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Analytical analysis of applying packet fragmentation mechanismon IEEE 802.11b DCF network in non ideal channel with infiniteload conditions
Mohand Yazid • Louiza Bouallouche-Medjkoune •
Djamil Aıssani • Lilia Ziane-Khodja
� Springer Science+Business Media New York 2013
Abstract The analytical modeling and performance
analysis of the 802.11 network in all its various extensions
(802.11b, 802.11a, 802.11g, 802.11e, 802.11n, etc.) have
already been widely explored over the past years. How-
ever, the packet fragmentation mechanism (PFM), which is
proposed by the IEEE work group to reduce the impact of
bit error rate (BER) on the packet error rate (PER), has not
been considered in the analytical models proposed in the
literature. Yet, the PFM constitutes a key parameter to
achieve the best performances of 802.11 networks. In this
paper, we extend the Bianchi’s Markov chain model with
the PFM and the PER. Then, we analyze the performance
improvement level achieved with the PFM in an IEEE
802.11 network under the impact of BER and packet
length. The proposed analysis has been applied on the basic
access method of 802.11b network in saturated traffic
conditions. So, we have analyzed the throughput and the
mean response time of the 802.11 network. The obtained
theoretical results are validated by simulation.
Keywords Packet fragmentation mechanism (PFM) �Packet error rate (PER) � IEEE 802.11 networks �Analytical analysis � Simulation and validation
1 Introduction
The IEEE 802.11 is an international standard (ISO/IEC
8802-11) for wireless local area networks (WLANs). It was
released in 1999 [1], then reissued in 2007 [2] grouping
some amendments. The IEEE 802.11 standard includes
detailed specifications for both medium access control
(MAC) and physical (PHY) layers. In the MAC layer, the
standard defines the distributed coordination function
(DCF) and the optional point coordination function (PCF).
DCF is an asynchronous data transmission function, it is
available in ad hoc or infrastructure networks. PCF is used
for real time services, it is only available in infrastructure
networks. The DCF is based on the carrier sense multiple
access with collision avoidance (CSMA/CA). The
retransmission of collided packets, is managed according to
the binary exponential backoff (BEB) rules. DCF describes
two methods for packet transmission. The main method
used in DCF, is called basic access method. The optional
method is called request to send/clear to send (RTS/CTS).
A comprehensive description of DCF function can be
found in [2].
The practical performance of the IEEE 802.11 network
depends on the availability of transmission opportunities at
the underlying 802.11 card. In all cases, when transmission
opportunities are lost, 802.11 stations will be affected by
throughput drops, higher delay and unfairness. The Loss of
transmission opportunities arises from the combined MAC
and PHY environment at both sender and receiver on each
802.11 link [3]. The transmission failures in an IEEE
802.11 network occur mainly because of collisions or noise
errors [4]. Thereby, the transmission of a given data packet
can fail due to collision with the other transmission(s).
Otherwise, transmission attempt can also fail without col-
lision, since the wireless channel itself is error-prone due
to path loss, multi-path fading, interferences, etc. Detail
arguing of noise errors sources can be found in [5]. To
reduce the influence of noise errors on the transmitted data
packets, the IEEE work group have proposed the packet
M. Yazid (&) � L. Bouallouche-Medjkoune � D. Aıssani �L. Ziane-Khodja
LAMOS, Laboratory of Modeling and Optimization of Systems,
University of Bejaia, 06000 Bejaıa, Algeria
e-mail: [email protected]
123
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DOI 10.1007/s11276-013-0653-2
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fragmentation mechanism. This mechanism consists on
subdividing the data packets, which are larger than a
fragmentation threshold, into fragments. Thus, the data
packets are transmitted as a continuous chain of data
frames, which contains sequential fragments [2].
The wide popularity of the IEEE 802.11 standard has
encouraged many researchers to analytically model its
access mechanisms (see [6–18]). Modeling the IEEE
802.11 access mechanisms allows networks designers: to
identify appropriate values for the various parameters that
can achieve the best performance, to decide appropriate
network size according to the expected traffic and required
performance, or to prove the efficiency of mechanisms
which are designed to improve the 802.11 network per-
formances. The special issue on Recent Advances in IEEE
802.11 WLANs: Protocols, Solutions and Future Direc-
tions, presented by Chatzimisios et al. and published in
2009 [19], gives a collection of selected papers that rep-
resents advances towards the performance evaluation and
enhancement of IEEE 802.11 WLANs. In this paper, we
focus on the performance improvement level achieved in
an IEEE 802.11b DCF network by applying the packet
fragmentation mechanism under non ideal channel and
infinite load conditions. So, we introduce the packet frag-
mentation mechanism and the packet error rate in the
Bianchi’s Markov chain model [6], and we develop
mathematical models to compute the overall throughput
and the mean response time of the 802.11b version of the
IEEE 802.11 standard. These mathematical models can
also be generalized for the other versions of the IEEE
802.11 protocol such as IEEE 802.11e [20].
The remainder of this paper is organized as follows: an
overview of the packet fragmentation mechanism is pre-
sented in Sect. 2. Section 3 gives a review of previous
studies and underlines the motivation of applying the PFM
in an IEEE 802.11 network. The extension of Bianchi’s
model with the PFM and the PER is described in Sect. 4. In
Sect. 5, we analyze the performance improvement level
achieved in the 802.11b network by applying the PFM. The
accuracy of the proposed analytical model is validated in
Sect. 6. Section 7 concludes the paper.
2 Packet fragmentation mechanism overview
The process of data packet partitioning into smaller MAC
level frames, fragments, is called the packet fragmentation
mechanism. This mechanism creates fragments smaller
than the original data packet length, in order to increase the
reliability of data packet transmission. So, the PFM
increases the probability of successful transmission of a
data packet in cases where channel characteristics limit the
reliable reception for longer frames.
2.1 Packet fragmentation process
A data packet shall be fragmented if its length exceeds a
fragmentation threshold. Therefore, when a data packet is
received from the logical link control (LLC) sublayer that
would result in a length greater than a fragmentation
threshold, before the MAC header and frame check sequence
(FCS) are added, the data packet shall be fragmented. So, the
data packet is divided into smaller data fragments, each of
them is a frame no larger than a fragmentation threshold. An
illustration of the packet fragmentation mechanism is shown
in Fig. 1. The fragments resulting from the fragmentation of
a data packet, are sent as independent transmissions.
Therefore, each data fragment is separately acknowledged.
Thereby, the PFM permits transmission retries to occur per
fragment, rather than per packet. Moreover, the data frag-
ments of a single data packet are sent as a burst, using a single
invocation of the DCF medium access procedure.
2.2 Multiple data fragments transmission
The shortest interframe space (SIFS) is used to provide an
efficient data packet delivery mechanism. Once the source
station has won the access to the wireless channel, it shall
continue to send its data fragments until either all the data
fragments of a single data packet are sent, or an
ACKnowledgment (ACK) is not received for at least one
data fragment. So, when the source station transmits a data
fragment, it immediately monitors the wireless channel for
an ACK. The destination station receiving a valid data
fragment, sends an ACK in order to notify the correct
reception of the data fragment. Then, the SIFS period
following the reception of the ACK, attributes to the source
station the priority to continue (if necessary) with another
fragment (see Fig. 2). Otherwise, If the source station does
not receive an ACK for the transmitted data fragment, it
means that the data fragment transmission is failed. Con-
sequently, the source station shall attempt to retransmit the
failed data fragment after performing the backoff proce-
dure and the contention process. The source station that
contends for the wireless channel to retransmit a data
packet, starts with the last data fragment that has not been
acknowledged.
Fig. 1 Packet fragmentation process
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2.3 RTS/CTS utilization with the PFM
The following is a description of using the RTS/CTS col-
lision avoidance mechanism with the packet fragmentation
mechanism. The Duration/ID field contained in the RTS
and CTS frames, is used to set the network allocation
vector (NAV) of the other stations to the total period of the
Fragment0/ACK0 exchange sequence. Thus, the RTS/CTS
exchange sequence allows only to reserve the wireless
channel for the Fragment0/ACK0 exchange sequence.
Thereby, to avoid collisions on the next Fragment1/ACK1
exchange sequence, the total period of this exchange
sequence is indicated in the Fragment0 and ACK0 frames
(see Fig. 3). This shall continue until the last fragment,
which shall have its Duration/ID field set to 0. So, each
Fragment/ACK exchange sequence acts as a virtual RTS/
CTS exchange sequence. Thus, no further RTS/CTS frames
need to be generated after the RTS/CTS frames that began
the first Fragment/ACK exchange sequence.
3 Previous studies and motivations
The performance analysis of IEEE 802.11 networks has
been covered in several research works by either simula-
tion and experiment (see [21–34]) or by mathematical
modeling (see [35–45]).
In 2000, Bianchi [6] was the first author in the literature
who used a Markov chain model to analyze the DCF
operations, and who calculated the saturation throughput
of the IEEE 802.11 network. The saturation throughput is
the system throughput when each station always has a data
packet pending for transmission. Since the offered load is
maximized, it is clear that the saturation throughput is the
maximum throughput that can be achieved by the system.
However, Bianchi’s model exhibits several severe con-
straints. Firstly, the model does not follow correctly the
backoff rules as specified in the standard [2]. So, the
Bianchi’s model omits the fact that a station in a backoff
stage will not always decrease its backoff timer, and it
will not keep in the mth backoff stage until the data packet
is successfully transmitted. Secondly, the Bianchi’s model
does not derive other performance metrics, such as: the
average packet delay and the delay jitter. Yet, these per-
formance metrics are critical, in order to support real time
applications. Thirdly, the IEEE 802.11 DCF performance
under finite load conditions has not been covered. Since
saturation may be viewed as the limiting mode of opera-
tion when the arrival rates at all nodes tends to infinity,
the non-saturation mode may equivalently be considered
as the finite rate or finite load mode of operation. Finally,
the saturation throughput was evaluated under ideal
channel conditions. Since electromagnetic noise in large
cities is inevitable, the calculated throughput may be
Fig. 2 Transmission of
multiple data fragments using a
SIFS
Fig. 3 RTS/CTS utilization with a fragmented data packet
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overestimated. To address this void in Bianchi’s analytical
model, considerable studies have been devoted in the
literature.
In 2002, Vishnevsky and Lyakhov [46] presented an
analytical method to estimate the saturation throughput of
the 802.11 network under the assumption of an ideal
channel. The proposed method generalizes the existing
802.11 analytical models and advances them to take the
seizing effect into account. The seizing effect means that,
the station which has just completed successfully its
transmission, will have a better chance to win once again
the wireless channel rather than the other stations in the
network.
In 2005, Lyakhov and Vishnevsky in [47] extended their
analytical model presented in [46], in order to estimate the
saturation throughput of the IEEE 802.11 network under
the presence of noise. In addition, the authors proposed and
studied a modification of the 802.11 MAC protocol. Thus,
the proposed protocol is able to recognize the reason of a
transmission failure (collision or noise). Consequently, the
contention window is not increased if a failure happens due
to noise. Pham [48] presented a Markov chain model to
provide a comprehensive analysis of the IEEE 802.11b
DCF network under finite load and packet loss due to
queue overflow. The performance metrics derived by the
author are: the overall throughput, the packet loss proba-
bility and the average packet delay. Ni et al. [49] investi-
gated the saturation throughput achieved at the MAC layer
in both congested and error-prone channel. The authors
showed that channel errors have a significant impact on the
system performance. Kim et al. [50] proposed a rate-
adaptive protocol with dynamic fragmentation to enhance
the system throughput. The authors proposed to use mul-
tiple fragmentation thresholds for different data rates rather
than one fragmentation threshold like in the IEEE 802.11
standard.
In 2006, Li et al. [51] presented a theoretical model to
evaluate the saturation throughput for the Block Trans-
mission and Acknowledgment (BTA) scheme under error
channel conditions in the ad hoc mode. The authors showed
some advantages of BTA over the legacy MAC, and ana-
lyzed how to select a proper number of frames for each
transmission block. Smadi and Szabados [52] developed a
service that allows the current IEEE 802.11b MAC proto-
col to perform dynamic packet sizing and forward error
correction. The proposed service is designed to allow the
deployment of the IEEE 802.11b protocol in industrial
environments characterized by high BER and fast time
variation. Hneiti and Ajlouni [53] analyzed and evaluated
several methods to improve the throughput performance of
WLANs. Through simulation the authors demonstrated that
WLAN performance can be improved by tuning parame-
ters, such as: slot time, short inter-frame spacing, minimum
contention window, fragmentation threshold and RTS
threshold.
In 2007, Chang et al. [54] proposed an algorithm to
enhance system goodput through the dynamic optimal
fragmentation. Using an adaptive SNR estimator, the sen-
der estimates the SNR of the receiver, and chooses a
fragmentation threshold to shape arbitrary sized packets
into optimal length packets.
In 2008, Szczypiorski and Lubacz [55] proposed a
Markov chain model of the IEEE 802.11g (ERP-OFDM)
network, taking into account the effect of backoff timer
freezing, the limitation of the number of retransmissions,
maximum size of the contention window and the impact of
transmission errors. The authors showed that the saturation
throughput depends on the PER, which is a function of
BER and packet length. Bae et al. [56] estimated the
characteristics of the IEEE 802.11 DCF network in non-
saturation mode. The authors took into account two fea-
tures inherent to the non-saturated 802.11 DCF: (1) the
probability of asynchronous transmission performed with-
out preceding backoff for the first packet arriving at the idle
station, and (2) so-called post backoff, meaning that a
station must perform a backoff once after any of its
transmissions even if its queue becomes empty. Li et al.
[57] proposed an analytical model to analyze the channel
access delay and delay jitter of the IEEE 802.11 DCF in
saturation traffic conditions for both basic access and RTS/
CTS-based scheme. Using the proposed analytical model,
the authors studied the impact of initial contention window,
maximal backoff stage and packet size on channel access
delay and delay jitter of the 802.11 DCF. Lin-Fang et al.
[58] analyzed the average packet delay of the IEEE 802.11
DCF network under finite load conditions. Therefore, the
authors had employed a Markov chain model to derive the
channel access delay, and they had used an M/G/1 queue to
derive the queueing delay. Zheng and Nelson [59] studied
the cross-layer (between MAC and PHY) design problem
for IEEE 802.11 wireless networks. The authors focused on
the design of the optimal length of frame body for the real
wireless channel conditions. Bykowski et al. [60] investi-
gated the influence of fragmentation on the throughput
performance of 802.11b networks. The authors demon-
strated that combining fragmentation threshold tuning with
line-rate selection, allows to achieve high performance
level.
In 2009, Peng et al. [61] proposed a three dimensional
Markov model to estimate the saturation throughput of
RTS/CTS scheme in a noisy channel. The proposed model
takes into account the effect of BER on all frames, station
short and long retry limits. The authors evaluated the
influence of different bit error rates and different packet
lengths on saturation throughput. The presented study
shows that the channel bit error affects the system
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throughput significatively and an optimal frame size exists,
it can maximize the system saturation throughput. Raptis
et al. [62] introduced a comprehensive packet delay ana-
lysis for wireless networks based IEEE 802.11 DCF. The
authors developed mathematical models that calculate a set
of packet delay metrics, namely the average packet delay
for successfully transmitted packets, the average packet
delay of successfully transmitted packets experiencing a
specific number of collisions, the average packet drop time,
the delay jitter and the delay distribution. Li et al. [63]
proposed a novel scheme called aggregation with fragment
Retransmission (AFR) that exhibits the required properties
to achieve high efficiency at the MAC layer of the IEEE
802.11 standard. The authors also developed an analytical
model to evaluate the throughput and delay performance of
AFR over noisy channels, and compared AFR with similar
schemes in the literature.
In 2010, Senthikumar and Krishnan [64] proposed and
analyzed a modified backoff (MB) mechanism to decrease
the channel idle time in the IEEE 802.11 DCF under a
noisy channel. The authors proposed a notion that instead
of doubling the contention window in case of erroneous
packet retransmission, the backoff counter selects a counter
value from the same contention window. Otherwise, if a
collision occurs, the contention window is doubled to
reduce the collision in the network. In [65], Senthikumar
and Krishnan proposed and validated, by mathematical
modeling, a collision aware rate adaptation (CARA)
algorithm in the IEEE 802.11 DCF network. The proposed
CARA algorithm is able to differentiate collisions from
channel errors at the sender side without any feedback from
the receiver station, by using adaptive request-to-send
(RTS) or clear-to-send (CTS) exchange and clear channel
assessment (CCA).
In 2011, Bayraktaroglu et al. [40] studied the perfor-
mance of the IEEE 802.11 MAC protocol under a range of
jammers that covers both channel-oblivious and channel-
aware jamming. The authors considered two channel-
oblivious jammers: a periodic jammer that jams determin-
istically at a specified rate, and a memoryless jammer whose
interfering signals arrive according to a Poisson process.
Prakash and Thangaradj [66] presented an analytical model
for performance evaluation of the IEEE 802.11 DCF taking
into account packet retry limits and transmission errors
under non-saturated traffic conditions. The authors devel-
oped an expression for the non-saturation throughput as a
function of the number of stations, packet size and also
calculated SNR values using slow Rayleigh fading channel.
Kumar and Krishnan [67] presented a performance study of
the DCF of 802.11 networks considering erroneous channel
and capture effects under non-saturated traffic conditions
employing a basic access method. The authors used a mul-
tidimensional Markov chain model to characterize the
behavior of DCF and derived a generalized expression for
the station’s transmission probability.
In 2012, Keene and Carruthers [42] examined an algo-
rithm to estimate the location of packet collision in the
presence of bandlimited multipath channel. Furthermore,
the authors proposed an improvement to the collision
localization algorithm to further enhance its performance,
to compensate for the increased impairments of the mul-
tipath channel. Senthikumar and Krishnan [68] provided an
extended model for analytical analysis of the IEEE 802.11
network under a noisy channel. So, a reservation stage is
introduced in the proposed Markov chain model to reduce
unnecessary retransmissions in case of transmission failure
caused by channel error.
Through the studies presented previously, we note that
many researchers have been interested to analyze and
enhance the performance of IEEE 802.11 networks in non
ideal channel conditions. However, performance modeling
and analysis of applying packet fragmentation mechanism
on IEEE 802.11 MAC protocol under an error-prone
channel were still missing in the available literature. Yet,
the PFM is considered as the only existing solution, pro-
posed by the IEEE 802.11 work group, to reduce the
impact of bit error rate and packet length on the packet
error rate by splitting the data packet into smaller data
fragments (see the IEEE 802.11 standard [2]). The impact
of packet fragmentation mechanism on the packet error rate
is illustrated in Figs. 4 and 5. These figures show com-
parisons of PER variations between the cases of non-
fragmented and fragmented data packets according to bit
error rate values (see Fig. 4) and data packet lengths (see
Fig. 5), the PER expression is given by the Eq. (1). We
note on Fig. 4 that, for a specific length of data packet
(12,000 bits, for example), more the BER value is high,
more the PER value becomes important, because the PER
is in linear relationship with BER. We also note that,
applying packet fragmentation mechanism allows to reduce
significatively the impact of BER on the PER. Figure 5
Fig. 4 PER versus BER
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shows that, for a specific value of BER (10-4, for exam-
ple), more the data packet length is great, more the PER
value is highly increased, because the PER is in expo-
nential relationship with the data packet length. Figure 5
also shows that, the PFM maintains the PER at a constant
value whatever the data packet length.
PER ¼ 1� ð1� BERÞP: ð1Þ
It is true that, the Figs. 4 and 5 are trivial, and the
conclusions done on these figures can be easily deduced.
But, the main goal of drawing these figures is to give an
idea on the behavior of the packet fragmentation mecha-
nism in non ideal channel conditions, and to show how it
reduces the influence of BER and packet length on the
PER. In other words, we have demonstrated the useful and
the efficiency of using the packet fragmentation mecha-
nism, in order to reduce the amount of data lost due to
noise errors. Theoretically, the PFM provides a better
chance to a data packet to be transmitted successfully.
Consequently, the PFM plays a central role to increase the
overall throughput and to decrease the average packet
delay in an IEEE 802.11 network in all its various exten-
sions. So, a formal validation of packet fragmentation
mechanism is necessary to obtain exact quantitative results
about its performance improvement level achieved in an
IEEE 802.11 network under a noisy channel. The PFM can
be also combined with the recent proposed protocols and
algorithms which aim to improve the performance of IEEE
802.11 networks in an error-prone channel (see [11, 15, 34,
38, 39, 41]).
4 Analytical model of the 802.11 DCF with PFM
and PER
In this section, we describe our analytical model of the
IEEE 802.11 DCF with PFM and PER. Firstly, we extend
the Bianchi’s Markov chain model [6] with the PFM and
the PER, in order to estimate the probability that a station
transmits its packet in a given time slot. Secondly, we use
the Bianchi’s throughput analysis, to develop the saturation
throughput expression of the 802.11 network. Thirdly, we
model the 802.11 station as an M/G/1 queueing system
[69], to derive the mean response time of a data packet, by
applying the second formula of Pollaczek-Khinchin [70].
4.1 Assumptions, parameters and probabilities
of the 802.11 analytical model
The following is a list of assumptions of our analytical
model. The lists of parameters and probabilities are pro-
vided in Tables 1 and 2, respectively.
1. The channel is not ideal. Thereby, noise errors can
occur on the transmitted data packets, and cause losses
in the network.
2. All the data packets are of the same size. They are
divided into smaller data fragments, if their length is
greater than a fragmentation threshold.
3. We assume a fixed number of stations, each always
having a data packet available for transmission. In
other words, we operate in saturation conditions.
Fig. 5 PER versus packet length
Table 1 802.11 Analytical model parameters
Parameter Description
n Number of stations in the network
CW Contention window
m Maximum retry limit
m0 Minimum retry limit
i ith transmission attempt
w0 Minimum contention window
2m0w0 Maximum contention window
BOF Random backoff time chosen in CW
P Data packet length (header ? payload)
�P Data packet payload length
F Data fragment payload length
NF Number of data fragments in a data packet
MAC The length of MAC header
PHY The length of PHY header
T�P
RPacket transmission time with data rate R
TRF Fragment transmission time with data rate R
TMAC Time of MAC header transmission
TPHY Time of PHY header transmission
ACK Time of acknowledgment transmission
DIFS Time interval of DIFS
SIFS Time interval of SIFS
d Time of signal propagation
r An empty slot time
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4. The collision probability of a data packet is constant
and is independent of retransmissions number.
4.2 Packet transmission probability
We study the behavior of a single station with a Markov chain
model, and we obtain the stationary probability s that the
station transmits a packet in a generic slot time. This proba-
bility will be used to determine the saturation throughput and
the mean response time of the 802.11 network.
Let b(t) be the stochastic process representing the
backoff time counter for a given station.
Let s(t) be the stochastic process representing the
backoff stage ð0; . . .;m0; . . .;mÞ of the station at the time t.
For a node in backoff stage i, the backoff window size
wi is:
wi ¼2iw0 i�m0;2m0w0 i 2 ½m0 þ 1;m�:
�ð2Þ
Once the key approximation in Bianchi’s analytical
model is assumed, which means that, at each transmission
attempt, and regardless of the number of retransmissions
suffered, each packet collides with constant and independent
probability Pc, it is possible to model the bi-dimensional
process {s(t), b(t)} with the discrete-time Markov chain
depicted in Fig. 6. Particularly, we find in this Markov chain
model the state (0, - 1), which represents the transmission
state of data fragments following the first data fragment
successfully transmitted. This state is necessary in order to
differentiate between the transmission of the first data
fragment, which can encounter a collision or undergo noise
errors, and the following data fragments, which can only
undergo noise errors.
In this Markov chain, the only non null one-step tran-
sition probabilities are:
Pfi;kji;kþ1g¼1; i2ð0;mÞ; k2ð0;wi�2Þ:Pf0;�1ji;0g¼ð1�PrÞð1�Pf Þ; i2ð0;mÞ:Pf0;�1j0;�1g¼ð1�PeÞð1�Pf Þ:Pfi;kji�1;0g¼ Pr
wi; i2ð1;mÞ; k2ð0;wi�1Þ:
Pf1;kj0;�1g¼ Pe
w1;k2ð0;w1�1Þ:
Pf0;kjm;0g¼ 1w0½Prþð1�PrÞPf �; k2ð0;w0�1Þ:
Pf0;kji;0g¼ ð1�PrÞPf
w0; i2ð0;m�1Þ; k2ð0;w0�1Þ:
Pf0;kj0;�1g¼ ð1�PeÞPf
w0; k2ð0;w0�1Þ:
8>>>>>>>>>>>><>>>>>>>>>>>>:
ð3Þ
Let pi;k¼ limt!1PfsðtÞ¼ i;bðtÞ¼ kg;i2ð0;mÞ;k2ð�1;
wi�1Þ be the stationary distribution of the chain. The
closed-form solution for this Markov chain is:
pi;k ¼wi � k
wi
� a � p0;�1 i ¼ 0; k 2 ð0;wi � 1ÞPi
r � b � p0;�1 i 2 ð1;mÞ; k 2 ð0;wi � 1Þ:
�
ð4Þ
where,
• a ¼ Pmr �Pe�ð1�Pf ÞþPf
ð1�Pf Þ:ð1�Pmþ1r Þ.
• b ¼PePr�ð1�Pf ÞþPf
ð1�Pf Þ�ð1�Pmþ1r Þ.
Thus, by the relation (4), all the values pi,k are expressed
as a function of the value p0,-1 and packet retransmission
probability Pr. p0,-1 is finally determined by imposing the
normalization condition, that can be simplified as follows:Fig. 6 Markov chain model of 802.11 DCF with PFM and PER
Table 2 802.11 Analytical model probabilities
Probability Definition
s Packet transmission probability
Pc Packet collision probability
Pe Packet error probability
Pr Packet retransmission probability
Pf Probability to reach the end of the data packet
transmission after having transmitted all its fragments
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1¼Xm
i¼0
Xwi�1
k¼�1
pi;k
¼ p0;�1þXm
i¼0
pi;0 �Xwi�1
k¼0
wi� k
wi
¼ p0;�1 1þw0ð2PrÞm
0Peð1�Pf ÞþPrPf
� �ð1�Pm�m0
r Þ2ð1�Pf Þð1�Pmþ1
r Þð1�PrÞ
"
þ PrPeð1�Pf ÞþPf
2ð1�Pf Þð1�Pmþ1r Þþ
Peð1�Pf ÞþPrPf
� �ð1�Pm
r Þ2ð1�Pf Þð1�Pmþ1
r Þð1�PrÞ
þw0 Peð1�Pf ÞþPrPf
� �ð1�ð2PrÞm
0Þ
ð1�Pf Þð1�Pmþ1r Þð1� 2PrÞ
#:
ð5Þ
Hence, we have:
p0;�1 ¼2ð1� Pf Þð1� PrÞð1� 2PrÞð1� Pmþ1
r Þ� �ð1� PrÞð1� 2PrÞ � 2ð1� Pf Þð1� Pmþ1
r Þþ�
PrPeð1� Pf Þ þ Pf
�þ Peð1� Pf Þ þ PrPf
� ��
2w0ð1� PrÞ 1� ð2PrÞm0
� �þ ð1� 2PrÞ�
�w0ð2PrÞm
0ð1� Pm�m0
r Þ þ ð1� Pmr Þ
� ��
266664
377775
:
ð6Þ
We can now express the probability s that a station
transmits in a random chosen slot time. As any
transmission occurs when the backoff time counter is
equal to 0, regardless of the backoff stage, it is:
s ¼ p0;�1 þXm
i¼0
pi;0
¼ 1
1� Pf
þ Peð1� Pmþ1r Þ
1� Pr
� p0;�1:
ð7Þ
However, s depends on the following probabilities:
• Pc (packet collision probability); the probability that a
transmitted packet encounters a collision, is the prob-
ability that, in a time slot, at least one of the n - 1
remaining stations transmits:
Pc ¼ 1� ð1� sÞn�1: ð8Þ
• Pe (packet error probability); the probability that a
transmitted packet undergoes an error, depends on the
bit error rate (BER), and on the packet length:
Pe ¼ 1� ð1� BERÞP: ð9Þ
• Pr (packet retransmission probability); a packet is
retransmitted, if it encounters a collision, or it
undergoes an error. Therefore, Pr is equal to the sum
of Pc and Pe:
Pr ¼ Pc þ Pe;
¼ 1� ð1� sÞn�1 þ 1� ð1� BERÞP:ð10Þ
• Pf (probability to reach the end of data packet
transmission); the probability that all fragments of a
given packet are transmitted, is equal to the ratio of
fragment payload length (F), and packet payload length
ð�PÞ:
Pf ¼F�P: ð11Þ
Equations (7) and (10) represent a non linear system in
the two unknown s and Pr, which can be solved using
numerical techniques.
4.3 Saturation throughput (THR)
We study the events that can occur within a generic slot
time, and we express the saturation throughput of basic
access method as a function of the computed value s.
We express the elementary parameters of THR:
• Let Ptr be the probability that there is at least a
transmission in the considered slot time:
Ptr ¼ 1� ð1� sÞn: ð12Þ
• Let Ps be the probability that the transmission occurring
on the channel is successful. It is given by the
probability that exactly one station transmits on the
channel, which is conditioned by the fact that at least
one station transmits:
Ps ¼nsð1� sÞn�1ð1� PeÞ
Ptr
;
¼ nsð1� sÞn�1ð1� PeÞ1� ð1� sÞn :
ð13Þ
• Let Ts be the time that the channel is sensed busy by a
successful transmission:
Ts ¼ DIFSþ T�P
R þ�P
FTPHY þ TMAC½
þ ACK þ 2ðSIFSþ dÞ� � SIFS:
ð14Þ
• Let Tm be the time that the channel is sensed busy by a
missed transmission:
Tm ¼ DIFSþ TPHY þ TMAC þ TFR þ d: ð15Þ
We define E[d], as the average delay of packet payload
successfully transmitted in a slot time, since a successful
transmission occurs in a slot time with probability PtrPs:
E½d� ¼ PtrPsT�P
R : ð16Þ
The average length of a slot time E[r], is obtained by
considering that, with (1 - Ptr) the slot time is empty, with
PtrPs it contains a successful transmission, and with the
probability Ptr(1 - Ps), it contains a collision. this yields:
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E½r� ¼ ð1� PtrÞrþ PtrPsTs þ Ptrð1� PsÞTm: ð17Þ
Now, we are able to express the saturation throughput
(THR) as the fraction of time (S) in which the channel is
used to transmit successfully the packet payload multiplied
by the data rate (R):
S ¼ E½d�E½r� ; ð18Þ
¼ PtrPsT�P
R
ð1� PtrÞrþ PtrPsTs þ Ptrð1� PsÞTm: ð19Þ
THR ¼ S� R: ð20Þ
4.4 Mean response time ð�TrÞ
In the following, we consider an M/G/1 queue [69] (see
Fig. 7) where arrivals occur according to a Poisson process
of rate k, service times are independent and identically
distributed with general distribution, there is a single server
operating a FIFO policy, and there is infinite queue. k is the
average arrival rate of customers per time unit. We denote
the mean service time by 1/l, and define q = k/l as the
fraction of time that the server is busy. We shall assume
that q\ 1, so that the queue is stable and does not below
up to infinity. We are now aiming to find an expression for
the mean response time in this queue. The formula for this
quantity is called the second formula of Pollaczek-Khin-
chin [70].
Let S be the service time distribution, and GS(Z) is its
generating function of probabilities:
GSðZÞ ¼Xm
i¼0
Psuccessi ZDsuccess
i þ PdropZDdrop
: ð21Þ
where,
• Pisuccess is the probability that a packet is transmitted
successfully at the stage i, after having undergone
i transmission failures at the stages 0; 1; 2; . . .; i� 1:
Psuccessi ¼ Pi
rð1� PrÞ: ð22Þ
• Pdrop is the probability that a packet is dropped after
reaching the maximum number m of retransmissions:
Pdrop ¼ Pmþ1r : ð23Þ
• Disuccess is the time to transmit successfully a packet at
the stage i, knowing that it has undergone transmission
failures at the stages 0; 1; 2; . . .; i� 1:
Dsuccessi ¼
Xi�1
j¼0
Tmj þ Ts
i : ð24Þ
• Ddrop is the time to destroy a packet after having
undergone m ? 1 transmission failures:
Ddrop ¼Xm
j¼0
Tmj : ð25Þ
With TRF (respectively Tj
m) is the time of a successfully
packet transmission exactly at the stage i (respectively, the
time of a packet transmission failure exactly at the stage j).
They are given as follows:
Tsi ¼ Ts þ E½cwi�E½�r�: ð26Þ
Tmj ¼ Tm þ E½cwj�E½�r�: ð27Þ
Such as, E[cwi] is the average number of backoff time
slots at the stage i:
E½cwi� ¼ wi=2: ð28Þ
and E½�r� is the average length of a slot time obtained by
considering n - 1 stations:
E½�r� ¼ ð1� �PtrÞrþ �Ptr�PsT
s þ �Ptrð1� �PsÞTm: ð29Þ�Ptr ¼ 1� ð1� sÞn�1: ð30Þ
�Ps ¼ðn� 1Þsð1� sÞn�2ð1� PeÞ
1� ð1� sÞðn� 1Þ : ð31Þ
Now, to obtain the mean response time ð�TrÞ, we apply
the second formula of Pollaczek-Khinchin:
�Tr ¼ E½S� þ kEðS2Þ2 1� kEðSÞð Þ : ð32Þ
where, E(S) and E(S2) are respectively the first and the
second moment of the service time distribution:
EðSÞ ¼ G0Sð1Þ: ð33Þ
EðS2Þ ¼ G0Sð1Þ þ G00Sð1Þ: ð34Þ
G0Sð1Þ ¼Xm
i¼0
Psuccessi Dsuccess
i þ PdropDdrop: ð35Þ
G00Sð1Þ ¼Xm
i¼0
Psuccessi Dsuccess
i Dsuccessi � 1
� �
þ PdropDdrop Ddrop � 1� �
: ð36Þ
Fig. 7 Modeling of a 802.11
station by an M/G/1 queuing
system
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5 Analytical results and analysis
In this section, we provide a comprehensive analysis on the
behavior of packet fragmentation mechanism in non ideal
channel conditions. So, we show how the packet frag-
mentation mechanism increases the overall throughput and
decreases the mean response time of the IEEE 802.11
network under the impact of packet error rate parameters
(bit error rate and data packet length). The analysis pre-
sented in this section, investigates for the first time in the
literature the performance improvement level achieved in
an IEEE 802.11 network by applying packet fragmentation
mechanism under an error-prone channel. The presented
analytical results, give a formal proof on the useful and
efficiency of packet fragmentation mechanism in a noisy
channel. Moreover, they underline the necessity to take the
packet fragmentation mechanism into consideration, when
the performances of the IEEE 802.11 MAC Protocol are
investigated, or a new MAC protocol is designed to
enhance the IEEE 802.11 network. The electromagnetic
noise in large cities is inevitable, it causes high delays and
worsens the throughput due to data distortion. Therefore,
the IEEE 802.11 work group has proposed the packet
fragmentation mechanism, to reduce the impact of noise
errors on the transmitted data packets. Furthermore, the
packet fragmentation mechanism is the only existing
solution since 1999, which is the date of the first release of
IEEE 802.11 standard [1]. The results presented in this
section are generated by solving the analytical model
described in Sect. 4. Table 3 lists all the parameters used in
this section.
The analytical analysis proposed in this section of
applying packet fragmentation mechanism on IEEE
802.11b DCF network, is presented as following: firstly, we
vary the BER value and the data packet length, to study the
performance improvement level achieved in an IEEE
802.11 network, when the packet fragmentation mecha-
nism is activated under the impact of packet error rate
parameters (BER and packet length). Secondly, we vary
the number of stations, as the network size has a direct
influence on channel saturation, to analyze the performance
of packet fragmentation mechanism with different BER
values, data packet lengths and data rates.
Figures 8 and 9 illustrate respectively the overall
throughput and the mean response time variation of the
IEEE 802.11 network according to BER value
(1 9 10-5 B BER B 20 9 10-5) in cases of fragmented
and non fragmented data packets. In case of non-frag-
mented data packets, we show on Figs. 8 and 9 that the
performances of the IEEE 802.11 network are highly
affected because of BER value; more the BER value
increases, more the overall throughput is lower (see Fig. 8)
and the mean response time is higher (see Fig. 9). This
degradation of IEEE 802.11 network performances is due
to data packets distortion that happens when the PER
increases. Since the PER is in linear relationship with BER,
it increases with the increase of BER value (see Eq. 1 and
Fig. 4). Furthermore, according to DCF operations, after
sending a data packet, if the source station does not receive
an acknowledgment, it assumes that its data packet is lost.
Consequently, the source station tries to retransmit its data
packet after a random backoff time, given by the binary
exponential backoff algorithm, in order to solve the wire-
less channel access contention. Unfortunately, the source
station assumes that, all transmission failures are due to
collisions. Thus, it does not consider the probability of
transmission errors due to bit error rate. So, each time the
source station experiences a transmission failure, the
backoff algorithm doubles the maximum backoff time to
reduce contention, without taking into account the real
reason of the data packet loss. Consequently, the backoff
algorithm adds additional delays, which cause poor channel
utilization at each time the loss of data packet is due toTable 3 802.11b Physical and MAC parameters
Parameter Numerical value
Signal propagation delay 1 ls
DIFS 50 ls
SIFS 10 ls
Slot time 20 ls
Physical basic rate (PHY header) 1 Mbits/s
Physical basic rate (MAC header) 2 Mbits/s
Physical data rate 11 Mbits/s
Minimum contention window 32
Maximum contention window 1,024
PHY header length 192 bits
MAC header length 34 bytes
ACK length 14 bytes
Maximum length of MAC frame 4,095 bytesFig. 8 Overall throughput versus BER
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noise errors. Thereby, some recent studies (see [64, 67,
68]) have proposed to enhance the performance of IEEE
802.11 network under a noisy channel. So, in case of
erroneous data packet retransmission, instead of doubling
the contention window, the backoff counter selects a
counter value from the same contention window. Indeed,
this solution allows to avoid the doubling of the contention
window in case of erroneous data packet retransmission,
and consequently it improves the channel utilization
because of reducing the waiting backoff time. However,
the loss of data packets because of noise errors, is not
solved. In case of fragmented data packets, we show on
Figs. 8 and 9 that, the use of Packet Fragmentation
Mechanism with the 802.11 DCF function, allows to
improve significatively the overall throughput and the
mean response time of the IEEE 802.11 network under the
influence of bit error rate. We note that, the packet frag-
mentation mechanism provides good performances at
MAC level of the IEEE 802.11 protocol, although the
increase of BER value. So, the PFM contributes consid-
erably to reduce the decrease of overall throughput (see
Fig. 8) and the increase of mean response time (see Fig. 9)
of the IEEE 802.11 network. This improvement level
achieved in an IEEE 802.11 network, is due to packet error
rate, which is considerably reduced, once the packet frag-
mentation mechanism is applied. So, the PER does not
increase in the same manner like in case of non-fragmented
data packets, when the BER value increases (see Fig. 4).
Therefore, the packet fragmentation mechanism provides a
better chance to a data packet to be successfully trans-
mitted. Thereby, the packet fragmentation mechanism
allows to increase the overall throughput and to decrease
the mean response time of the IEEE 802.11 network.
Furthermore, we think that, to improve the performance of
the IEEE 802.11 network under the impact of bit error rate,
the packet fragmentation mechanism must be used with the
802.11 DCF function, in order to reduce the influence of bit
error rate on the packet error rate. Then, if the transmitted
data fragments undergo transmission errors, it is very
interesting to use the solutions proposed in the papers [64,
67] and [68], to avoid the doubling of the contention
window.
Figures 10 and 11 illustrate respectively the overall
throughput and the mean response time variation of the
IEEE 802.11 network according to data packet length
(4,000 bits B packet B 32,000 bits) in cases of frag-
mented and non-fragmented data packets. We note on
Figs. 10 and 11 respectively that, more the length of data
packets is great, more the overall throughput of IEEE
802.11 network is considerably decreased and the mean
response time is highly increased. This is due to packet
error rate, which is in exponential relationship with the data
packet length. So, the PER increases quickly with the
increase of data packet length (see Eq. 1 and Fig 5).
Consequently, it causes frequent data packets losses. These
losses reduce severely the amount of data successfully
transmitted and add additional delays to transmit the data
packets. Thereby, we can conclude that, increasing the
length of data packets in an IEEE 802.11 network is not
always a good way to increase the useful use of the wire-
less channel, or to attribute a privilege for a given station in
the network. Unfortunately, the wireless stations in an
IEEE 802.11 network perform several applications, which
require to exchange a huge amount of data, for example:
FTP application, Remote Access, Remote Data Processing,
Remote Surveillance, etc. These applications which are
widely deployed and used in industries, companies and
universities, are highly affected by the packet error rate.
Furthermore, the IEEE 802.11 wireless network is cur-
rently proposed for several control-command industrial
applications, for example: Remote Control, Remote
Maintenance, etc. However, this kind of applications are
sensitive to mean response time, which is highly affected,
in case of wireless networks, by the packet error rate. In the
objective to improve the performance of the IEEE 802.11Fig. 9 Mean response time versus BER
Fig. 10 Overall throughput versus packet length
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network, and to support applications with quality of service
(QoS) requirements, the IEEE work group published the
IEEE 802.11e standard. However, the IEEE 802.11e stan-
dard does not provide any solution to reduce the influence
of packet error rate on the transmitted data packets.
Otherwise, we note on Figs. 10 and 11 a highly improve-
ment level on the performances of the IEEE 802.11 net-
work, when the packet fragmentation mechanism is used
with the 802.11 DCF function. We show that, more the
length of data packets is great, more the overall throughput
is increased (see Fig. 10) and the mean response time is
acceptable (see Fig. 11). This exceptional improvement
level of the IEEE 802.11 network performances is due to
the packet fragmentation mechanism, which allows to
maintain the packet error rate at a constant value for a
given value of BER, whatever the length of data packets
(see Fig. 5). Therefore, the packet fragmentation mecha-
nism allows in an IEEE 802.11 network to increase the
amount of data successfully transmitted. Consequently, it
enhances the useful use of the wireless channel. According
to the presented results and to the best of our knowledge,
we think that, the packet fragmentation mechanism can be
combined with the packet aggregation mechanism (PAM),
which is used in both IEEE 802.11e and IEEE 802.11n
MAC protocols. In IEEE 802.11e MAC protocol, the
packet aggregation mechanism is called Burst ACK. It is
used to privilege voice and video streaming rather than data
and background streaming, in order to provide a differen-
tiation of service (DiffServ) at MAC level of the IEEE
802.11 network (see the reference [20]). While, in IEEE
802.11n MAC protocol, the packet aggregation mechanism
is called Block ACK. It is used to enhance the wireless
channel utilization, in order to reach higher throughput in
IEEE 802.11 network (see the reference [71]). The packet
aggregation mechanism has been previously studied and
proved efficient (see the references [38, 11] and [41]).
However, these studies have been done in ideal channel
conditions, i.e, without considering the effect of packet
error rate. Therefore, the efficiency of packet aggregation
mechanism in an error-prone channel is questionable, as we
have shown in Figs. 10 and 11: the length of data packet
affects severely the packet error rate. So, when we aggre-
gate many data packets, and we transmit them as a single
frame, the packet error rate will be more important.
Therefore, we think that, the use of packet fragmentation
mechanism with the packet aggregation mechanism will
certainly enhance the performances of both IEEE 802.11e
and IEEE 802.11n MAC protocols.
Figures 12, 13, 14, 15, 16 and 17 show the variation of
the IEEE 802.11 network performances according to the
network size with different BER values, data packet
lengths and data rates, in cases of fragmented and non-
fragmented data packets.
We note on Figs. 12 and 13 that, the packet fragmen-
tation mechanism is efficient to improve significatively the
performances of the IEEE 802.11 network under the
influence of bit error rate whatever the number of stations
in the network. These results generalize and validate, for
various numbers of stations in the network, the resultsFig. 11 Mean response time versus packet length
Fig. 12 Overall throughput variation according to the network size
and BER value
Fig. 13 Mean response time variation according to the network size
and BER value
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presented in Figs. 8 and 9, about the performance
improvement level of packet fragmentation mechanism
under the influence of bit error rate. Through the results
presented in Figs. 12 and 13, we show clearly that, the
packet fragmentation mechanism is an incontestable solu-
tion to reduce the impact of bit error rate on the perfor-
mances of the IEEE 802.11 network, particularly when the
wireless channel is strongly disturbed. We note that, when
the BER value is high (BER = 10-4), the performance
improvement level of packet fragmentation mechanism is
phenomenal, it is about 50 %. We also note that, when the
BER value is moderate (BER = 5 9 10-5), the perfor-
mance improvement level of packet fragmentation mech-
anism is good, it is about 13 %.
In Figs. 14 and 15, we also generalized and validated,
for different network sizes, the results presented in Figs. 10
and 11, about the performance improvement level of
packet fragmentation mechanism under the influence of
data packet length. In Figs. 14 and 15, we show clearly
that, the packet fragmentation mechanism is a very
appropriate solution, not only to reduce the impact of
packet error rate on the performances of the IEEE 802.11
network, but also to allow the IEEE 802.11 MAC protocol
to reach the higher throughput with acceptable delays,
merely by increasing the length of data packets. When the
length of data packet is middle (packet = 8,000 bits), we
note that, the performance improvement level of Packet
Fragmentation Mechanism is very interesting, it is about
25 %. The efficiency of packet fragmentation mechanism
appears more when the length of data packet is doubled
(packet = 16,000 bits), we note that, the performance
improvement level of Packet Fragmentation Mechanism is
exceptional, it is about 66 %.
In Figs. 16 and 17, we study the performance
improvement level of packet fragmentation mechanism
with different data rates. The 802.11 physical layer pro-
vides multiple data rates by employing different modula-
tion and channel coding schemes. In the Figs. 16 and 17,
we show that, the packet fragmentation mechanism allows
to improve the performances of the IEEE 802.11 network
whatever the data rate used at physical layer. We note that,
the performance improvement level of packet fragmenta-
tion mechanism is about 48 % when the high rate
(11 Mbits/s) is used, and it is about 55 % when the low rate
Fig. 14 Overall throughput variation according to the network size
and packet length
Fig. 15 Mean response time variation according to the network size
and packet length
Fig. 16 Overall throughput variation according to the network size
and data rate
Fig. 17 Mean response time variation according to the network size
and data rate
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(5.5 Mbits/s) is used. Some recent papers (see the reference
[65]) propose rate adaptation algorithms which aim to
decrease the data rate only when transmission errors occur
on the transmitted data packets. We affirm that, the packet
fragmentation mechanism can be considered in these
algorithms to more enhance the performances of IEEE
802.11 networks.
6 Simulation and analytical model validation
To validate our analytical model, we have compared its
results with that obtained by Bianchi’s analytical model
and simulation. To obtain the simulation results, we have
implemented the IEEE 802.11 DCF function without and
with the packet fragmentation mechanism (see Figs. 18 and
19, respectively) in a custom-made simulator. Our simu-
lator is an event-driven simulation program, written in
C?? programming language under Linux operating sys-
tem. It closely follows all the IEEE 802.11 DCF function
details in cases of non-fragmented and fragmented data
packets, for each independently transmitting station. The
simulator works in procedural-oriented basis and the source
code of each station runs in parallel using multi-threads
programming. Each station in the network constitutes dif-
ferent threads that execute the code that would be imple-
mented in a real platform. The main motivations for
implementing the Packet Fragmentation Mechanism in a
custom-made C?? simulator rather than in any other well
known simulators (such as ns-2, for example), are the
possibility of isolating the IEEE 802.11 MAC protocol
performance from the rest of the network and the faster
execution of the simulations. All the parameters used in
this section are mentioned in Table 1 of Sect. 4. The values
of protocol parameters used to obtain numerical results for
the analytical model and simulation are given in Table 3 of
Sect. 5.
In Fig. 20, we show, in one hand, a comparison between
our analytical model and the analytical model of Bianchi
[6] in the case of an ideal channel (BER = 0) and non-
fragmented data packets. In other hand, we show com-
parisons between the obtained analytical and simulation
results under a noisy channel (BER = 10-4) in cases of
non-fragmented and fragmented data packets. Through the
Fig. 20, we show clearly that, our analytical model is
validated by both Bianchi analytical model and simulation.
In the case of an error-free channel and without activating
the Packet Fragmentation Mechanism, our analyticalFig. 18 Flowchart of the IEEE 802.11 DCF
Fig. 19 Flowchart of the IEEE 802.11 DCF with PFM
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results mesh well with the Bianchi’s analytical results. It is
evident, since our analytical model is an extension of the
Bianchi’s model with the PFM and the PER. Therefore,
when we do not consider the PER and the PFM, we must
find the same results. Otherwise, when the wireless channel
is error-prone, we show that our analytical results also
mesh very well with the obtained simulation results in both
cases of non-fragmented and fragmented data packets.
According to numerical results obtained by the developed
model, Bianchi’s model and simulation, our analytical
model is quite exact.
7 Conclusion
In this paper, we have focused our study on the Packet
Fragmentation Mechanism which is the solution proposed
by the IEEE work group to enhance the performances of
IEEE 802.11 networks under a noisy channel. The noise
related losses is the second major problem after the colli-
sion induced losses which cause poor channel utilization
and higher delays in an IEEE 802.11 network. It is true
that, IEEE published 802.11e standard to support applica-
tions with Quality of Service requirements, and 802.11n
standard to provide the higher throughput in the network.
Also, several studies have been done to enhance the per-
formances of IEEE 802.11 networks under a noisy channel.
However, the impact of packet error rate on the perfor-
mances of IEEE 802.11 networks has not been solved. The
only one way to reduce the influence of packet error rate on
the performances of IEEE 802.11 networks is to apply the
Packet Fragmentation Mechanism. Indeed, the perfor-
mance modeling and analysis of the IEEE 802.11 network
in all its various extensions have been the subject of several
studies. However, the performance improvement level of
packet fragmentation mechanism on the IEEE 802.11
network under the impact of packet error rate parameters
(Bit Error Rate and data packet length) has been missed in
the available literature. Therefore, we have focused in this
paper to extend an existing and valid Markov chain model,
in order to consider the packet fragmentation mechanism
and the packet error rate. So, we have developed mathe-
matical models to compute the overall throughput and the
mean response time of the IEEE 802.11 network. The
presented analytical results have been obtained for differ-
ent BER values, data packet lengths, network sizes and
data rates. These results have allowed us to quantify, for
the first time in the literature, the performance improve-
ment level of packet fragmentation mechanism, and to give
all the cases where the Packet Fragmentation can be used to
enhance the performances of IEEE 802.11 networks. The
accuracy of the developed analytical model is validated by
simulation.
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Author Biographies
Mohand Yazid is currently a
Ph.D. student at LAMOS labora-
tory (Laboratory of Modeling and
Optimization of Systems), Alge-
ria. He received the engineer
degree in 2008 in Computer Sci-
ence (Distributed and Parallel
Systems option) from the Univer-
sity of Bejaıa (Algeria). He was the
Networks Administrator of CE-
VITAL Enterprise during 3 years,
where he has done many training
about Cisco Networking (ICND1,
ICND2, IUWNE, CVOICE and
CWLMS). Since he had received
his Magister degree in 2011 in Computer Science (Networking and Dis-
tributed Systems option) at the University of Bejaıa (Algeria), he works as a
teacher at the Department of Applied Mathematics at the University of
Bejaıa (for Programming and Algorithmic, Data structures, Computer
networks, Security of networks, Modeling and Simulation of systems,
Performance evaluation of networks). His research interests are in: Mod-
eling, Simulation, Performance evaluation and Analysis of wireless net-
works (IEEE 802.11 Standard) and Industrial networks (Real-time MAC
protocols).
Louiza Bouallouche-Medjko-une received the engineer
degree in Computer Science
from University of Setif (Alge-
ria), the Magister degree in
Applied Mathematics from
University of Bejaıa (Algeria),
the doctorate degree in Com-
puter Science from University
of Setif (Algeria) in 2006 and,
the HDR (Habilitation a Diriger
des Recherches) from the Uni-
versity of Constantine (Algeria)
in 2009. BOUALLOUCHE-
MEDJKOUNE works as a tea-
cher at the Department of Computer Science of University of Bejaıa
and as a researcher at the LAMOS Laboratory (Modeling and Opti-
mization of Systems). She is head of the research team EPSIRT
(Evaluation de Performances des Systemes Informatiques et Reseaux
de Telecommunication) since 2005 and head of Department of
Operation Research since January 2010. Her publications have
appeared in various publishing houses: Taylor Francis, Elsevier,
Springer, AMS, BCS, … Her research interests are: Performance
evaluation of Computer Systems and Telecommunication Networks
(Markov chains, Queuing networks, Simulation, …), stability of
Wireless Netw
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systems, Quality of service, Routing and Protocols of systems and
networks (mobiles, ad hoc, sensors, …).
Djamil Aıssani was born in
1956 in Biarritz (Basque Coun-
try, France). He started his
career at the University of
Constantine (Algeria) in 1978.
He received his Ph.D. in
November 1983 from Azer-
baidjan State University (Bak-
ou) and Kiev State University
(Soviet Union). He is at the
University of Bejaia since its
opening in 1983/1984. Director
of Research, Head of the Fac-
ulty of Science and Engineering
Science (1999–2000), Director
of the LAMOS Laboratory (Modeling and Optimization of Systems),
Scientific Head of the Computer Science Doctorate School ReSyD, he
has taught in many universities (USTHB Algiers, Annaba, Rouen,
Dijon, ENITA, INPS Ben Aknoun, Boumerdes, Tizi Ouzou, Setif,
EHESS Paris, …). He has supervised more than 20 Ph.D. Thesis. He
has published many papers on Markov chains, Queuing systems,
Reliability theory, Performance evaluation and their applications in
such industrial areas as Electrical, Telecommunication networks and
Computer systems.
Lilia Ziane-Khodja is a Ph.D.
of Computer Science. She
received an engineer degree in
Computer Science (Parallel and
Distributed Systems option) in
2008 from the University of
Bejaıa (Algeria), a master
degree in Computer Science
(Distributed Systems and Net-
works option) in 2009 from the
University of Rennes 1 (France)
and, a Ph.D. in Computer Sci-
ence in 2013 from the Univer-
sity of Franche-Comte (France).
She worked as a teacher at the
department of Computer Science of the IUT Belfort-Montbeliard (for
Programming and Algorithmic, Networks and Systems, Hardware
architectures and, Data Bases). Currently, she works as a postdoctoral
researcher at the French Institute for Research in Computer Science
and Control (INRIA) in Bordeaux Sud-Ouest, France. Her research
interests include parallel and distributed computation, numerical
algorithms, GPU computing, asynchronous iterative algorithms and,
modeling and simulation of parallel HPC applications and modern
multicore nodes.
Wireless Netw
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