Differentiation, QoS guarantee, and optimization for real-time traffic over one-hop ad hoc networks

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.

Full text

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 IEEEPublished 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.
2CSMA/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).

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