2007 International Symposium on Information Technology Convergence
An Improved Analytical Model for IEEE802.11e Enhanced
Distributed Channel Access
Ye Yan
School of Electrical Engineering
and Computer Sciences
Seoul National University
Seoul, South Korea 151–744
Email: yy@cnslab.snu.ac.kr
Ce Pan
School of Electronics
and Information Engineering
Chonbuk National University
Jeonju Jeollabuk-do South Korea 561-756
pance@chonbuk.ac.kr
Abstract
hanced distributed channel access (EDCA) and HCF
controlled channel access (HCCA). EDCA is a contention based access mechanism, whereby HCCA is an
optional polling based access mechanism.
In this paper, we propose an improved discrete threedimension Markov chain model to describe the IEEE
802.11e EDCA characteristics. The unifying model is
designed to compute the sustained probabilistic properties for each prioritized AC under saturation condition. In this framework, we consider elaborately the
modified the AIFS and backoff co-operation process in
EDCA defined by the IEEE 802.11e standard rather
than those previous literature which concern the original EDCF protocol defined by draft version. Comprehensive simulation studies validate our analytical approach is quite fair in predicting the system saturation
throughput. Ultimately, our model and analysis can
provide an in-depth understanding and insights into the
IEEE 802.11e EDCA features.
Many previous works [7]-[11] have conducted the analytical modeling of EDCA which is the basic MAC
mechanism of IEEE 802.11e standard. Basically, the
analytical modeling is derived form the discrete Markov
chain model for IEEE 802.11 DCF introduced by
Bianchi[12]. However, all of these models do not
consider the modified backoff countdown operation in
the IEEE 802.11e EDCA accurately, which should cooperate with the AIF countdown operation. As a typical one among these works, Xiao [10] extends the
model to the prioritized schemes by introducing multiple ACs with distinct parameter settings, such as the
minimum and maximum contention windows (CWmin
and CWmax). Furthermore, this model also introduces
finite retry limits. A very important differentiation
mechanism lacking in Xiao’s model, however, is the
AIFS procedure. Xiao assumed equal AISFN to all
access category. So, Xiao’s model only develops a twodimensional markov chain model for the case of general ACs. Although this type of models reflects some
modified behaviors of the EDCA backoff countdown,
there are some very important points not considered
accurately: the channel must be sensed idle during the
whole AIFS period before the backoff countdown procedure starts. Meanwhile the remaining backoff counter
should cut down advance one before the backoff process. So these models which only have two-dimension
markov chain model could not cover this co-operation
process in EDCA accurately because of the inherent
limitation.
1. Introduction
Recently, the popularity of WLANs, especially the
appearing of IEEE 802.11 standard [1], has generated
many interests in modeling and further improving the
performance of the original protocol. Due to the inherent capacity limitations of wireless technologies, the
IEEE 802.11 WLAN always tends to be a bottleneck
for multimedia communication. Therefor, one of the
recent major interests is on the quality of service (QoS)
improvement of the original IEEE 802.11 standard,
which is specified by the IEEE 802.11e standard [2]. As
an extension to the IEEE 802.11 standard, the IEEE
802.11e protocol is designed to enhance QoS supporting of WLAN in MAC layer. The IEEE 802.11e standard defines hybrid coordination function (HCF) as
its access mechanism, which uses two modes, i.e. en-
0-7695-3045-1/07 $25.00 © 2007 IEEE
DOI 10.1109/ISITC.2007.74
Some researchers [13]-[15] have realized this problem in those previous works and have tried to handle
135
the retry limit of retrying counter, if the transmission
is still unsuccessful after (Li + 1)th backoff stage, the
packet will be dropped. Then:
 j
for j = 0, 1, · · · , mi − 1, if Li > mi
 2 Wi,0
2m
for j = mi , · · · , Li , if Li > mi
Wi,j =
i Wi,0
 j
2 Wi,0
for j = 0, 1, · · · , Li , if Li ≤ mi
(1)
Figure 1. Backoff process rule difference between EDCA and DCF
3. ANALYTICAL MODEL
3.1
it by extending two-dimensional markov chain model
into three-dimensional one. For instance, the T.F.M
’s model [14] introduces a three-dimensional markov
chain, it can handle the co-operation problem easily
and obtain a more accurate model to the EDCA mechanism. However, since these models consider different
ACs individually, the corresponding analysis procedure
should also be separate, which makes the complexity of
the whole EDCA system modeling and analysis much
further. The rest of the paper is organized as follow:
Section 2 provides a brief summary of some important
IEEE 802.11e EDCA features. Section 3 describes the
improved model and the corresponding analytical development. The comprehensive comparisons of the numerical outputs of our proposed model to both the simulation results and some previous related researches are
provided in Section 4. The conclusions of this paper are
drawn in Section 5.
Markov chain model analysis
For each unsuccessful transmission attempt, the
backoff instance moves to next state in a row below
at probability . If a packet has not been transmitted
successfully after attempts, the packet will be dropped
at the accumulated frame dropping probability :
Pi,drop = PiLi +1 bi,0,0,0
The probability of an unsuccessfully transmission attempt at stage j is , then
bi,j,0,0 = Pij bi,0,0,0
bi,j,k,0 =
And
bi,j,k,d =
Backoff and AIFs co-operation
Wi,j − k
bi,j,0,0 0 ≤ j ≤ Li , 1 ≤ k ≤ Wi,j − 1
Wi,j
(4)





Pi bi,j,k+1,0 +bi,j,0,0 /Wi,j
(1−qi )d




bi,j,0,0 /Wi,j
(1−qi )d
1 ≤ d ≤ Ai , 1 ≤ k ≤ Wi,j − 2, 0 ≤ j ≤ Li
1 ≤ d ≤ Ai , k ≤ Wi,j − 1, 0 ≤ j ≤ Li
(5)
By substituting (2) into (5) and (6), through normalizing all the stable probability distribution bi,j,k,d can be
express with Ai , Li , Pi , qi , Wi,j , and bi,0,0,0 . Therefore,
bi,0,0,0 is
In the IEEE 802.11e standard, the first backoff
countdown occurs only after its corresponding AIFS.
Specially, the EDCA backoff instance advances one
time slot further comparing to the DCF operation
whenever channel becomes busy. At the meanwhile,
it will wait one extra slot after counter reached zero
before its transmission. Fig.1 shows a simple example
for this backoff and AIFS co-operation process (in the
case of AIFS=DIFS).
2.2
(3)
From chain regularities, we have:
2. FEATURES IN EDCA
2.1
(2)
bi,0,0,0 =
1
Li
j=0
i)
[ 1−(1−q
(1−qi )Ai
Ai
1 Wi,j −1
Pi
qi (
2
+ 1) +
Wi,j +1
]Pij
2
(7)
Contention Windows (CW)
3.2
For each ACi (i = 0, · · · , 3), let Wi,j denote the
contention window size in the jth backoff stage, after jth continuous unsuccessful transmission. we define Wi,0 = CWi,min + 1. we also denote j = mi as
the jth backoff stage when the contention window size
has reached CW max + 1. Finally, we let Li denote
System equations
The channel is deemed idle if and only if no single
ACi is using. As a result, the probability τi that the
channel stays busy is
pi = 1 −
3
(1 − τi )ni
i=0
136
(8)
Wi,j
Ai
−2 Li
1=
j=0
=
bi,j,k,d +
Ai
Li bi,j,Wi,j −1,d +
j=0 d=1
k=0 d=1
Li
j
P W (W −1)
1−(1−qi )Ai Pi
bi,0,0,0 {
[ i i,j 2 i,j
(1−qi )Ai qi Wi,j
j=0
Li
Wi,j
−1
j=0
k=0
+ Wi,j − 1] +
1/W0
pi
pi
0,1,0
qi
1-qi
0,2,0
...
pi
0,W0-1,0
1-pi
...
1-pi
...
1-qi
...
1-qi
qi
j,0,1
j,Wj-1,Ai
1-qi
1-qi
qi
qi
j,1,1
pi
j,0,0
j,Wj-1,1
1-qi
pi
j,1,0
1-pi
Pi
qi
j,2,1
1-qi
1-qi
1-Pi
j,2,Ai
...
j,1,Ai
j,0,Ai
...
1/Wj
1-qi
j,2,0
...
Li
j=0
j
1−(1−qi )Ai Pi
(1−qi )Ai qi Wi,j
+
The probability qi that the ACi
busy during the AIF period is

0



3


(1−τi )ni
1−
qi =
i=2

3



 1−
(1−τi )ni
i=1
j,Wj-1,0
...
Li,0,1
1-pi
Li,1,0
qi
1-qi
pi
Li,2,0
qi
Li,Wm-1,1
Li,2,1
1-qi
pi
1-qi
1-qi
qi
Li,1,1
1-qi
Li,Wm-1,Ai
...
qi
...
...
1-qi
...
(9)
senses the channel
d=0
d=1
(10)
d≥2
Where d is the remaining AIF time period in term of
the number of time slots.
Due to both external collision and virtual internal
collision, the conditional collision probability of ACi is
Pi = 1 − (1 − τi )ni −1
Li,2,Ai
Li,1,Ai
1-qi
Pi
(6)
3
(1 − τh )nh
(11)
h>i
Li,0,Ai
1-Pi
j=0
Wi,j +1 j
Pi }
2
j=0
1-pi
1/WL
Li,0,0
Li
where ni is the total number of active ACi .
Let τi denote the transmission attempt probability
that backoff instance in priority class i transmits during a generic slot time, independent on weather the
transmission results in a collision or not:

Li



bi,j,0,0
i = 3 (highest priority)

j=0
τi =
Li



bi,0,0,0 i = 3
 (1 − Pb )
0,W0-1,1
1-qi
1-pi
Pi
qi
0,2,1
1-qi
0,0,0
...
qi
0,1,1
1-qi
1-qi
...
qi
0,0,1
1-Pi
1-qi
...
1-qi
...
1-qi
0,W0-1,Ai
0,2,Ai
0,1,Ai
0,0,Ai
bi,j,k,0
1-qi
...
Li,Wm-1,0
1-pi
If we don’t consider the virtual collisions which occur
only within the station between internal access categories, we have Pi = pi in equation (11) instead.
Equations (8)-(11) form a set of nonlinear equations.
It can be solved by means of numerical methods, then
all the transition probabilities and steady state probabilities can be obtained.
3.3
PERFORMANCE ANALYSIS
Let Pi,s denotes the probability that a packet from
any of the backoff instances of priority class i is transmitted successfully at probability Pi,s in a time slot:
Drop
Figure 2. Markov chain for the EDCA procedure of ACi
Pi,s = ni τi (1 − Pi )
(12)
Let Ps denote of the probability that a packet from any
class is transmitted successfully in a time slot:
Ps =
3
i=0
137
Pi,s
(13)
Then the throughput of priority class i, can be calculated as the average duration of successfully transmitted packets by the average duration of a contention slot
that follows the special time scale of our model:
Normalized
throughput
(14)
where Ti,M SDU denotes the average time required to
transmit the MSDU of a data packet, T e denotes the
duration of a time slot, while T s and T c denote the
duration of a slot containing a successfully transmitted
packet and of a containing two or more colliding packet
respectively. The value of T s and T c can be calculated
by
0.3
0.2
0.1
5
10
15
20
25
30
35
Number of QSTAs
AC_VO(Xiao's model)
AC_VO(Proposed model)
TSbasic = TH + TE[P ] + SIF S + δ + TACK + AIF Smin + δ
TCbasic = TH + TE[P ] + AIF Smin + δ
(15)
for basic access mode and optional RTS/CTS mode
respectively. Where denote the time to transmit the
header (including MAC header, physical layer header
and/or tail), the time to transmit an ACK, SIFS, and
the time to transmit a payload with the mean length
respectively. TRT S and TCT S denote the time to transmit an RTS frame and a CTS frame, respectively. δ is
the maximum propagation delay.
AC_VO(T.F.M's model)
AC_VO(Simulation)
Figure 3. Saturation throughput comparison
among some numerical models and Simulation results in AC VO
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
NUMERICAL AND SIMULATION
RESULTS
5
10
15
20
25
30
35
Number of QSTAs
AC_BE(Xiao's model)
AC_BE(Proposed model)
In this part, we compared numerical computations
of our analytical model with some other previous ones
and ns-2 simulation results as well. We apply the IEEE
802.11b [16] PHY parameters set. For demonstration
purposes, we adopt two different priority access categories, i.e., AC VO and AC BE. However, our proposed unified analytical model is very general so that
we can adopt it for every access category under same
frame work. Fig.3 and 4 shows the numerical saturation throughput comparison of our proposed analytical
model to simulation results and some related previous
works as well over the number of station increasing
from 5 to 35 with two different priority access category
AC VO and AC BE. As illustrated in this figure, we
can observe the almost exact match between the numerical results of our proposed analytical model and
the simulation results as the total number of participated stations increasing while these two different priorities ACs will show their different capacity in form
of saturation throughput.
For the difference between with and without virtual collision handling, we
show both the saturation throughput of higher priority AC(AC VI) and lower one(AC BE) in Fig.5. we can
AC_BE(T.F.M's model)
AC_BE(Simulation)
Normalized throughpu
(AC_VO)
Figure 4. Saturation throughput comparison
among some numerical models and Simulation results in AC BE
0.035
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.03
0.025
0.02
0.015
0.01
0.005
0
5
10
15
20
25
30
35
Number of stations
AC_VO(With virtual collision handling)
AC_VO(Without virtual collision handling)
AC_BE(With virtual collision handling)
AC_BE(Without virtual collision handling)
Figure 5. Saturation throughput with/without
virtual collision
138
Normalized throughpu
(AC_BE)
4
0.4
0
Normalized
throughput
Pi,s Ti,M SDU
Si =
(1 − Pb )Te + Ps Ts + (Pb − Ps )Tc
0.5
easily find the fact that virtual collision mechanism favors even higher priority AC (AC VI), meanwhile devest the priority form the lower one (AC BE) . Also
the results show the virtual collision has little effect on
throughput performance under saturation condition especially the outer collisions are getting extremely drastic when the number of participated stations increasing.
5
[6] Robinson, J.W.; Randhawa, T.S., ”Saturation
throughput analysis of IEEE 802.11e enhanced
distributed coordination function,” Selected Areas
in Communications, IEEE Journal on Volume 22,
Issue 5, June 2004 Page(s):917 - 928.
[7] Engelstad, P.E.; Osterbo, O.N., ”Delay and
Throughput Analysis of IEEE 802.11e EDCA
with Starvation Prediction,” Local Computer Networks, 2005. 30th Anniversary. The IEEE Conference on 15-17 Nov. 2005 Page(s):647 - 655.
Conclusion
[8] Hua Zhu; Chlamtac, I., ”Performance analysis
for IEEE 802.11e EDCF service differentiation,”
Wireless Communications, IEEE Transactions on
Volume 4, Issue 4, July 2005 Page(s):1779 - 1788
In this paper, we have presented a unified three dimensional discrete Markov model to analyze the IEEE
802.11e EDCA mode under saturation condition. All
the important new features of the EDCA, viz., AIFS
and backoff co-operation process, different CW parameter setting, retransmission limit and virtual collision
handling have been taken into account in our analytical
modeling. So, this model can capture these new operations that defined in the final version of the IEEE
802.11e standard rather than those previous works
which are mostly based on the draft version.
The model and analysis provide an in-depth understanding and insights into IEEE 802.11 EDCA mechanism. They can also provide helpful and powerful analytical supports for further study, such as parametrization for different types of traffic, call admission control
schemes and active queue management for further QoS
improvement in WLANs.
[9] Yang Xiao, ”Performance analysis of priority
schemes for IEEE 802.11 and IEEE 802.11e
wireless LANs,” Wireless Communications, IEEE
Transactions on Volume 4, Issue 4, July 2005
Page(s):1506 - 1515.
[10] Jie Hui; Devetsikiotis, M., ”A unified model
for the performance analysis of IEEE 802.11e
EDCA,” Communications, IEEE Transactions on
Volume 53, Issue 9, Sept. 2005 Page(s):1498 1510.
[11] G. Bianchi, ”Performance analysis of the IEEE
802.11 distributed coordination function,” IEEE
JSAC, vol. 18, no. 3, March 2000.
[12] Tzu-Chieh Tsai; Ming-Ju Wu;, ”An analytical model for IEEE 802.11e EDCA,” Communications, 2005. ICC 2005. 2005 IEEE International Conference on Volume 5, 16-20 May 2005
Page(s):3474 - 3478 Vol. 5.
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