, it isvery difficult, if not impossible, to derive a closed-formexpression for the optimal CWmin combination in ourstudy, because the CWmin values and the number ofactive stations are mutually dependent in the case ofTCP.

6.2 Effects of TXOPLimit sizes

Figure 7 shows the aggregate download TCP through-put and the average number of active stations (ex-

1 5 10 15 20 25 30312.5

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3.5

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5

5.5

6

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(M

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AP TXOPLimit (packets)

Analysis, STA TXOPLimit = 1Simulation, STA TXOPLimit = 1Analysis, STA TXOPLimit = 2Simulation, STA TXOPLimit = 2Analysis, STA TXOPLimit = 4Simulation, STA TXOPLimit = 4

(a) Aggregate TCP throughput

1 5 10 15 20 25 30310

2

4

6

8

Ave

rage

num

ber

of a

ctiv

e S

TA

s

AP TXOPLimit (packets)

Analysis, STA TXOPLimit = 1Simulation, STA TXOPLimit = 1Analysis, STA TXOPLimit = 2Simulation, STA TXOPLimit = 2Analysis, STA TXOPLimit = 4Simulation, STA TXOPLimit = 4

(b) Average number of active stations (excluding AP)

Figure 7 Download TCP performance when the TXOP mechan-ism is used. CWmin is set to 31 for both the AP and stations

cluding the AP) when the TXOP mechanism is usedfor both the AP and stations. CWmin is set to 31for both the AP and stations. Note that setting theTXOPLimit to one packet is equivalent to not usingthe TXOP mechanism. As shown in the figure, whenthe TXOPLimits of both the AP and stations arelarge, the aggregate throughput can be improvedfurther. This is because the TXOP mechanism allowsmultiple packet transmissions without additional con-tention overhead (i.e., backoff or wasted time due tocollisions). When the AP TXOPLimit is small, differentstation TXOPLimit sizes do not make much differencein the aggregate throughput. This is because the APis bottleneck, and hence the number of active stationsis small as shown in Fig. 7b and active stations donot have many packets to transmit even though theirTXOPLimits could be large. On the other hand, whenthe AP TXOPLimit is much larger than the station TX-OPLimit, a larger station TXOPLimit yields a higherthroughput, because most of the packets reside in thequeues of stations and a larger station TXOPLimitallows more packets to be transmitted during a TXOP.Similar trends have also been observed with otherCWmin values for the AP and stations, and simulationresults are omitted due to space limitation.

6.3 Effects of AP PIFS access

Figure 8 plots the aggregate TCP throughput and thecollision rate when the AP uses PIFS Access for its

Mobile Netw Appl

3 7 15 31 63 127 2553.5

4

4.5

5

5.5

STA CWmin

Agg

rega

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(M

b/s)

Analysis, DownloadSimulation, DownloadAnalysis, UploadSimulation, Upload

(a) Aggregate TCP throughput

0 0.1 0.2 0.3 0.4 0.5 0.6 0.73.5

4

4.5

5

5.5

Collision rate

Agg

rega

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(M

b/s)

DownloadUpload

(b) Collision rate vs. aggregate throughput

Figure 8 TCP performance when the AP uses PIFS Access butthe TXOP mechanism is not used

downlink transmissions but the TXOP mechanism isnot used. In the case of download, we observe that themaximum aggregate TCP throughput of PIFS Access ismuch higher than the previous two cases in Section 6.1.This is because, with PIFS Access, there is no colli-sion between the AP and stations, and hence less timeis wasted due to collisions. For example, when onlydownload TCP flows are present in the network, theAP transmits long TCP Data to stations and stationsrespond by transmitting short TCP Ack back to the AP.In this situation, if with PIFS Access, there are onlycollisions among stations, and hence the wasted time isequal to the TCP Ack transmission time; on the otherhand, if without PIFS Access, the AP’s transmissionmay collide with stations’ transmissions, the wastedtime is then equal to the TCP Data transmission time,which is about 4 times the TCP Ack transmission time.

Note that, with PIFS Access, the AP’s queue isalways empty and all the stations always have packetsto transmit. That is, PIFS Access makes the stationsbehave like saturated UDP stations. As a result, thedifficult problem of maximizing the TCP throughputis simplified and becomes equivalent to the easierproblem of maximizing the UDP saturation through-put. In [18], the authors showed that the maximumthroughput of a saturated UDP network is independentof the number of stations and, with 1000-byte MACframes, the maximum throughput is achieved when the

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Analysis, STA TXOPLimit = 1Simulation, STA TXOPLimit = 1Analysis, STA TXOPLimit = 2Simulation, STA TXOPLimit = 2Analysis, STA TXOPLimit = 4Simulation, STA TXOPLimit = 4

(a) Aggregate download TCP throughput

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Analysis, STA TXOPLimit = 1Simulation, STA TXOPLimit = 1Analysis, STA TXOPLimit = 2Simulation, STA TXOPLimit = 2Analysis, STA TXOPLimit = 4Simulation, STA TXOPLimit = 4

(b) Aggregate upload TCP throughput

Figure 9 TCP performance when the AP uses PIFS Access,stations use CWmin = 31, and the AP and stations use differentTXOPLimits

collision rate experienced by a station is about 0.2. Thisconforms to our simulation results shown in Fig. 8b.

Figure 9 shows the aggregate TCP throughput ofdownload case (Fig. 9a) and upload case (Fig. 9b) whenthe AP uses PIFS Access and the TXOP mechanismis used. CWmin is set to 31 for stations. Comparingwith Fig. 8a (i.e., PIFS Access without TXOP), onecan see that the throughput performance is much im-proved. This is due to the reduced contention amongstations by the usage of TXOP. As shown in the figure,the aggregate throughput is not affected by the APTXOPLimit size. Since AP PIFS Access makes mostof the TCP packets reside in the queues of stationsregardless of the AP TXOPLimit size, the aggregatethroughput depends only on the transmissions of thestations. Therefore, a larger station TXOPLimit yieldsa higher throughput.

So far, we have evaluated the effects of CWminvalues, TXOPLimit sizes, and AP PIFS Access with/outTXOP on the aggregate TCP throughput, but withoutconsidering TCP Ack processing delay, wireline delay,and packet loss. Next, we study the effects of theseparameters via simulation.

6.4 Effects of TCP Ack processing delay

Figure 10 shows the effects of TCP Ack processingdelay on the aggregate TCP throughput. We assume no

Mobile Netw Appl

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= CWminSTA

= 31

250 300 350 400 450 5004.4

4.45

4.5

4.55

4.6

4.65

4.7

Simulation

Analysis

µ

Figure 10 The effects of TCP Ack processing delay (with nowireline delay) when all stations download data from FTP servers

wireline delay in this scenario. In general, we observethat, with non-zero TCP Ack processing delay, theaggregate throughput deviates little from our analysisresult (i.e., 4.46 Mbps) by at most 5%. This means thatour analysis is reasonably accurate even with the sim-plifying assumption of no TCP Ack processing delay.As shown in the figure, the throughput increases whenthe TCP Ack processing delay is around 308 μs. This isdue to the immediate access behavior that was discussedin Section 2.1. The reason can be explained as follows.Figure 11 shows the timing diagram of the AP and astation that receives a TCP Data from the AP. If theTCP Ack is generated within duration A in Fig. 11, theMAC starts backoff at the end of duration A becauseit senses the channel busy. On the other hand, if theTCP Ack is generated within duration B, the MAC

TCP DATA

ACK

BusyBackoff

SIFS AIFS

A B

ACK processing delay

The two cases of TCP ACK arrival at MAC

TCP Client in aTCP station

MAC of TCP

MAC of AP

station

Figure 11 Illustration of the TCP Ack processing delay in astation when it downloads data from a server via the AP

might send the TCP Ack immediately without backoff.Note that the length of duration A is 308 μs = SIFS(10 μs) + TACK (248 μs) + AIFS (50 μs). In the lattercase, in order to have immediate access, the stationshould satisfy the following two conditions when itreceives TCP Data from the AP:

– It has already finished the post backoff;– It is not contending for the channel to transmit a

packet (i.e., TCP Ack).

Most stations satisfy the above conditions because theyremain idle for most of the time while waiting for TCPData from the AP due to AP bottleneck and TCP flowcontrol.

050

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hput

(M

b/s)

(b) W = 12

Figure 12 The effects of wireline delay and packet loss on theaggregate TCP throughput when all stations download data fromFTP servers. W is the maximum TCP receive window size (inpackets)

Mobile Netw Appl

6.5 Effects of wireline delay and packet loss

Figure 12 shows the effects of wireline delay (from 0to 200 ms) and the end-to-end packet loss rate (from0.1% to 5% according to [14]) on the aggregate TCPthroughput. Results with the maximum TCP receivewindow sizes of W = 4 and W = 12 are shown inFigs. 12a and 12b, respectively. It is clear from thefigure that our model produces accurate results whenthe wireline delay is small and the packet loss rate islow, i.e., when the WLAN is the bottleneck.

However, when the wireline delay gets larger, theWLAN is not the bottleneck anymore. That is, theaggregate TCP throughput is dominantly-determinedby the wireline delay. We observe that the aggregateTCP throughput decreases as the wireline delay in-creases. Moreover, packet loss accelerates the through-put degradation. We observe that the higher the packetloss is, the more quickly the aggregate throughput de-creases as the wireline delay increases. The reason isas follows. High packet loss rate causes TCP timeoutand in turn reduces the number of outstanding TCPpackets, because TCP send window shrinks to one MSSafter timeout.

Figure 12b shows that a larger maximum TCP re-ceive window results in a bigger applicable region (i.e.,the flat region) for our model. This is because, with alarger maximum TCP receive window, more outstand-ing TCP packets are allowed in the network, and hencethe WLAN may remain as the bottleneck even in thepresence of larger wireline delay and/or higher packetloss rate.

7 Conclusion

In this paper, we conduct rigorous and comprehensivemodeling and analysis of the TCP performance overEDCA-based IEEE 802.11e WLANs, and show thatthe aggregate TCP throughput can be enhanced via aproper selection of channel access parameters for theAP and stations. In particular, we show that the bestaggregate throughput performance can be achieved viaAP’s contention-free access for downlink transmissionsand the TXOP mechanism. Moreover, some of theassumptions used in our model are evaluated via sim-ulation, and results show that our model is reasonablyaccurate, particularly, when the wireline delay is smalland/or the packet loss rate is low. Future work includesoptimization of the 802.11e performance when consid-ering other types of traffic such as VoWLAN.

Acknowledgements This work was in part supported by theITRC support program of MKE/IITA (IITA-2008-C1090-0801-0013 and IITA-2008-C1090-0803-0004).

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Jeonggyun Yu received his B.E. degree in School of ElectronicEngineering from Korea University, Seoul, Korea in 2002. Heis currently working toward his Ph.D. in the School of Elec-trical Engineering at Seoul National University (SNU), Seoul,Korea. His research interests include QoS support, algorithmdevelopment, performance evaluation for wireless networks, inparticular, IEEE 802.11 wireless local-area networks (WLANs).He is a student member of IEEE.

Sunghyun Choi is currently an associate professor at the Schoolof Electrical Engineering, Seoul National University (SNU),Seoul, Korea. Before joining SNU in September 2002, he waswith Philips Research USA, Briarcliff Manor, New York, USAas a Senior Member Research Staff and a project leader for threeyears. He received his B.S. (summa cum laude) and M.S. degreesin electrical engineering from Korea Advanced Institute of Sci-ence and Technology (KAIST) in 1992 and 1994, respectively,and received Ph.D. at the Department of Electrical Engineeringand Computer Science, The University of Michigan, Ann Arborin September, 1999.

His current research interests are in the area of wireless/mobile networks with emphasis on wireless LAN/MAN/PAN,next-generation mobile networks, mesh networks, cognitive ra-dios, resource management, data link layer protocols, and cross-layer approaches. He authored/coauthored over 120 technicalpapers and book chapters in the areas of wireless/mobile net-works and communications. He has co-authored (with B. G.Lee) a book “Broadband Wireless Access and Local Networks:Mobile WiMAX and WiFi,” Artech House, 2008. He holds 15

US patents, nine European patents, and seven Korea patents, andhas tens of patents pending. He has served as a General Co-Chairof COMSWARE 2008, and a Technical Program Committee Co-Chair of ACM Multimedia 2007, IEEE WoWMoM 2007 andIEEE/Create-Net COMSWARE 2007. He was a Co-Chair ofCross-Layer Designs and Protocols Symposium in IWCMC 2006,2007, and 2008, the workshop co-chair of WILLOPAN 2006, theGeneral Chair of ACM WMASH 2005, and a Technical ProgramCo-Chair for ACM WMASH 2004. He has also served on pro-gram and organization committees of numerous leading wirelessand networking conferences including IEEE INFOCOM, IEEESECON, IEEE MASS, and IEEE WoWMoM. He is also serv-ing on the editorial boards of IEEE Transactions on MobileComputing, ACM SIGMOBILE Mobile Computing and Com-munications Review (MC2R), and Journal of Communicationsand Networks (JCN). He is serving and has served as a guesteditor for IEEE Journal on Selected Areas in Communications(JSAC), IEEE Wireless Communications, Pervasive and MobileComputing (PMC), ACM Wireless Networks (WINET), Wire-less Personal Communications (WPC), and Wireless Communi-cations and Mobile Computing (WCMC). He gave a tutorial onIEEE 802.11 in ACM MobiCom 2004 and IEEE ICC 2005. Sinceyear 2000, he has been a voting member of IEEE 802.11 WLANWorking Group.

He has received a number of awards including the YoungScientist Award (awarded by the President of Korea) in 2008;IEEK/IEEE Joint Award for Young IT Engineer of the Year2007 in 2007; the Outstanding Research Award in 2008 and theBest Teaching Award in 2006 both from the College of Engi-neering, Seoul National University; the Best Paper Award fromIEEE WoWMoM 2008; and Recognition of Service Award in2005 and 2007 from ACM. Dr. Choi was a recipient of the KoreaFoundation for Advanced Studies (KFAS) Scholarship and theKorean Government Overseas Scholarship during 1997–1999 and1994–1997, respectively. He is a senior member of IEEE, and amember of ACM, KICS, IEEK, KIISE.

Daji Qiao is currently an assistant professor in the Departmentof Electrical and Computer Engineering, Iowa State Univer-sity, Ames, Iowa. He received his Ph.D. degree in ElectricalEngineering-Systems from The University of Michigan, AnnArbor, Michigan, in February 2004. His current research inter-ests include modeling, analysis and protocol/algorithm design forvarious types of wireless/mobile networks, including IEEE 802.11Wireless LANs, mesh networks, and sensor networks. He is amember of IEEE and ACM.