=Paper=
{{Paper
|id=Vol-1256/paper7
|storemode=property
|title=Analytical Modeling of the IEEE 802.11e EDCA Network
|pdfUrl=https://ceur-ws.org/Vol-1256/paper7.pdf
|volume=Vol-1256
|dblpUrl=https://dblp.org/rec/conf/vecos/MohandNBA14
}}
==Analytical Modeling of the IEEE 802.11e EDCA Network==
https://ceur-ws.org/Vol-1256/paper7.pdf
69
Analytical Modeling of the IEEE 802.11e
EDCA Network with Contention Free Burst
Mohand Yazid Nassim Sahki Louiza Medjkoune-Bouallouche
LAMOS Laboratory Department of Operations Research LAMOS Laboratory
University of Bejaia University of Bejaia University of Bejaia
06000 Bejaia, Algeria 06000 Bejaia, Algeria 06000 Bejaia, Algeria
yazid.mohand@gmail.Com nass mi@yahoo.fr louiza medjkoune@yahoo.fr
Djamil Aı̈ssani
LAMOS Laboratory
University of Bejaia
06000 Bejaia, Algeria
lamos bejaia@hotmail.com
Contention Free Burst (CFB) is a promising burst transmission scheme defined in the IEEE 802.11e Medium
Access Control (MAC) protocol to achieve differentiated Quality of Service (QoS) and improve the utilization
of the wireless scarce bandwidth. Although modeling and performance analysis of the IEEE 802.11e network
have attracted tremendous research efforts from both the academia and industry, most existing analytical
models do not give attention to the CFB QoS parameter. In this paper, we aim to propose a simple analytical
model of the IEEE 802.11e Enhanced Distributed Channel Access (EDCA) function including mainly the CFB,
in order to study its effect on the improvement of the achievable throughput of Video and Voice Access
Categories (ACs). Therefore, we propose a new two-dimensional Markov chain model of the IEEE 802.11e
EDCA function with CFB. Then, we develop a mathematical model to derive the saturation throughput. Finally,
performance analysis has allowed us to estimate the maximum sustainable throughput with CFB in an IEEE
802.11e-EDCA network under infinite load conditions.
IEEE 802.11e EDCA Function, CFB, Markov Chains, Modeling, Throughput Analysis
1. INTRODUCTION defines the Hybrid Coordination Function (HCF)
access mechanism, which uses two mechanisms
The IEEE 802.11 standard is currently one of for the support of QoS differentiation. They are
the most popular wireless access technologies. It Enhanced Distributed Channel Access (EDCA) and
allows for quick and simple configuration of local, HCF Controlled Channel Access (HCCA) (Lee et al.
broadband networks at home, in offices, or in public (2007)).
places and greatly facilitates Internet access (Kosek-
Szott et al. (2011)). With the increasing demand of The EDCA function defines several QoS enhance-
Wireless Local Area Networks (WLANs), especially ments to the legacy IEEE 802.11 Distributed Coor-
of the IEEE 802.11 (IEEE 802.11 Standard (1999)), dination Function (DCF). EDCA operation is based
the support of differentiated Quality of Service (QoS) on different priority levels through the definition of
has become one of the recent critical challenges Access Categories (ACs). There are four ACs (Voice
for the success of IEEE 802.11 Medium Access – VO, Video – VI, Best Effort – BE, and Background
Control (MAC) protocols for the future wireless – BK), each with a separate queue. To provide traffic
communications. It is important to develop a new differentiation, the following medium access parame-
medium access scheme that can support the ters are defined for each AC: the Contention Window
differentiated QoS requirements over IEEE 802.11 minimum (CWmin ) and maximum (CWmax ) size, the
WLANs, which is specified by the IEEE 802.11e Arbitration Inter-Frame Space Number (AIF SN ),
(IEEE 802.11e Standard (2005)). The IEEE 802.11e and the Contention Free Burst (CFB). The functions
standard specifies differentiated service classes in of the access parameters are as follows: CWmin and
the MAC layer to enable different kind of packet CWmax determine the initial size of the contention
priorities and have drawn tremendous interest window and the maximum possible backoff value,
from both industry and academia. IEEE 802.11e
70
respectively. AIF SN determines the minimum num- of throughput, delay, delay jitter, and frame loss
ber of idle slots before a frame transmission may probability are derived.
begin. The CFB allows consecutive frame transmis-
sions after gaining channel access (Kosek-Szott et In this paper, we propose a simple analytical model
al. (2011)). A comprehensive description of EDCA of the IEEE 802.11e EDCA function with Contention
function can be found in (IEEE 802.11e Standard Free Burst. Therefore, we use a two-dimensional
(2005)). Markov chain to model the behavior of a single
access category. Then, we develop a mathematical
After the new EDCA function was defined, the model to derive the saturation throughput of a given
previously proposed analytical models of the IEEE access category.
802.11 DCF became unsatisfactory because they
lacked traffic differentiation. However, they were The remainder of this paper is organized as
a solid starting point for further research. Most following: an overview of the CFB scheme is given
of all, they resolved the complicated problem in section 2. In section 3, we describe the proposed
of representing multiple states of the channel analytical model of the IEEE 802.11e ECDA function
access procedure by using Markov chains (Kosek- with CFB. The obtained analytical results about the
Szott et al. (2011)). In this area, Kong et al. sustainable overall throughput in an IEEE 802.11e-
(2004) presented an analytical model of the IEEE EDCA network, are presented in section 4. In section
802.11e EDCA taking into account AIFS and CW. 5, we conclude the paper.
The authors analyzed the throughput performance
of differentiated service traffic and proposed a
2. OVERVIEW OF THE CFB SCHEME
recursive method enable to provide the mean access
delay. Vassis and Kormentzas (2005) presented In DCF, the system efficiency is considerably
an analytical model for the performance evaluation affected by various overheads referred to as Physical
of IEEE 802.11e EDCA scheme under finite load (PHY) layer headers, control frames, backoff, and
conditions on the basis of various instances of delay inter-frame space. The overhead problem becomes
metric (access delay, queuing delay and total delay). more serious as the data rate increases. To mitigate
Banchs and Vollero (2006) presented an analytical the impact of the overheads and improve the system
model to analyze the throughput performance of efficiency, the TXOP scheme has been proposed in
an EDCA WLAN as a function of its parameters the IEEE 802.11e protocol (Min et al. (2011)).
(AIF S, CWmin , CWmax and TXOPLimit). The
authors searched for the optimal EDCA configuration SIFS SIFS SIFS
which maximizes the throughput performance of the DATA DATA DATA CW
WLAN. Serrano et al. (2007) presented a model ACK ACK ACK
to analyze the throughput and delay performance SIFS SIFS AIFS
of the EDCA mechanism under non-saturation CFB
conditions. The proposed model can be used to
Figure 1: Contention Free Burst scheme.
analyze generic source models, as it neither makes
any assumption on the source’s arrival process
nor requires all packets be of the same length. Different from DCF where a station can transmit
Varposhti and Movahhedinia (2009) analyzed the only one frame after winning the channel, the
effect of loss and delay caused by fading channel TXOP scheme allows a station gaining the
on EDCA performance. Then, they proposed a channel to transmit the frames available in its
modification to the media access scheme, called buffer successively provided that the duration of
Collision Avoidance with Fading Detection (CAFD) transmission does not exceed a certain threshold,
to enhance performance in wireless environments namely the CFB. As shown in Figure 1, each
subject to failure. Hu et al. (2011) proposed an frame is acknowledged by an ACKnowledgement
analytical model for the TXOP service differentiation (ACK) after a Short Inter-Frame Space (SIFS) upon
scheme in single-hop ad hoc networks in the receiving this ACK. If the transmission of any
presence of unbalanced stations with different traffic frame fails, the burst is terminated and the station
loads. The QoS metrics including throughput, end- contends again for the channel to retransmit the
to-end delay, frame dropping probability, and energy failed frame. The TXOP scheme is an efficient
consumption are derived. Hu et al. (2012) proposed way to improve the channel utilization because the
an analytical model to accommodate the integration contention overhead is shared among all the frames
of the three QoS schemes including AIFS, CW and transmitted in a burst. Moreover, it enables service
TXOPLimit in an IEEE 802.11e-EDCA network with differentiation between multiple traffic classes by
finite buffer capacity under unsaturated traffic loads. virtue of various CFBs. Another advantage of using
The important QoS performance metrics in terms the TXOP scheme is that the channel occupation
time in multi-rate WLANs can be fairly distributed by
71
allocating the larger CFB to faster stations. The slow the packets available in its queue consecu-
stations, therefore, no longer severely degrade the tively, provided that the duration of transmis-
performance of those with the higher rate (Min et al. sion does not exceeds the specific CFB.
(2011)).
2. We assume a fixed number of wireless
stations, where each access category h always
3. MODELING 802.11E EDCA WITH CFB having a packet available for transmission.
In other words, we operate in saturation
In this section, we describe a new two-dimensional conditions.
discrete time Markov chain model for the IEEE
802.11e EDCA function including the CFB. The 3. The collision probability of a packet of
resolution of stationary probabilities equations of any access category h is constant and is
this Markov chain model allows us to compute the independent of the number of retransmissions.
packet transmission probability τ [h] of each access
category h (AC[h]), where h ∈ {V O, V I, BE, BK}. 3.2. Packet Transmission Probability
This probability will be used to develop a mathe-
We study the behavior of a single access category
matical model to derive the overall throughput of a
h with a Markov chain model, and we obtain the
given access category h in an IEEE 802.11e-EDCA
stationary probability τ [h] that the AC[h] transmits a
network.
packet in a generic slot time. This probability will be
3.1. Assumptions of 802.11e ECDA Analytical used to determine the saturation throughput of the
Model IEEE 802.11e-EDCA network.
1/W0 [h]
The following is a list of assumptions of our
analytical model for the IEEE 802.11e EDCA 0, - TL[h]+1 ... 0, -1 0, 0 0, 1 .... 0, W0 [h]- 1
function. Table 1 (resp. Table 2) includes Parameters 1 1 1-P[h] 1 1
(resp. Probabilities) of the 802.11e analytical model. P[h]
1/W1 [h]
Table 1: Parameters of the 802.11e analytical model.
1, - TL[h]+1 ... 1, -1 1, 0 1, 1 .... 1, W1 [h]- 1
1 1 1-P[h] 1 1
Parameter Description
P[h]
n Number of stations in the network. 1/W2 [h]
m[h] Maximum backoff stage of the AC[h].
W0 [h] Minimum contention window of the AC[h].
Wm [h] Maximum contention window of the AC[h].
Wi [h] Contention window size of the AC[h] at
ith transmission attempt. i, - TL[h]+1 ... i, -1 i, 0
1
i, 1 ....
1
i, Wi [h]- 1
1 1 1-P[h]
T L[h] Maximum number of packets can be
P[h]
transmitted in burst during the 1/Wi+1 [h]
CF B[h] of the AC[h].
P Packet payload length.
TP Time of a packet payload transmission.
TM AC Time of a MAC layer header transmission.
TP HY Time of a PHY layer header transmission. m[h],-TL[h]+1 ... m[h], -1 m[h], 0 m[h], 1 .... m[h],Wm[h]- 1
1 1 1-P[h] 1 1
ACK Time of an acknowledgment transmission.
AIF S[h] Time interval of AIFS of the AC[h]. P[h]
1/Wm [h]
SIF S Time interval of SIFS.
δ Time of a signal propagation. Figure 2: Markov chain model of an access category h
σ An empty slot time. running the 802.11e EDCA function.
Table 2: Probabilities of the 802.11e analytical model. Let S[h] (t) be the stochastic process representing the
backoff stage i (i = 0, 1, . . . , m[h]) of the AC[h] at the
Probability Definition
time t.
τ Packet transmission probability
of a wireless station.
Let B[h] (t) be the stochastic process representing ei-
τ [h] Packet transmission probability of a AC[h].
P [h] Packet collision probability of a AC[h]. ther the backoff time counter j (j = 0, 1, . . . , Wi [h]) or
the k th transmitted packet (k = 0, −1, . . . , −T L[h]+1)
during the CF B[h] for a given AC[h].
1. All packets are of the same length. Each sta-
tion that gains the channel access transmits For a given AC[h], the Wi [h] and the T L[h] are given
by the Equations 1 and 2, respectively.
72
Wi [h] = 2i · W0 [h]. (1)
∑ ∑
m[h] Wi [h]−1
∑ ∑
m[h] T L[h]−1
1 = πi,k + πi,−k ,
i=0 k=0 i=0 k=1
[ ]
λ1 + λ2
= π0,0 · + (T L[h] − 1) . (5)
CF B[h] λ3
T L[h] = .
TP HY + TM AC + TP + 2 × SIF S + ACK + 2δ
(2)
Where,
•λ1 = (W0 [h] + 1) · (1
[ − 2P [h]). ]
Once the key approximation in Bianchi’s Markov m[h]
chain model (Bianchi (2000)) is assumed (which •λ2 = P [h] · W0 [h] · 1 − (2P [h]) .
means that, at each transmission attempt, and •λ3 = 2 · (1 − 2P [h]) · (1 − P [h]).
regardless of the number of retransmissions
suffered, each packet collides with constant and Hence, we have:
independent probability P [h]) it is possible to model
the bi-dimensional process {S[h] (t), B[h] (t)} with the λ3
discrete-time Markov chain depicted in Figure 2. π0,0 = . (6)
λ1 + λ2 + λ3 · (T L[h] − 1)
In this Markov chain, the only non null one-step
transition probabilities are: We can now express the probability τ [h] that an
AC[h] transmits in a random chosen slot time. It is
the sum of all the steady-state probabilities of states
P {i, k/i, k + 1} = 1, i ∈ (0, m[h]), k ∈ (−T L[h] + 1, −2). πi,k , i = 0, 1, · · · m[h], and k = 0, −1, · · · − T L[h] + 1.
P {i, k/i, k + 1} = 1, i ∈ (0, m[h]), k ∈ (0, Wi [h] − 2). In these states, an AC[h] attempts to transmit its
packets. Thus:
P {i, −1/i, 0} = 1 − P [h], i ∈ (0, m[h]).
1
P {0, k/i, −T L[h] + 1} = , i ∈ (0, m[h]), k ∈ (0, W0 [h] − 1).
W0 [h]
P [h]
P {i, k/i − 1, 0} = , i ∈ (1, m[h]), k ∈ (0, Wi [h] − 1). (3a) ∑ ∑
m[h] T L[h]−1
∑
m[h]
W i [h] τ [h] = πi,−k + πi,0 ,
P [h] i=0 k=1 i=0
P {m[h], k/m[h], 0} = , k ∈ (0, Wm [h] − 1).
Wm [h] T L[h] · (1 − P [h]) + P [h]
= · π0,0 ,
1 − P [h]
Let πi,k = limt→∞ P {S[h] (t) = i, B[h] (t) = k}, i ∈ λ4
= . (7)
(0, m[h]), k ∈ (−T L[h]+1, Wi [h]−1) be the stationary λ1 + λ2 + λ3 · (T L[h] − 1)
distribution of the chain. The closed-form solution for
this Markov chain is: Where,
•λ4 = 2 · (1 − 2P [h]) · (T L[h] · (1 − P [h]) + P [h])
i
α · γ · π0,0 , i ∈ (0, m[h] − 1), k ∈ (0, Wi [h] − 1); From the viewpoint of a wireless station, the
θ · γ · π0,0 , i = m[h], k ∈ (0, Wi [h] − 1); probability τ that the wireless station accesses the
πi,k =
αi · β · π0,0 , i ∈ (0, m[h] − 1), k ∈ (−1, −T L[h] + 1); channel is given by the Equation 8, where the access
categories VO, VI, BE and BK are represented by the
θ · β · π0,0 , i = m[h], k ∈ (−1, −T L[h] + 1).
(4) priorities 3, 2, 1 and 0, respectively.
∏
3
Where, τ =1− (1 − τ [h]) (8)
•α = P [h]. h=0
•β = 1 − P [h].
•γ = WWi [h]−k
i [h]
. The probability P [h] that a transmitted packet of a
[h]m[h] given AC[h] encounters a collision, is the probability
•θ = P1−P [h] .
that, in a time slot, at least one of n − 1 remaining
Thus, by the relation (4), all the values πi,k are wireless stations transmits, or at least one of AC[i]
expressed as a function of the value π0,0 and packet (i > h) of the same wireless station transmits. i > h
collision probability P [h]. π0,0 is finally determined means that, AC[i] has higher priority than AC[h].
by imposing the normalization condition, that can be Hence, we have:
simplified as follows:
73
∏
P [h] = 1 − (1 − τ )n−1 · (1 − τ [i]). (9) EI [h] = Ps [h] · P · T L[h]. (15)
i>h
The average length of a slot time E[σ], is obtained
Equations 7, 8 and 9 form a set of nonlinear by considering that:
equations. It can be solved by means of numerical • With the probability (1−Ptr ), the slot time is empty;
methods. All the transition probabilities and steady- ∑3
state probabilities can be obtained. • With the probability Ptr (1 − Ps [h]), the slot time
h=0
contains a collision;
3.3. Saturation Throughput (T H[h]) ∑
3
• With the probability Ptr Ps [h], the slot time
We study the events that can occur within a generic h=0
slot time, and we express the saturation throughput contains T L[h] packets successfully transmitted.
of a given AC[h] in an IEEE 802.11e-EDCA network,
as a function of the computed value τ [h]. ( )
∑
3
We express the elementary parameters of T H[h]: E[σ] =(1 − Ptr ) · σ + Ptr 1− Ps [h] · T c+
h=0
• Let Ptr be the probability that there is at least a ( 3 )
∑
transmission in the considered slot time: Ptr Ps [h] · Ts [h]. (16)
h=0
Ptr = 1 − (1 − τ )n . (10)
Now, we are able to express the saturation
throughput (T H[h]) of a given AC[h], as the
• Let Ps [h] be the probability that the AC[h] gets ratio of the average amount of useful information
the channel access. It is given by the probability that successfully transmitted EI [h] to the average length
exactly one AC[h] transmits on the channel: of a slot time E[σ]:
EI [h]
∏
3
T H[h] = . (17)
Ps [h] = nτ [h](1 − τ [h])n−1 · (1 − τ [i])n . (11) E[σ]
i=0,i̸=h
4. SATURATION THROUGHPUT ANALYSIS
• Let Tc be the time that the channel is sensed busy
by a collided transmission of the first packet of any In this section, we present and analyze the obtained
AC[h]: analytical results about the overall throughput of
the IEEE 802.11e-EDCA network. These results
are obtained after solving and programming the
analytical model described in section 3 under Matlab
Tc = min{AIF S[h]} + TM AC + TP HY + TP + δ (12) software. The numerical values of parameters used
to get the below figures, are listed in Tables 3 and 4.
Where,
The throughput analysis of the IEEE 802.11e-EDCA
network provided in this section, is done with
AIF S[h] = AIF SN [h] × σ + SIF S. (13) different BER values, packet lengths and network
sizes, in cases of aggregated and non-aggregated
packets. This analysis is original and leads to new
• Let Ts [h] be the time that the channel is sensed
conclusions that could not be intrusively expected.
busy by a successful transmission of all the packets
of the AC[h]: In Figure 3, we compare the overall throughput of
AC[VO] and AC[VI] obtained with and without CFB
according to the number of stations in the network.
Ts [h] =AIF S[h] + T L[h] · [TM AC + TP HY + TP + We observe that, the overall throughput of both
AC[VO] and AC[VI] is decreasing with the increase
2SIF S + 2δ + ACK] − SIF S. (14)
of the network size. This due to the number of
collisions which increases with the increase of the
We define EI [h], as the average amount of useful number of stations in the network. We note on Figure
information successfully transmitted by the AC[h] in 3 that, the use of CFB allows significant channel
a slot time. It is given as follows: utilization improvement of both AC[VO] and AC[VI].
74
Table 3: 802.11b PHY and MAC parameters.
Parameter Numerical value
δ 1 µs
σ 20 µs
SIF S 10 µs
Basic rate (PHY header) 1 Mbits/s
Basic rate (MAC header) 2 Mbits/s
Data rate 11 Mbits/s
PHY header length 192 bits
MAC header length 34 bytes
ACK length 14 bytes
Maximum payload length 2304 bytes Figure 4: Overall throughput variation according to the
packet length.
Table 4: 802.11e-EDCA default parameters.
AC[h] m AIFSN W0 Wm CFB In Figure 5, we analyze the overall throughput of
AC[BK] 5 7 32 1024 0 AC[VO] and AC[VI] according to the number of
AC[BE] 5 3 32 1024 0 MPDUs in cases of middle and maximum packet
AC[VI] 1 2 16 32 6016 s length (1500 bytes and 2312 bytes, respectively).
AC[VO] 1 2 8 16 3264 s We show clearly that, the overall throughput of both
AC[VO] and AC[VI] increases with the increase of the
number of MPDUs allowed to be transmitted during a
We also note that, when CFB is used, the overall CFB. We also note that, increasing the packet length
throughput obtained with AC[VI] is greater than the allows to increase the efficiency of CFB. Through the
one obtained with AC[VO]. This is due to the number presented analytical results, we can affirm that, the
of consecutive MPDUs sent by the AC[VI] which is CFB is a promising burst transmission scheme which
greater than the one sent by the AC[VO]. allows to enhance the utilization of the bandwidth
and to achieve QoS differentiation.
Figure 3: Overall throughput variation according to the
network size. Figure 5: Overall throughput variation according to the
CFB.
In Figure 4, we compare the overall throughput
of both AC[VO] and AC[VI] obtained with and
without CFB according to the packet length. We 5. CONCLUSION
show on this figure that, on one hand, the use of
CFB permits considerably to improve the channel In this paper, we have proposed a simple analytical
utilization compared to the case without CFB. On model of the IEEE 802.11e-EDCA network taking
other hand, with CFB the overall throughput of into account the CFB. So, we have proposed a
AC[VO] and AC[VI] increases considerably with the new two dimensional discrete time Markov chain
increase of packet length. When the CFB is used, model. Then, we have developed a mathematical
the collision can occur only on the first packet in model to compute the saturation throughput with
burst and the other packets are spared from collision CFB of a given AC[h]. The obtained analytical
related losses. This is why the throughput in case of results have allowed us to estimate the maximum
CFB increases significantly with the increase of the throughput of the IEEE 802.11e-EDCA network with
packet length. CFB. Particularly, the presented analytical results
show how the Contention Free Burst permits to
75
increase significantly the throughput of video and Varposhti M. and Movahhedinia N. (2009) Support-
voice access categories. ing QoS in IEEE 802.11e Wireless LANs over
Fading Channel. Computer Communications, 32,
985–991.
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