I. J. Communications, Network and System Sciences. 2008; 1: 1-103
Published Online February 2008 in SciRes (http://www.SRPublishing.org/journal/ijcns/).
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
Influence of the Limited Retransmission on the
Performance of WLANs Using Error-Prone
Channel
Haider M. ALSABBAGH1, Jianping CHEN, Youyun XU
Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, P.R.China
Abstract
In WLANs, stations sharing a common wireless channel are governed by IEEE 802.11 protocol. Many conscious
studies have been conducted to utilize this precious medium efficiently. However, most of these studies have been done
either under assumption of idealistic channel condition or with unlimited retransmitting number. This paper is devoted
to investigate influence of limited retransmissions and error level in the utilizing channel on the network throughput,
probability of packet dropping and time to drop a packet. The results show that for networks using basic access
mechanism the throughput is suppressed with increasing amount of errors in the transmitting channel over all the range
of the retry limit. It is also quite sensitive to the size of the network. On the other side, the networks using four-way
handshaking mechanism has a good immunity against the error over the available range of retry limits. Also the
throughput is unchangeable with size of the network over the range of retransmission limits. However, the throughput
does not change with retry limits when it exceeds the maximum number of the backoff stage in both DCF’s mechanisms.
In both mechanisms the probability of dropping a packet is a decreasing function with number of retransmissions and
the time to drop a packet in the queue of a station is a strong function to the number of retry limit, size of the network,
the utilizing medium access mechanism and amount of errors in the channel.
Keywords: IEEE802.11 DCF, WLAN, MAC Protocol, Throughput, Error-prone Channel.
1. Introduction
Next generation communications networks are being
investigated thoroughly to satisfy its ultimate goal:
accessible at any time and anywhere. One key point to
satisfy such aim is to increase both data rate and
processing speed [1][2]. The Wireless local area networks
(WLANs) are able to comply with such demands and
have become one of the fastest growing segments in the
communications industry, especially with utilizing the
new version of its protocol IEEE 802.11n [3]. The
worldwide shipments of the WLAN equipment products
reach $5.9 billion in 2006, and it is expected that WLAN
equipment will continue to grow in 2007 to reach around
$6.5 billion level as new IEEE 802.11n and VoWi-Fi
equipment is introduced and the infrastructure for
traditional Wi-Fi expands [3][4]. In 1997 IEEE’s
committee standardized 802.11 protocol for WLANs [5].
Since that time several versions of this protocol have been
made. The physical media in the WLANs is shared
between all stations and has limited connection range
compared with its wired counterpart. The standard defines
three PHY technologies and a unified MAC protocol to
support 1 and 2 Mbps transmission over wireless media.
The MAC protocol has two functions, namely distributed
coordination function (DCF) and the optional point
coordination function (PCF). DCF has superior
attractiveness over PCF in many aspects [6], therefore
this study is conducted to investigate WLANs utilizing
DCF. DCF defines two mechanisms to access
transmission medium: the basic access scheme, which is
the default scheme and the request to send/clear to send
(RTS/CTS) scheme, also known as four-way handshaking
scheme [4][7][8]. Recently, considerable studies have
been concentrated on modeling the IEEE 802.11 DCF
medium access method. Bianchi in [9] modeled the
idealistic assumption of collision only errors and packet
retransmits are unlimited; a packet is being transmitted
continuously until its successful reception. Wu in [10]
extended Bianchi’s analysis to include the finite packet
retry limits as defined in the standard. Both studies used
Markov chain model to analyze DCF operation and
calculated the saturated throughput of 802.11 protocol.
Periklais et al. [11] extended the work in [9] and [10] by
taking into account both: transmission errors and packet
retry limits for basic access of the IEEE802.11a protocol.
X. Wang et al. [12] evaluate the impact of transmission
error rate on the contention and the system throughput in

50 H.M.ALSABBAGH ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
WLAN’s protocol. However, [11] and [12] considered the
probability of bit errors appearing on the transmission
channel is the same in the two access mechanisms. Z.
Tang et al. [13] presented an analytical model to evaluate
the performance of the DCF in the case of bit errors
appearing on the transmission channel and taking type of
the used mechanism into account. However, Tang’s study
was under assuming of unlimited retransmitting. In this
paper we extend Tang’s work by taking into account
influence of retransmissions and investigate its impacts
on the performance of the WLANs. The results show that
the throughput is insensitive to the number of the
retransmissions when it exceeds the maximum number of
backoff stages in both mechanisms. This insensitive trend
does not change with amount of BER in the utilizing
channel. However, adopting four-way handshaking
mechanism show that the throughput is more immunes
than its counterpart mechanism when WLAN‘s channel
suffers from much error. This paper is organized as
follows: Section 2 devoted to explain the used model in
this study. Explanations for the achieved results are given
in Section 3 and then our conclusions are drawn to
Section 4.
2. The Model
The analysis employs the Markov chain model in [8]
and [10] and makes use of the same assumptions as in
[13]: all stations always have a packet available for
transmitting (saturation case) into an error prone-channel.
2.1. A Brief Description of the Backoff Process in
IEEE 802.11 DCF
When stations sense that the medium is idle for a
period, more than DCF, the backoff timer value for each
station is uniformly chosen within the interval ,
where is the current contention window (cw) size and
i is the backoff stage and m represents the
station’s retry limit. The backoff counter for every station
depends on the collision and on the successful packet
transmissions experienced by the station in the past. At
the beginning: and after each retransmitting due
to a packet collision or error, is doubled up to a
maximum value,, where m' is the maximum
number of the backoff stages. When reaches , it
will stay at this value until it is reset to again either
after the successful data the counter reaches to its limit.
2.2. The analytical modeling1
As in [10], the probability of a station to transmit a
packet in a randomly chosen slot time is:
(1)
where:
does not depend on the type of the mechanism
adapted by a station: basic access or four-way
handshaking, P is the unsuccessful probability when a
transmitted packet encounters a collision with at least
one of the remaining stations in a time slot. So:
(2)
Influence of errors in the transmitting channel is
included through the parameter PC as [13]: In the case of
basic access mechanism:
(3-a)
where . In the case of
four-way handshaking:
(3-b)
When a station transmits and the remaining n- 1
stations defer their transmissions, the packet would be
arriving successfully with probability PS. Considering the
probability that a random slot is empty (1-Ptr), probability
of successful transmission is PtrPs and probability of the
collision is Ptr (1-PS), the average length of a slot time is:
(4)
Consequently, the system throughput,, can be
expressed by dividing the successfully transmitted
payload data over a slot time. The probability of dropping
a packet when the retry limit is reached is known as the
packet drop probability and given as:
(5)
A packet is dropped when it reaches the last backoff stage
and experiences another collision or an error.
3. Performance Analysis
3.1. Influence of the Retry Limits on the Network
Characteristics
This analysis is based on the model in [13] and we
have included influence of limited number of
retransmissions. To validate our evaluation and highlight
influence of limited retries we compare our results, after
taking influence of limited retries, with results that have
been gotten by using the model in [12] and with that
using model given in Ref. [13]. The results are illustrated
in Figure 1. The same parameters values in [13] have
1Definition and values of all the rest parameters that do not
mentioned here are as in Ref. [13].

INFLUENCE OF THE LIMITED RETRANSMISSION ON THE PERFORMANCE OF WLANS 51
USING ERROR-PRONE CHANNEL
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
been used in this study in order to facilitate the
comparison purpose. In Figure 1 our results denoted as (a),
results of Ref. [13] denoted as (b) and the results that
obtained by using the model in [12] denoted as (c). The
system throughput has been estimated for three different
network sizes: 5 (small), 20 (middle), and 50 (large).
Figure 1 shows that: for networks utilizing the basic
access, results (a) are much closer to results (b) in the
small and middle network sizes and much close to results
(c) for the large networks over all the range of BERs. This
can be justified since on the small and middle networks
the rate of collisions is relatively small compared with
that in large networks, which indicates that influence of
retransmission at small and middle networks is also small.
For networks utilizing the four-way handshaking, all
results: (a), (b) and (c) show that the throughputs are
insensitive to size of the networks over all the examined
range of the BERs. While almost all the results are mostly
closed when BERs less than 10-5, there is a difference
between the results (a) and (b) in one side and results (c)
on the other side when 10-5 <BER<10-4. This difference is
due to the effect of the parameter PC on P, which could be
much sensible at higher level of BERs. Considering errors
in the channel, PC in the Ref. [12] did not distinguish the
used access mechanism as it did in [13] and in ours as
shown in Eq. 3.
Figure 2 illustrates variation of the network throughput
with number of retransmissions at low level of BERs =
10-5 (Figure 2a) and at relatively high level of BERs 10-4
(Figure 2b). It is obvious that trend of the network
throughput is almost unchangeable with level of errors in
the channel when a network uses the four-way
handshaking scheme. In the contrary side, when the
networks use basic access, the throughput level is
obviously decreased with increasing errors in the channel
over all the retransmission range. Figure 3 shows that
probability to drop a packet is exponentially decreasing
with number of retransmissions and has undistinguishable
differences between the two access mechanisms.
However, this probability is increasing function of errors
in the channel. Probability of dropping a packet is
ignorable when the network exceeds the maximum
number of backoff stage2 with low level of BER (see
Figure 3 a). This leads to enforce packets stay at queue of
the transmitter for a long time and cause much delay,
which could be unacceptable for some delay-sensitive
applications. Furthermore, Figure 4 a and b show that the
average time to drop a packet when adapting four-way
handshaking is lower than that when using basic access at
low level of BER and it becomes more obvious at high
level of BER (as in Figure 4-b). These are beneficial of
using RTS/CTS packets by reserving the channel in
advance before starting to transmit a long data packet and
hence supporting reduction the rate of collisions.
3.2. Network Characteristics with Specific
Number of Retransmissions
In this section, the model that developed in the section
2 will be used to investigate some characteristics of
WLANs. IEEE 802.11b is considered with retry limits = 5.
Figure 5 shows packet delay with channel capacity C= 1,
5.5 and 11 Mbps against the number of contending
stations. Results indicate that packet delay increases
linearly with increasing number of stations due to
increase rate of collisions and hence increasing number of
retry, which also causes increase of packet drop
probability as clarified in Figure 6. However, Figure 7
shows that as transmission rate increases the packet drop
time decreases remarkably. This is due to the time spent
for packet transmission decreases as the data rate
increases [11]. For large network sizes, the probability of
collision increases and hence number of retransmitting
increases for each sharing station. As a result, a station to
get a chance to establish the new transmitting at large
networks is lower than that in the small networks. Thus,
the time to drop a packet in small networks is much
suppressed, compared with that in large networks. For
instance, for an access point in WLAN covering an area
of 50 contending stations, the drop time is 7.57 s at
1Mbps bit rate and is 1.12 s at 11 Mbps bit rate. Thus,
from Figure 5, the corresponding packet delays are 573
ms and 85 ms, respectively. Figures 8 and 9 indicate that
using long packet payload leads to large packet delay and
packet drop times. This is due to the collision time, TC
which is proportional to the packet size as: ,
where L= (PHY header + MAC header) + packet payload,
and δis the propagation delay. The collision time is
defined as the average time the channel is sensed busy by
the stations during a collision. On the other side, the delay
of a successful packet depends on the average number of
slots required for a packet to experience m+1 collisions in
the (0,1,……,m) stages and also depends on average slots
time, which is proportional to the number of contending
stations, and channel bit rates. Results in figures 8 and 9
investigate three different WLAN sizes: 5, 40, and 70
with three different channel bit rates: 1, 5.5 and 11 Mbps,
the packet delay and packet drop time is linearly
increasing with size of payload.
4. Conclusion
In this paper, an analytical model is developed to
include influence of limited number of retransmissions on
the main characteristics of WLANs that use error-prone
channels. The model has been applied on the two
available mechanisms in the DCF functions. We validate
our evaluations by comparing our results with the results
in two considered references. This study shows that: the
networks using four-way handshaking mechanism have a
2 Extensive calculations for different values have been done, and all the
obtained results were valid and assist the result stated in this paper:
Probability of dropping a packet is ignorable when the network exceeds
the maximum number of backoff stage.

52 H.M.ALSABBAGH ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
good immunity against the increasing error in the
transmitting channel over the range of retransmissions,
also WLAN’s throughput is unchangeable with size of the
network over the range. On the other side, for the
networks using basic access mechanism, the throughput is
suppressed with increasing amount of errors in the
transmission channel over all the available range of the
retry limits as well as it is sensitive to the size of the
network. Further, the throughput does not change with
retry limits when it exceeds the maximum number of
backoff stages in both DCF’s mechanisms. In the both
mechanisms probability of dropping a packet is
decreasing function with number of retransmissions and
the time to drop a packet in the queue of a station is
strong function to the number of retry limits, size of the
network, the utilized mechanism and the amount of errors
in the transmitting channel. Also, the study investigates
characteristics of the IEEE 802.11b with a specific
number of retry limits. The achieved results indicate that
packet delay increases linearly with increasing number of
stations due to increasing rate of collisions and hence
increasing number of retry, which also causes increase of
packet drop probability. Also, the network performance is
strongly dependent on channel bit rate and the used
packet length with adapting specific number of
retransmission.
5. References
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[4] M. Etoh, “Next Generation Mobile Systems 3G and
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[6] H. Zhu and I. Chlamtac, “An Analytical Model for
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INFLUENCE OF THE LIMITED RETRANSMISSION ON THE PERFORMANCE OF WLANS 53
USING ERROR-PRONE CHANNEL
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
Figure 1. Throughput comparison for different network size
(n=5, 20 and 50): (a) our results, (b) results from Ref. [13],
and (c) results obtained using the model in Ref.[12]
(b) BER = 10-4
Figure 2. Throughput efficiency of the two mechanisms as a
function of retry limit for different network sizes
(b) BER = 10-4
Figure 3. Impact of retry limit on the drop probability for
different network sizes

54 H.M.ALSABBAGH ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
(b) BER = 10-4
Figure 4. Influence of retry limit on the time to drop a
packet for different network sizes
Figure 5. Packet delay with different channel capacities as a
function of number of contending stations.
Figure 6. Packet drop probability against number of
contending stations.
Figure 7. Packet drop time with different channel bit rates
versus number of contending stations.
Figure 8. Packet delay against packet payload size for
different contending stations and channel bit rates.
Figure 9. Packet drop time against packet payload length for
different WLANs sizes and channel bit rats.