Page 1

Differentiation, QoS Guarantee, and

Optimization for Real-Time Traffic

over One-Hop Ad Hoc Networks

Yang Xiao, Senior Member, IEEE, and Yi Pan, Senior Member, IEEE

Abstract—Nodes having a self-centrically broadcasting nature of communication form a wireless ad hoc network. Many issues are

involved to provide quality of service (QoS) for ad hoc networks, including routing, medium access, resource reservation, mobility

management, etc. Previous work mostly focuses on QoS routing with an assumption that the Medium Access Control (MAC) layer can

support QoS very well. However, contention-based MAC protocols are adopted in most ad hoc networks since there is no centralized

control. QoS support in contention-based MAC layer is a very challenging issue. Carefully designed distributed medium access

techniques must be used as foundations for most ad hoc networks. In this paper, we study and enhance distributed medium access

techniques for real-time transmissions in the IEEE 802.11 single-hop ad hoc wireless networks. In the IEEE 802.11 MAC, error control

adopts positive acknowledgement and retransmission to improve transmission reliability in the wireless medium (WM). However, for

real-time multimedia traffic with sensitive delay requirements, retransmitted frames may be too late to be useful due to the fact that the

delay of competing the WM is unpredictable. In this paper, we address several MAC issues and QoS issues for delay-sensitive real-

time traffic. First, a priority scheme is proposed to differentiate the delay sensitive real-time traffic from the best-effort traffic. In the

proposed priority scheme, retransmission is not used for the real-time traffic, and a smaller backoff window size is adopted. Second,

we propose several schemes to guarantee QoS requirements. The first scheme is to guarantee frame-dropping probability for the real-

time traffic. The second scheme is to guarantee throughput and delay. The last scheme is to guarantee throughput, delay, and frame-

dropping probability simultaneously. Finally, we propose adaptive window backoff schemes to optimize throughput with and without

QoS constraints.

Index Terms— Distributed medium access control, IEEE 802.11, quality of service, real-time transmission, ad hoc networks.

?

1

A

hoc wireless networks, peer-to-peer nodes conduct initi-

alization, organization, and administration of networks.

Many challenges must be overcome to obtain the practical

benefits of ad hoc networks, including routing, medium

access control (MAC), mobility management, power man-

agement, security, and quality of service (QoS) issues [1].

The nodes of an ad hoc network communicate directly with

one another in a peer-to-peer fashion, and each node must

function as a router. Power capacity and transmission range

are further limited by the mobility of these nodes. Due to

the mobility, the network topology is dynamically changed.

Furthermore, the limited bandwidth of wireless channels

and hostile transmission characteristics impose additional

constraints. For ad hoc networks with a contention-based

MAC layer, the nature of contentions further imposes

challenges for QoS support.

Many researches [1], [2], [3], [4], [5] on ad hoc networks

have been reported, and real-time transmissions for

Ethernet and cellular networks have been well studied [6],

INTRODUCTION

D hoc wireless networks consist of a collection of

mobile stations without a fixed infrastructure. In ad

[7], [8], [9], [10]. However, most researches [1], [2], [3], [4],

[5] focus on ad hoc routing protocols under the assumption

that some underline MAC protocols can provide good

services to higher layers. In this paper, we focus on

designing good MAC mechanisms for real-time transmis-

sions in ad hoc networks. Without the MAC layer’s support,

QoS support solely in higher layers is not possible.

Carefully designed distributed medium access techniques

must be used for channel resources so that mechanisms are

needed to recover efficiently from the inevitable frame

collisions [1].

We are particularly interested in ad hoc networks with

the underneath IEEE 802.11 distributed MAC since it is

available. The IEEE 802.11 MAC employs a mandatory

contention-based channel access function called Distributed

Coordination Function (DCF), and an optional centrally

controlled channel access function called Point Coordina-

tion Function (PCF) [11]. The popularity of the IEEE 802.11

market is largely due to the DCF, whereas the PCF is barely

implemented in current products due to its complexity and

inefficiency for normal data transmissions. The DCF adopts

a carrier sense multiple access with collision avoidance

(CSMA/CA) with binary exponential backoff. Functions of

the DCF and the PCF determine when a station/node,

operating within a Basic Service Set (BSS) or Independent

BSS (IBSS), is permitted to transmit. There are two types of

802.11 networks: Infrastructure Network (BSS) in which an

access point (AP) is present and ad hoc Network (IBSS) in

which an AP is not present. In this paper, we are

particularly interested in ad hoc networks formed by

multiple IBSSs in which no AP is present. There have been

538IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16,NO. 6,JUNE 2005

. Y. Xiao is with the Computer Science Division, The University of

Memphis, 373 Dunn Hall, Memphis, TN 38152.

E-mail: yangxiao@ieee.org.

. Y. Pan is with the Department of Computer Science, Georgia State

University, University Plaza, Atlanta, GA 30303.

E-mail: pan@cs.gsu.edu.

Manuscript received 29 Dec. 2003; revised 16 Sept. 2004; accepted 19 Sept.

2004; published online 21 Apr. 2005.

For information on obtaining reprints of this article, please send e-mail to:

tpds@computer.org, and reference IEEECS Log Number TPDS-0243-1203.

1045-9219/05/$20.00 ? 2005 IEEE Published by the IEEE Computer Society

Page 2

many performance studies for the DCF. Bianchi [13]

proposed a simple and accurate analytical model to

compute saturation throughput. Bianchi and Xiao enhanced

Bianchi’s original model in [18]. Calı ` et al. [20] studied an

optimization method for a p-persistent WLAN MAC.

Several priority studies have been reported in the

literature for the DCF. Deng and Chang [12] proposed a

priority scheme by differentiating the backoff window: the

higher priority class uses the window ½0;2jþ1? 1? and the

lower priority class uses the window ½2jþ1;2jþ2? 1?, where j

is the backoff stage. Aad and Castelluccia [21] proposed a

priority scheme achieved by differentiating interframe

spaces (IFS). Ahn et al. [19] proposed priority schemes by

differentiating the initial backoff window size and the

maximum window size. Pallot and Miller [22] proposed a

prioritized backoff time distribution mechanism, in which

the backoff time is chosen in the current window range with

different distributions for different priorities. All the

priority schemes [12], [19], [21], [22], [23] were based on

simulations. Related recent work also includes Sheu et al.

[25] about priorities for Ad hoc networks, and Ge and Hou

[26] about priority analysis for p-persistent WLANs.

In the DCF, error control adopts positive acknowl-

edgment and retransmission to improve transmission

reliability in the wireless medium (WM). In other words,

every transmitted frame needs a positive acknowledgment.

If an acknowledgement for a transmitted frame has not

been received for a timeout period, the transmitted frame is

assumed corrupted, and the frame will be retransmitted for

many times until a positive acknowledgement is received or

the number of retransmissions reaches a limit. In the later

case, the frame is dropped. Therefore, the DCF is a very

robust protocol for the best-effort service in the WM.

However, the current DCF is unsuitable for real-time

applications with QoS requirements. In the DCF a station

might have to wait an arbitrarily long time to send a frame

so that real-time applications such as voice and video may

suffer [12]. Furthermore, for real-time multimedia traffic

with sensitive delay requirements, retransmitted frames

may be too late to be useful due to the unexpected delay.

In this paper, we consider two classes of traffic: delay

sensitive real-time (RT) traffic and best-effort (BE) traffic.

The RT traffic can be voice or video. The BE traffic is normal

data transmission. A priority scheme is proposed to

differentiate RT and BE classes. For the RT class, retrans-

mission is not used and a smaller backoff window size is

adopted. The BE class still follows the original DCF. Such a

scheme is similar to video/multimedia over UDP. The

rationale is the same as the rationale of UDP. An analytical

model for the proposed priority scheme (differentiating the

RT and the BE priority classes) is proposed to evaluate

system performance, and validated via simulations. The

proposed real-time differential mechanisms are a little

similar to recently IEEE 802.11e draft [24]. However, the

proposed mechanisms are much simpler than IEEE 802.11e

as well as other priority schemes in the literature, and more

likely to be used in real products in which the IEEE 802.11e

has not been implemented. In other words, they can be

implemented in the original IEEE 802.11a/.11b/.11g with

very little effort.

We further consider several QoS and optimization issues.

WeproposeseveralschemestoguaranteeQoSrequirements:

the first scheme is to guarantee frame-dropping probability

for the real-time traffic; the second scheme is to guarantee

throughput and delay; the last scheme is to guarantee

throughput, delay and frame-dropping probability simulta-

neously. Finally, we propose adaptive window backoff

schemes to optimize throughput with and without QoS

constraints, based on the fact that there exists an optimal

initial backoff window size for a fixed traffic load.

The rest of the paper is organized as follows: The IEEE

802.11 CSMA/CA is introduced in Section 2. Service

differentiation, its analytical model, and results are studied

in Section 3. QoS guarantee mechanisms are presented in

Section 4. Optimization schemes with adaptation and QoS

guarantee are proposed in Section 5. We conclude this

paper in Section 6.

2 CSMA/CA IN THE DCF

The IEEE 802.11 MAC employs a mandatory DCF and an

optional PCF. In a long run, time is divided into repetition

intervals called superframes. Each superframe starts with a

beacon frame, and the remaining time is further divided

into a contention-free period (CFP) and a contention period

(CP). The DCF works during the CP and the PCF works

during the CFP. If the PCF is not active, a superframe will

not include the CFP.

In the DCF, a station with a frame to transmit monitors

the channel activities until an idle period equal to a

distributed interframe space (DIFS) is detected. After

sensing an idle DIFS, the station waits for a random backoff

interval before transmitting. The backoff time counter is

decremented in terms of slot time as long as the channel is

sensed idle. The counter is stopped when a transmission is

detected on the channel, and reactivated when the channel

is sensed idle again. The station transmits its frame when

the backoff time reaches zero. At each transmission, the

backoff time is uniformly chosen in the range ½0;CW ? 1?,

where CW is the current backoff window size. At the very

first transmission attempt, CW equals the initial backoff

window size CWmin. After each unsuccessful transmission,

CW is doubled until a maximum backoff window size

value CWmaxis reached. Once it reaches CWmax, CW shall

remain at the value CWmaxuntil it is reset. CW shall be reset

to CWminafter every successful attempt to transmit, or the

retransmission counter reaches the retry limit Lretry. In the

later case, the frame will be dropped. After the destination

station successfully receives the frame, it transmits an

acknowledgment frame (ACK) following a short interframe

space (SIFS) time. If the transmitting station does not

receive the ACK within a specified ACK Timeout, or it

detects the transmission of a different frame on the channel,

it reschedules the frame transmission according to the

previous backoff rules.

The above mechanism is called the basic access mechan-

ism. To reduce the hidden station problem, an optional

four-way data transmission mechanism called Request-To-

Send (RTS)/Clear-To-Send (CTS) is also defined in DCF. In

the RTS/CTS mechanism, before transmitting a data frame,

a short RTS frame is transmitted. The RTS frame also

follows the backoff rules introduced above. If the RTS frame

succeeds, the receiver station responds with a short CTS

frame. Then, a data frame and an ACK frame will follow.

All four frames (RTS, CTS, data, and ACK) are separated by

an SIFS time. In other words, the short RTS and CTS frames

XIAO AND PAN: DIFFERENTIATION, QOS GUARANTEE, AND OPTIMIZATION FOR REAL-TIME TRAFFIC OVER ONE-HOP AD HOC...539

Page 3

reserve the channel for that data frame transmission which

follows.

3SERVICE DIFFERENTIATION

In this section, we study service differentiation between the

delay sensitive real-time (RT) traffic and the best-effort (BE)

traffic. We first introduce the priority scheme; then we

propose an analytical model to study performance of

service differentiation; and, finally, we present simulation

and numerical results.

3.1

The original IEEE 802.11 DCF does not support any priority

scheme. In this paper, we consider two classes of traffic: the

delay sensitive RT traffic and the BE traffic. The RT traffic

can be voice or video, and the BE traffic is normal data

transmission. The BE class still follows the original DCF.

For the RT-traffic, retransmission is not used no matter

whether the previous transmission successful or not.

Furthermore, The RT class has a smaller backoff window

size than the BE class: CWmin;RT< CWmin;BE, where

CWmin;RT and CWmin;BE are the initial backoff window

sizes for the RT class and the BE class, respectively. Let

CWmax;RTand CWmax;BEbe the maximum window sizes for

the RT class and the BE class, respectively. We have

CWmax;RT¼ CWmax;BE.

To implement the mechanism, we can simply let the

retransmission limit for the RT traffic become zero. There-

fore, retransmission mechanism will be automatically

disabled. Such a scheme is similar to video/multimedia

over UDP. The rationale is the same as the rationale of UDP.

A Priority Scheme to Differentiate RT and BE

3.2

In this section, based on Bianchi’s model [13], an analytic

model for the proposed priority scheme under high traffic

condition is proposed. The advantage of our model is to

provide priorities of the RT class and the BE class, whereas

Bianchi’s model [13] is for the original DCF. Furthermore,

compared to Bianchi’s model, many aspects are improved

such as underline assumptions and a very accurate delay

model. We assume that each station belongs to one and only

one priority class and always has frames ready to send.

Analytical Model

3.2.1 An Analytical Model

For convenience, let class 0 denote the RT class and class 1

denote the BE class. Let W0;0and W1;0denote CWmin;RTand

CWmin;BE, respectively. For the RT class, the backoff stage j

can only be zero, and the retry-limit Lretryis zero also. For

the BE class, let jðj ¼ 0;1;...;LretryÞ denote the jth backoff

stage and let W1;jdenote CW in the jth retry/retransmis-

sion (or the jth backoff stage). The relationships among

W1;j, CWmin;BE, CWmax;BE, and Lretryare given as follows:

W1;j¼

2jW1;0

2mW1;0¼ CWmax;BE

2jW1;0

for j¼0;1;...;m?1;

for j¼m;...Lretry;

for j¼0;1;...;Lretry;

if Lretry>m

if Lretry>m

if Lretry?m;

8

>

>

:

where m ¼ log2ðCWmax;BE=W1;0Þ and W1;0¼ CWmin;BE.

To understand the relationship of Lretryand m, we give

the following example: In the IEEE 802.11 MAC, the default

value of Lretryfor short packets is 7, however, the m value,

the maximum backoff stage, may be larger than Lretry or

smaller than Lretry depending on the values of CWmin;BE

and CWmax;BE. If CWmax;BE¼ 1;024 and CWmin;BE¼ 32, we

have m ¼ 5 < 7 ¼ Lretry; on the other hand, if CWmax;BE¼

2;048 and CWmin;BE¼ 8, we have m ¼ 8 > 7 ¼ Lretry.

For a given station in the priority i class ði ¼ 0;1Þ, bði;tÞ

is defined as a random process representing the value of the

backoff counter at time t, and sði;tÞ is defined as the

random process representing the backoff stage j, where j ¼

0 for class 0 and 0 ? j ? Lretryfor the BE class. The values of

the backoff counter bð0;tÞ and bð1;tÞ are uniformly chosen

in the ranges ½0;1;...W0;0? 1? and ½0;1;...W1;j? 1?, respec-

tively. Let pidenote the probability that a transmitted frame

collides, and pialso equals the probability that a station in

the backoff stage senses the channel busy. The bidimen-

sional random process fsði;tÞ;bði;tÞg is discrete-time

Markov chain under the assumptions that piis independent

to the backoff procedure. Therefore, the state of each station

in the priority i class is described by fi;j;kg, where j stands

for the backoff stage, and k stands for the backoff delay in

timeslots.

The state transition diagram for the priority 0 class is

shown in Fig. 1. As illustrated in Fig. 1, the retry limit is

zero. The state transition diagram for the priority 1 class is

shown in Fig. 2. As illustrated in the Fig. 2, in the Lretryth

backoff stage, the frame is dropped if a collision occurs. In

<

ð1Þ

540IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,VOL. 16,NO. 6,JUNE 2005

Fig. 1. State transmission diagram for the RT class (Class 0).

Fig. 2. State transmission diagram for the BE class (Class 1).

Page 4

Fig. 1, the non-null transition probabilities for class 0 are

listed as follows: We have the following transition

probabilities between states:

Prfð0;0;kÞjð0;0;0Þg ¼ 1=W0;0; for 0 ? k ? W0;0? 1

Prfð0;0;kÞjð0;0;kÞg ¼ p0; for 1 ? k ? W0;0? 1

Prfð0;0;kÞjð0;0;k þ 1Þg ¼ 1 ? p0; for 0 ? k ? W0;0? 2:

In Fig. 2, the non-null transition probabilities for class 1

are listed as follows:

Prfð1;0;kÞjð1;j;0Þg ¼1 ? p1

W1;0

and 0 ? j ? Lretry

for 0 ? k ? W1;0? 1

Prfð1;0;kÞjð1;Lretry;0Þg ¼ 1=W1;0; for 0 ? k ? W1;0? 1

Prfð1;j;kÞjð1;j;kÞg ¼ p1for 1 ? k ? W1;j? 1

and 0 ? j ? Lretry

Prfð1;j;kÞjð1;j;k þ 1Þg ¼ 1 ? p1for 0 ? k ? W1;j? 2

and 0 ? j ? Lretry

Prfð1;j;kÞjð1;j ? 1;0Þg ¼

W1;j

and 1 ? j ? Lretry:

Tounderstandhowtoobtaintheaboveequations,wegive

thefollowingexample:theoutputofthestateð1;Lretry;0Þwill

go into the state ð1;0;kÞ randomlyin Fig.2 and,therefore, we

have Prfð1;0;kÞjð1;Lretry;0Þg¼1=W1;0. Let bi;j;k¼limðt?>

1Þ Prfsði;tÞ ¼ j;bði;tÞ ¼ kg be the stationary distribution of

the Markov chain, where i ¼ 0;1. In steady state, we can

derive following relations through chain regularities. For

class 0, we have

p1

for 0 ? k ? W1;j? 1

b0;0;k¼W0;0? k

W0;0

1

1 ? p0b0;0;0for 1 ? k ? W0;0? 1

ð2Þ

X

W0;0?1

k¼0

b0;0;k¼ 1:

ð3Þ

Plugging (2) into (3), we have

b0;0;0¼

1

1 þ

1

1?p0

PW0;0?1

2ð1 ? p0Þ

k¼1

W0;0?k

W0;0

¼

2ð1 ? p0Þ þ ðW0;0? 1Þ:

ð4Þ

For class 1, we have

b1;j;0¼ pj

b1;j;k¼W1;j? k

1b1;0;00 ? j ? Lretry

1 ? p1b1;j;0;0 ? j ? Lretry;1?k? W1;j?1 ð6Þ

X

From (5), (6), and (7), we have

ð5Þ

W1;j

1

X

Lretry

j¼0

W1;j?1

k¼0

b1;j;k¼ 1:

ð7Þ

b1;0;0

1

PW1;j?1

PLretry

j¼0

1 þ

1

1?p1

k¼1

W1;j?k

W1;j

hi

pj

1

:

ð8Þ

Let ?iði ¼ 0;1Þ be the probability that a station in the

priority i class transmits during a generic slot time. A

station transmits when its backoff counter reaches zero, i.e.,

the station is at any of states fi;j;0g.

?0¼ b0;0;0

X

Let niði ¼ 0;1Þ denote the number of stations in the

priority i class. The probability pi that a station in the

backoff stage for the priority i class senses the channel busy

is given

ð9Þ

?1¼

Lretry

j¼0

b1;j;0¼ b1;0;01 ? pLretryþ1

1

1 ? p1

:

ð10Þ

p0¼ 1 ? ð1 ? ?oÞn0?1ð1 ? ?1Þn1

p1¼ 1 ? ð1 ? ?0Þn0ð1 ? ?1Þn1?1:

Note that pi is also the probability that a transmitted

frame collides when one more station also transmits during

a slot time. Substituting (1) and (11) and (12) to (9) and (10),

we can solve unknown parameters numerically. Then, we

can calculate pi from (11) and (12). Let pb denote the

probability that the channel is busy. It happens when at

least one station transmits during a slot time. Please note

that pbis different from pi. Therefore, we have

ð11Þ

ð12Þ

Pb¼ 1 ? ð1 ? ?0Þn0ð1 ? ?1Þn1:

ð13Þ

3.2.2 Saturation Throughput

Let ps;iði ¼ 0;1Þ denote the probability that a successful

transmission occurs in a slot time for the priority i class, and

let psdenote the probability that a successful transmission

occurs in a slot time. We have

ps;0¼ n0?0ð1 ? ?0Þn0?1ð1 ? ?1Þn1

ps;1¼ n1?1ð1 ? ?1Þn1?1ð1 ? ?0Þn0

ps¼ ps;0þ ps;1:

Let Siði ¼ 0;1Þ denote the normalized throughput for the

priority i class. Let ?, TEðLÞ, Ts, and Tcdenote the duration of

an empty slot time, the time to transmit the average

payload, the average time that the channel is sensed busy

because of a successful transmission, and the average time

that the channel has a collision, respectively. The prob-

ability that the channel is idle for a slot time is ð1 ? pbÞ, and

the probability that the channel is neither idle nor successful

for a slot time is ½1 ? ð1 ? pbÞ ? ps? ¼ ðpb? psÞ. We have,

Si¼

Eðpayload transmission time in a slot time for the i classÞ

Eðlength of a slot timeÞ

¼

ð14Þ

ð15Þ

ð16Þ

ps;iTEðLÞ

ð1 ? pbÞ? þ psTsþ ½pb? ps?Tc:

ð17Þ

Let TH, TACK, SIFS, L?, and TEðL?Þdenote the time to

transmit the header (including MAC header, PHY header,

and/or tail), the time to transmit an ACK, SIFS time, the

length of the longest frame in a collision, and the time to

transmit a payload with length EðL?Þ, respectively. For the

basics access method, we have

XIAO AND PAN: DIFFERENTIATION, QOS GUARANTEE, AND OPTIMIZATION FOR REAL-TIME TRAFFIC OVER ONE-HOP AD HOC...541

Page 5

Tbasic

s

Tbasic

c

¼ THþ TEðLÞþ SIFS þ TACKþ DIFS

¼ THþ TEðL?Þþ DIFS:

Please refer to [14] for calculating TEðL?Þ. Let TRTS and

TCTSdenote the time to transmit an RTS frame and the time

to transmit a CTS frame, respectively. For the RTS/CTS

access model, we have

ð18Þ

ð19Þ

Trts=cts

s

¼ TRTSþ SIFS þ TCTSþ SIFS þ THþ TeðLÞ

þ SIFS þ TACKþ DIFS

¼ TRTSþ DIFS:

ð20Þ

ð21Þ

Trts=cts

c

3.2.3 Frame Dropping Probability

Let Pi;dropði ¼ 0;1Þ denote the frame-dropping probability

for the priority i class. From Fig. 1, we observe that a frame

can be dropped only in state f0;0;0g if a collision occurs.

From Fig. 2, we observe that a frame can be dropped only in

state f1;Lretry;0g if a collision occurs. In other words, a

frame can be dropped when the retransmission counter

reaches the retry limit Lretry. Therefore, we have

P0;drop¼ p0

P1;drop¼ pLretryþ1

ð22Þ

ð23Þ

1

:

3.2.4 Saturation Delay

Saturation delay is the average delay under the saturation

condition, and it includes the medium access delay (due to

backoff, collisions, etc.), transmission delay, and interframe

spaces (such as SIFS). The average backoff delay depends

on the value of a station’s backoff counter and the duration

when the counter freezes due to others’ transmissions. Let

Xiði ¼ 0;1Þ denote the random variable representing the

total number of backoff slots, which a frame encounters

without considering the case when the counter freezes, for

the priority i class. For class 1, the probability that the frame

is successfully transmitted after the jth retry (which is the

ðj þ 1Þth transmission) is pj

backoff slots after the jth retry is

1ð1 ? p1Þ. The average number of

X

j

h¼0

ðW1;h? 1Þ=2:

Note that only successful transmissions are considered.

EðX0Þ ¼ð1 ? p0Þ

1 ? p0

X

W0;0? 1

2

¼W0;0? 1

X

2

ð24Þ

EðX1Þ ¼

Lretry

j¼0

pj

1 ? pLretryþ1

1ð1 ? p1Þ

1

j

h¼0

W1;h? 1

2

:

ð25Þ

Let Biði ¼ 0;1Þ denote the random variable representing

the total number of slots when the counter freezes, which a

frame encounters, for the priority i class. The portion of idle

slots is ð1 ? piÞ, which is used to decrease EðXiÞ. We have

EðBiÞ ¼

EðXiÞ

ð1 ? piÞpi:

ð26Þ

We can treat EðXiÞ and EðBiÞ as the total number of idle

slots and the total number of busy slots, which the frame

encounters during backoff stages, respectively. Let EðNretryÞ

denote the average number of retries for the priority 1 class.

The number of retries for the priority 0 class is zero. We

have

EðNretryÞ ¼

X

Lretry

j¼0

jpj

1 ? pLretryþ1

1ð1 ? p1Þ

1

:

ð27Þ

Let Diði ¼ 0;1Þ denote the random variable representing

the frame delay for the priority i class. Let T0 denote the

time that a station has to wait when its frame transmission

collides before sensing the channel again. Let TACK timeout

and TCTS timeout denote the duration of the ACK timeout

and the duration of the CTS timeout, respectively. Note that

EðNretryÞ is one less than the number of transmissions. The

average slot lengths are ?, ½Tsps=pbþ Tcðpb? psÞ=pb?, Tcþ To,

and Tsfor a idle slot at states fi;j;kg ðk > 0Þ, a busy slot at

states fi;j;kg ðk > 0Þ, a failed transmission slot for this

station at states fi;j0g, and a successful transmission at

states fi;j;0g, respectively. We have

EðD0Þ ¼ EðX0Þ? þ EðB0Þps

EðD1Þ ¼ EðX1Þ? þ EðB1Þps

þ EðNreryÞðTcþ ToÞ þ Ts

Tbasic

o

¼ SIFS þ TACK timeout

Trts=cts

o

¼ SIFS þ TCTS timeout:

pbTsþpb? ps

pbTsþpb? ps

pb

Tc

?

?

?

?

þ Ts

ð28Þ

pb

Tc

ð29Þ

ð30Þ

ð31Þ

3.3

In this section, we first validate the analytical model with

simulation results. Then, we study the proposed priority

scheme for delay sensitive real-time transmissions and best-

effort transmissions.

We use IEEE 802.11a as an example. IEEE 802.11a

parameters can be found in [14], [16], as well as how to

calculate THþ TEðLÞaccurately [14]. The data rate is 6Mbps

and the control rate is 6Mbps. The frame size is fixed as

1,024 bytes. As assumed in the analytical model, stations

always have frames ready to send.

Results

3.3.1 Simulation Validations

In this section, we conduct simulations to validate the

proposed analytic model. The IEEE 802.11a simulation

models had been developed based on IEEE 802.11a

standard [16] and OPNET Wireless LAN simulation model

8.0A (for IEEE 802.11b DCF). Furthermore, we adapt our

simulation model with similar assumptions as those in the

analytical model. The data rate is 6Mbps and the control

rate is 6Mbps. The frame size is fixed as 1,024 bytes. All the

simulation results have over 95 percent confidential inter-

vals. The simulation executing time is long: about 2 hours

per run in order to get long term results, and multiple runs

per case to calculate the confidential intervals.

Table 1 shows the simulation results vs. numerical results

when adopting the following parameters: Lretry¼ 7, W0;0¼

16, W1;0¼ 64, n0¼ n1, and CWmax;BE¼ 1;024. As illustrated

in the table, analytical results and simulation results match

542IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 6,JUNE 2005