Analysis of the Total Delay of IEEE 802.11e EDCA
and 802.11 DCF
Paal E. Engelstad
Olav N. Østerbø
UniK/Telenor R&D
1331 Fornebu, Norway
paal.engelstad@telenor.com
Telenor R&D
1331 Fornebu, Norway
olav-norvald.osterbo@telenor.com
Keywords-802.11e; Queueing Delay; Performance Analysis;
EDCA; Z-transform of the Delay; Virtual Collision; NonSaturation.
I.
INTRODUCTION
Due to the inherent capacity limitations of wireless
technologies based on the IEEE 802.11 standard [1], the
WLAN easily becomes a bottleneck for communication. In
these cases, the Enhanced Distributed Channel Access (EDCA)
of the IEEE 802.11e standard [2] will be beneficial to prioritize
for example voice and video traffic over more elastic data
traffic. EDCA allows for differentiation between four different
access categories (ACs) at each station and a transmission
queue associated with each AC. Each AC at a station has a
conceptual "backoff instance" responsible for channel access
for each AC, often referred to as the Enhanced Distributed
Channel Access Function (EDCAF).
The majority of analytical work on the performance of
802.11e EDCA (and of 802.11 DCF) focuses on predicting the
throughput [3-7] and the mean delay of the medium access [47]. However, before the packet is being transmitted, it might be
stored in the reliable protocol buffer of the IP layer or in the
interface driver or be waiting in a transmission queue on the
network interface. Surprisingly little focus has been on
predicting also this type of delay, referred to as the “queueing
delay”.
The main contribution of this paper is that it makes an
analysis of the total delay in terms of both the queueing delay
and the medium access delay. While upper and lower bounds
of the total delay are provided in [8], this paper presents a more
exact estimation of the total delay, and validates it against
simulation results. The delay expressions are based on the
analysis on the delay distribution of 802.11 DCF and 802.11e
EDCA presented in [9].
The importance of the queueing delay is evident. In realistic
network scenarios, most of the MAC frames will carry a
higher-layer packet, such as a TCP/IP or a RTP/UDP/IP packet,
in the payload. A higher layer protocol or application will
normally not interfere with the inner workings of the IP or
MAC layer. It might observe that it is subject to delay (which is
the case for TCP and many applications running on top of
RTP), but it will normally not be able to distinguish between
different types of delays. Thus, in most cases it is the total
delay that counts. For analytical predictions of the delay of
802.11e EDCA (and of 802.11 DCF) to be useful, both the
queueing delay and the medium access delay should be
considered.
4000
AC[3]: Delay
Input = Output
3500
Throughput per AC [Kb/s ]
Abstract— A packet sent from an upper-layer protocol or
application over IEEE 802.11 [1] will first be placed in a
transmission queue. The packet delay caused by waiting here is
referred to as the queueing delay. When the packet reaches the
head of the queue it will start contending for channel access until
it is successfully transmitted over the medium (or finally
dropped). The delay associated with the medium access is
referred to as the MAC delay. The majority of analytical work on
the delay performance of IEEE 802.11 focuses on predicting only
the mean MAC delay, although higher layer applications and
protocols are interested in the total performance of the MAC
layer. The main contribution of this paper opposed to other
works is that it provides analytical predictions of the total delay,
which also includes the queueing delay. The analyses presented
apply to the priority schemes of the Enhanced Distributed
Channel Access (EDCA) mechanism of the IEEE 802.11e
standard [2]. However, by using an appropriate parameter
setting, the results presented are also applicable to the legacy
802.11 Distributed Coordination Function (DCF) [1]. The model
predictions are calculated numerically and validated against
simulation results.
3000
AC[3] (AC_VO)
2500
2000
1500
AC[2] (AC_VI)
1000
AC[0] (AC_BK)
500
AC[1] (AC_BE)
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Traffic g e ne rate d pe r AC [Kb/s ]
Figure 1. Simulation results showing the throughput performance of EDCA.
We now use Fig. 1 to explain at which level of traffic
intensity an analysis of the total delay is of primary interest.
The figure shows results from a simulation with a number of
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stations contending for channel access, and with equal amount
of traffic generated per AC and per station. The curves in solid
lines show the throughput of the four different ACs. With low
traffic load (i.e. in the left side of the figure) the channel is far
from saturated, and practically all generated traffic is sooner or
later successfully transmitted on the medium. This situation is
trivial; it exhibits very low delays, and a delay analysis is of
little interest here.
On the other hand, when the traffic load increases (i.e. to
the right in the figure) the throughput are below the dashed
“input=output” line. This means that the channel is saturated,
and only a fraction of the generated traffic is successfully
transmitted. The frames that are not transmitted, are mainly
stacked on queues (or buffers), resulting in queueing overflow
or queues that grow to infinite lengths. This situation is not
useful to analyze, since no realistic communication will be
possible.
Hence, it is the intermediate region between the fully nonsaturated and fully saturation situations that is of primary
interest in terms of analysis of the total delay. For AC[3] this
region is marked with the dashed oval in the figure. The curve
in broken line in Fig. 1 shows the mean queueing delay
observed in the simulation, and the linear scale on the y-axis is
chosen so that 3000 kbps corresponds to 30 µs of queueing
delay for this curve. We observe that the queueing delay
increases quickly to infinity within the region marked with the
dashed oval.
 2 jW
Wi , j =  mi i , 0
2 Wi , 0
j = 0,1,...., mi − 1
j = mi ,...., Li
.
(1)
The behavior of 802.11e EDCA is analyzed by considering
a bi-dimensional Markov chain S ni , Bni for AC i where S ni is
(
)
a stochastic process representing the backoff stage and Bni is
the backoff counter. To model the post-backoff properly we
add an “extra” state S ni = −1 representing the case where the
post-backoff starts with an empty queue, and we take S ni = 0
for the case when the post-backoff starts with a non-empty
queue. The state space of the Markov chain S ni , Bni is denoted
( j , k ) where k = 0,1,...., Wi , j and j = −1,0,1,...., Li and where
(
)
we also have Wi , −1 = Wi ,0 . Fig. 2 illustrates the Markov chain
for the transmission process of a EDCAF of priority class i .
The Markov chain and its transition probabilities have been
described in detail in [9].
In order to analyze the total delay in the region of interest,
we need an analytical model that applies to the whole range
from a lightly loaded, non-saturated channel to a heavily
congested, saturated medium. The model presented in this
paper applies to the whole range and describes the priority
schemes of the Enhanced Distributed Channel Access (EDCA)
mechanism of the IEEE 802.11e standard [2]. By setting the
number of ACs, N, to one, and by using an appropriate
parameter setting, the results presented are also applicable to
the legacy 802.11 Distributed Coordination Function (DCF)
[1].
The remaining part of the paper is organized as follows:
The next section presents the analytical model used in the
subsequent analyses. Analyses of the MAC delay, the queueing
delay and the total delay are provided in Section III, Section IV
and Section V, respectively. In Section VI, the analytical
results are validated against simulation results. Finally follow
conclusions and proposed directions for further work.
II.
ANALYTICAL MODEL
For each AC, i (i = 0,...,3) , let Wi, j denote the contention
window size in the j th backoff stage i.e. after the j th
unsuccessful transmission; hence the minimum contention
window is given as Wi , 0 . Let also j = m i denote the j th
backoff stage where the contention window has reached the
maximum contention window, given by 2m Wi , 0 . Finally, let Li
i
denote the retry limit of the retry counter. Then:
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Figure 2. Generic Markov Chain for a EDCAF of Access Category i (for both
Bianchi’s and Xiao’s models).
Let bi , j ,k denote the steady state distributions of the Markov
chain. An EDCAF transmits when it is in any of the states
where
Since
bi , j , 0 = pij bi , 0, 0
( j , 0)
j = 0,1,..., Li .
for j = 0,1,..., Li , the probability, τ i , of a transmission attempt
in a generic time slot is given as:
Li
τ i = ∑ bi , j , 0 = bi , 0, 0
j =0
1 − piLi +1
.
1 − pi
In [9] it is shown that τ i can be expressed as:
1
τi
+
=
Ai = AIFSN [i ] − AIFSN [ N − 1] .
(2)
Our results are valid for any of the three models
presented in Eq. (6), Eq. (7) and Eq. (8).
qi :
(1 − 2 p )
*
i
*
i
2(1 − p )
(
)
Wi ,0 (1 − p i )(1 − (2 p i ) mi ) + (1 − 2 p i )(2 p i ) mi (1 − p iLi − mi +1 ) (3)
2(1 − p )(1 − 2 p i )(1 − p
*
i
Li +1
i
)
(Wi , 0 − 1)q i p i
1 − p i (1 − ρ i )
+(
)
(1 +
) .
Li +1
qi
2(1 − p i* )
1 − pi
(
i
If each station is transmitting traffic of more than one
AC, there will be virtual collision handling between the
queues [10]. Then, the probability of unsuccessful
transmission, p i , is given by:
pi = 1 −
1 − pb
,
i
∏ (1 − τ
c
ps =
qi∗ :
)
(4)
c =0
where p b denotes the probability that the channel is
busy:
N −1
pb = 1 −
∏ (1 − τ )
i
ni
,
i =0
(5)
ρ :
probability, p i∗ , is the probability that the EDCAF
remains in the state between two transmission slots.
Different analytical models use different settings for
this parameter. The original Bianchi model [3] uses:
(Bianchi [3]) (6)
which assumes that the backoff counter is decremented
in each slot, even when there is a transmission or
collision on the channel. The model by Xiao [5], on the
contrary, assumes that the countdown is blocked in
busy slots, by setting:
pi∗ = pi .
(Xiao [5]) (7)
Finally, the model in [6-7] incorporates AIFS
differentiation into the model as a blocking probability:

A p 
pi∗ = min1, pi + i b  ,
1 −τ i 

where
(E/Ø [6-7]) (8)
N −1
∑ n τ (1 − p )
i =0
i i
i
.
i e
p
p
1 − p  s e −λ T + (1 − s )e −λ T
pb
 pb
i s
ρ :
i
i c



.
(12)
Let DiSAT denote the mean medium access delay where
the post-backoff delay is also included. In [9] it is
shown that DiSAT represents the service time of an
EDCAF. The utilization factor, ρ i , is therefore given
by [11]:
ρ i = min(1, λi DiSAT ) ,
∗
(11)
e − λ T (1 − pi* )
*
i
Unlike the collision probability, pi , the blocking
pi∗ = 0 ,
. (10)
In [9] it is shown that the probability that a packet
arrives during countdown blocking, qi∗ , in any of the
states (-1,k) in Fig. 1 can be expressed as:
qi* = 1 −
i
pi* :
)
where Te , Ts and Tc denote the real-time duration of an
empty slot, of a slot containing a successfully
transmitted packet and of a slot containing two or more
colliding packets, respectively, as detailed in [6].
Furthermore, p s is the probability that a time slot
contains a successfully transmitted packet:
estimated in the following:
pi :
In Fig.1 q i denotes the probability that at least one
packet will arrive in the transmission queue during the
following generic time slot while in the state (-1,0).
Thus, a condition is that the queue is empty at the
beginning of the slot. Furthermore, it is assumed that
the traffic arrives according to Poisson processes with a
packet rate of λi for each EDCAF of AC i. Then, q i is
calculated as:
qi = 1 − p s e − λiTs + (1 − pb )e − λiTe + ( pb − p s )e − λiTc
The various terms of this expression - and their physical
interpretations - have been explained in detail in [6]. The
remaining parameters pi , pi* , qi , qi∗ ρ ,and ρ ∗ , will be
i
(9)
(13)
ρi∗
denotes the probability that there is a
In Fig. 1
packet waiting in the transmission queue of the
EDCAF of AC i at the time a transmission is
completed (or a packet dropped). As shown in [9], ρi∗
can be determined by:
1 − ρi = Pi PB (1 − ρi∗ ) .
(14)
where Pi PB , is the probability of not receiving any
packets in the transmission queue while performing a
complete empty-queue post-backoff procedure. Pi PB
can be expressed in terms of qi∗⋅ by:
Pi PB =
III.
1 − (1 − q i* )
Wi , 0
.
Wi ,0 q i*
(15)
where the factor 1 / Wij reflects the uniform distribution of the
selection of the number of backoff slots at each stage.
i
For simplicity the term Dlevel , j ,s ( z ) is introduced as:
ANALYSIS OF THE MAC DELAY
j
A. The z-Transform of the Countdown Delay
Due to the slotted operation of the wireless protocol, the ztransform (rather than Laplace transform) is applied in order to
describe the delay [7]. The slot-length of the analytical model
must be chosen so that Te , Ts and Tc are equal to or multiple
integers of the slot-length.
i
i
Dlevel
, j , s ( z ) = ∏ Dstage ,l ( z ) .
Here, s is set to 0 to find the delay when the post-backoff is
undertaken before the transmission of each packet. This type of
i
, because under
delay is referred to as the saturation delay, DSat
saturation the post-backoff must always be taken into account.
The transform for this delay may be written as:
Using the model with countdown blocking [expressed by
Eq. (7) or Eq. (8)], the weighted average delay while being
blocked
during
countdown
can
be
written
as
Ts ps / pb + Tc (1 − ps / pb ) , with the corresponding z-transform
z T ps / pb + z T (1 − ps / pb ) . While the EDCAF is counting
s
Li
i
i
D Sat
( z ) = (1 − p i )∑ p ij z Ts + jTc Dlevel
, j ,0 ( z )
the probability of being blocked is pi∗ . When it is not blocked
anymore, the EDCAF will spend an empty time-slot, Te , when
moving to the next countdown state. Hence, the z-transform of
the total delay associated with one countdown state is:
i
Dstate
( z) = zT
e
1 − pi*
.
1 − p z ps / pb + z T (1 − ps / pb )
*
i
(
Ts
)
c
i
+ p iLi +1 z ( Li +1)Tc Dlevel
, Li , 0 ( z ) .
p
 pi*
p
Distate = Te +  s Ts + (1 − s )Tc 
,
pb  (1 − pi* )
 pb
(17)
while the second order moment, Distate 2 , can be determined by:
p
 pi*
2
p
Distate = Te 2 +  s Ts (2Te + Ts ) + (1 − s )Tc (2Te + Tc )
*
pb
 pb
 1 − pi
p

p
+ 2 s Ts + (1 − s )Tc 
pb
 pb

2
 pi* 


 1 − p* 
i 

2
(18)
The queuing delay analysis presented in this paper is also
applicable to Bianchi's model without countdown blocking,
which is expressed by Eq. (6). However, to reflect the
countdown delay of the Bianchi model, the expression
i
for Dstate
(z) in Eq. (16) and the resulting expressions for Distate
state 2
i
would need to be modified. These alternative
and D
expressions are provided in the appendix of this paper.
B. The z-Transform of the MAC Delay
The total delay in a backoff stage is derived by a geometric
sum over the probabilities associated with each countdown
state:
i
Dstage
, j ( z) =
Wij
i
( z ))
1 1 − ( Dstate
i
Wij 1 − Dstate
( z)
,
Under extreme non-saturation conditions, on the contrary,
the post-backoff is always completed before a new packet
arrives in the transmission queue. Thus, under these conditions
the post-backoff will not add to the transmission delay, as it did
when the saturation delays were calculated above, and s is now
set to 1 in Eq. (20). The transform of the non-saturation delay
can be found by [9]:
(16)
The first order moment of this countdown delay, Distate , is
found as:
(19)
(21)
j =0
c
down, the probability of facing an empty slot is 1 − pi∗ while
(20)
l =s
(22)
i
i
i
DSat
( z ) = Dstage
, 0 ( z ) DNon − Sat ( z ) .
i
The factor Dstage,0 ( z ) in Eq. (22) represents the delay
distribution of a complete post-backoff, and the equation
i
i
(z ) and DNon−
expresses that DSat
Sat (z ) form an upper and
lower bound on the MAC delay. These bounds were studied in
[8].
In this paper, on the contrary we let D i ( z ) denote the ztransform of a more exact MAC delay where only the last part
of the post-backoff might be included. The reason is that the
first part might be completed when a new packet arrives in the
empty queue, and only the remaining part of the post-backoff
should add to the MAC delay of that packet. Using the results
in [9], it is easy to show that D i ( z ) can be written:
i
i
D i ( z ) = D † stage,0 ( z ) DNon
− Sat ( z ) ,
(23)
where
i
i
D † stage , 0 ( z ) = Dstage
,0 ( z )
[
+ (1 − ρi ) (1 − D
∗i
stage , 0
( z )) − pi (1 − D
i
stage , 0
]
(24)
( z )) .
represents the delay distribution of the actual post-backoff. The
i
“extra” z-transform, D ∗ stage,0 ( z ) , in the first term stems from
the possibility that a packet arrives in an empty queue before
the post-backoff is completed and is given by:
i
D ∗ stage, 0 ( z ) =
W
i
( z)
1 (1 − q i* ) i , 0 − Dstate
PB
*
i
Pi Wij
(1 − q i ) − Dstate ( z )
Wi , 0
. (25)
i
The last term pi (1 − Dstage
,0 ( z ) ) in Eq. (24) stems from the “listenbefore-talk” mechanism and can be dropped if this mechanism
is not considered.
C. The Mean Medium Access Delay
Finally, the mean medium access delay when the postbackoff delay is taken into account, DiSAT , is found directly by
differentiation of the transform in Eq. (21):
DiSAT = (1 − p iLi +1 )(T s + Tc*
where
Distate
pi
D state
)+ i
1 − pi
2
Li
∑p
j =0
j
i
Note that DiSAT 2 − DiSAT ≥ 0 , since the slot-length of the analytical
model must be chosen so that Te , Ts and Tc are equal to or
multiple integers of the slot-length.
According to Eq. (32) the second order moment of the
2
delay, DiSAT , is needed in order to find the mean queueing
delay. By differentiating Eq. (21) twice we find the second
order moment as:
(
(
is defined in Eq. (17).
The mean MAC delay can be found by differentiating Eq.
(23), using Eq. (22), Eq. (24) and Eq. (25). This gives
Di =
DiSAT
− (1 − ρ i ) Di
PB
(
(27)
,
Wi , 0 − 1  state
 1 − P PB
 Di
Di PB =  ∗ iPB − p i
.
2 
q
P
 i i
(28)
D. The Variance of the MAC Delay
The variance of the MAC delay is found by double
differentiation of the transform in Eq. (21):
σ
IV.
( )
2
= D (1) + Di − Di
( 2)
i
(29)
ANALYSIS OF THE QUEUEING DELAY
1
DiSAT
∞
∞
∑ ∑d
k = 0 m = k +1
i , Sat
m
i
λ 1 − D Sat
( z)
z = i
.
ρi
1− z
k
1 − ρi
(30)
2
where expressions for Distate and Distate are given by Eq. (17)
and Eq. (18) and the sums R1i ,.., R5i are defined as:
Li
Li
i
R1i = ∑ pij (Wij − 1) , R2i = ∑ (Wij − 1) , R3 =
j =0
j =0
Li
R = ∑ pi (Wij − 1)(Wij − 2)
i
4
j
j =0
B. The Mean Queueing delay
Using Eq. (31), the mean M/G/1 queueing delay, ∆ i , can
be given by the second order moment of the delay:
λi  DiSAT − DiSAT 
2
λ D i ( 2 ) (1)
∆ i = ∆ (1) = i Sat
=
2(1 − ρ i )
i (1)

2(1 − ρ i )
.
Li
jpij (Wij − 1) ,
∑
j =1
and R i = L p j (W − 1) j −1 W .
∑ i ij ∑ is
5
i
j =1
(34)
s =0
C. The Variance of the Queueing Delay
We can go further to find the variation of the queueing
delay through its second order moment, found by
differentiation of Eq. (31) twice:
∆i ( 2) (1) =
( )
i ( 3)
(1)
λi DSat
+ 2 ∆i
3(1 − ρi )
2
.
(32)
(35)
Thus, the variance of the queueing delay is expressed as:
( )
λ D (1)
=
+ ∆ (∆ + 1) .
3(1 − ρ )
σ ∆2 = ∆i ( 2 ) (1) + ∆ i − ∆ i
2
i
(31)
.
i
1 − ρ i Dˆ Sat
( z)
)
i
2 i
2 R
R
R i − R3i 
+  Distate   4 + 5
+ Distate 1 ,

  3
2 
2
Then, the z-transform of the waiting time follows by the
Pollaczek-Khintchine formula [11]:
∆i ( z ) =
(33)
Explicit expressions for the sums are given in [8]. They are
not repeated here, due to the space limitations of this paper.
A. The z-Transform of the Queueing Delay
Due to the use of the z-transform in a slotted time system,
we apply a slightly modified form of the Pollaczek-Khintchine
formula to obtain the z-transform of the queueing delay. The
service time is determined by the saturation-delay, DiSAT , as
seen from Eq. (21). Thus, the z-transform of the residual
service time distribution in the queue is:
i
Dˆ Sat
( z) ≡
)


pi  i
 R1 − p Li +1R2i + Tc Ri3 
+ Distate  Ts + Tc

i
1 − pi 


where
2
Di
)

2
2
pi 

DiSAT = 1 − p Li +1  Ts 2 + Tc
i
1 − pi 


pi  pi

+ 2Tc 1 − ( Li + 1) p Li + Li p Li +1  Ts + Tc
i
i
−
1
pi  1 − pi

(Wij − 1) , (26)
i
i ( 3)
Sat
i
(36)
i
i
V.
ANALYSIS OF THE TOTAL DELAY
One of the main performance measures of IEEE 802.11
EDCA is the total delay for a packet to be transmitted over the
wireless medium, and this includes the MAC delay as well as
the queueing delay. If Ti represents the total delay, then the
corresponding z-transform is simply the product of the ztransform D i (z ) of the MAC delay in Eq. (23), and the z-
transform ∆i (z ) of the queueing delay in Eq. (31):
T i ( z ) = D i ( z )∆i ( z ) .
(37)
λi  DiSAT − DiSAT 
2
Ti = Di + ∆ i = Di +

2(1 − ρ i )
(38)
 ,
where Di is given by Eq. (27) and Eq (28) and the expressions
2
for DiSAT and DiSAT are found in Eq. (26) and Eq. (33).
Similar the variance of the total delay is the sum of the
variances of the MAC delay and the queueing delay, and
hence:
σ T2 = σ D2 + σ ∆2
i
i
(39)
,
i
where σ D2 i is given by Eq. (29) and σ ∆2 is given by Eq. (36).
i
VI.
VALIDATIONS
A. Simulation Setup
We compared numerical computations in Mathematica with
ns-2 simulations, using the TKN implementation of 802.11e
[12] for the ns-2 simulator.
The scenario selected for validations is 802.11b with long
preamble and without the RTS/CTS-mechanism. The
parameter settings for 802.11b are found in [13]. Based on
these, the model parameters Te = 20µs , Ti ,MSDU = T1024 = 520µs
and TS = Tc = 1321.1 µs were estimated.
Parameters such as CWmin and CWmax are overridden by
the use of 802.11e [2]. For the validations, the default 802.11e
values were used, after setting aCWmin equal to 31 according
to the 802.11b specification.
The node topology of the simulation uses five different
stations, QSTAs, contending for channel access. Each QSTA
uses all four ACs, and virtual collisions therefore occur.
Poisson distributed traffic consisting of 1024-bytes packets was
generated at equal amounts to each AC.
B. Validation of the Medium Access Delay Predictions
Fig. 3 compares the mean MAC delay predicted by the
analyses presented in this paper with simulation results. It is
observed that the analytical model gives a fairly good
description of the mean MAC delay. However, the simulation
curves are considerably more “smooth” than the analytical
curves. The figure also shows that the MAC delay of AC[0]
and AC[1] goes to infinity. This is a situation referred to as
medium access starvation, because AC[0] and AC[1] are
starved, and may not access the channel. The analysis predicts
that this starvation occurs at slightly lower channel load than
what was observed in the simulations.
C. Validation of the Queueing Delay Predictions
Fig. 4, Fig. 5, Fig. 6 and Fig. 7 present analytical
predictions of the queueing delay for AC[3], AC[2], AC[1] and
AC[0], respectively, and compare the predictions with
simulation results.
The figures show that the queueing delay of all the ACs
goes to infinity. This is a situation referred to as queueing
starvation, because all higher layer protocols are starved from
communication when the queueing delay is infinite (or when
buffered packets are dropped).
It is observed that the analysis gives a fairly good
description for the queueing delay experienced by the
simulations. However, there are some discrepancies between
the analysis and the simulations, especially for AC[1] and
AC[2].
250
AC[3] - Analysis
Mean Queueing Delay (ms)
The mean total delay is then simply:
200
AC[3] - Simulation
150
100
50
Mean Medium Access Delay (ms)
45
0
40
0
35
500
1000
1500
2000
2500
3000
Traffic generated per AC [Kb/s]
30
Figure 4. Mean queueing delay comparison of AC[3] between analytical and
simulation results.
25
20
15
10
5
0
0
1000
2000
3000
4000
5000
6000
Traffic generated per AC [Kb/s]
AC[3] - Analysis
AC[2] - Analysis
AC[1] - Analysis
AC[0] - Analysisl
AC[3] - Simulation
AC[2] - Simulation
AC[1] - Simulation
AC[0] - Simulation
Figure 3. Mean MAC delay comparison between analytical (numerical) and
simulation results of all ACs.
Earlier work has mostly focused on the mean saturation
delay of the medium access [4-5], while the mean nonsaturation delay is provided in [6-7]. These two results form an
upper and a lower bound on the actual mean medium access
delay. Likewise, an upper and a lower bound on the queueing
delay are provided in [8]. In this paper, on the contrary, more
exact expressions for the MAC delay and the queueing delay
are found. The results are validated against simulation results.
250
Mean Queueing Delay (ms)
AC[2] - Analysis
200
AC[2] - Simulation
150
100
It is observed that the predictions of the mean MAC delay
and the mean queueing delay match relatively well with
simulations.
50
0
0
500
1000
1500
2000
2500
Traffic generated per AC [Kb/s]
VIII. FURTHER WORK
Figure 5. Mean queueing delay comparison of AC[2] between analytical and
simulation results.
250
Mean Queueing Delay (ms)
AC[1] - Analysis
200
AC[1] - Simulation
150
At the time of writing, however, a new version of the TKN
simulation module has been released (as of February 16 2006).
The new release implements the backoff changes seen in the
final draft version 13 of the standard.
100
50
0
0
500
1000
1500
2000
Traffic generated per AC [Kb/s]
Figure 6. Mean queueing delay comparison of AC[1] between analytical and
simulation results.
AC[0] - Analysis
200
AC[0] - Simulation
150
100
50
0
0
250
500
In follow-up work, we plan to compare the impact of the
backoff countdown method on the predictions of the total
delay, by comparing Bianchi's model with Xiao's model, and
by comparing simulation results with different methods for
decrementing the backoff counter.
B. Analysis of Jitter and of the Delay Variance
An expression of the variance of the total delay is found
through Eq. (39), Eq. (29) and Eq. (36). Further work should
find this variance by deriving explicit expressions for Di( 2) (1) ,
i ( 3)
and for DSat
(1) . The variance of total delay can then be
compared with simulation results. We plan to undertake this
work as a first step on the way to an analytical jitter analysis of
802.11 EDCA and of 802.11 DCF.
250
Mean Queueing Delay (ms)
A. Refining the Model for the Countdown Delay
This paper uses the model of Xiao - with the expression for
i
Dstate
( z) found in Eq. (17) - primarily because it easily
incorporates AIFS differentiation into the model through Eq.
(8). It is also convenient, since the TKN module used for
simulation of 802.11e EDCA in ns-2 implements the draft
version 4 of the standard, where this model is adequate.
750
1000
1250
1500
Traffic generated per AC [Kb/s]
Figure 7. Mean queueing delay comparison of AC[0] between analytical and
simulation results.
VII. CONCLUSION
The mean medium access delay and the mean queueing
delay together constitute the average total delay of the MAC, as
seen from an upper layer protocol or application.
This paper predicts both the medium access delay and the
queueing delay. The analysis is based on a Markov model that
covers the full range from a non-saturated to a fully saturated
channel.
C. Delay-Oriented Admission Control
Queueing starvation occurs when the utilization factor
ρi = min(1, λi DiSAT ) equals 1, and the queue length is thus
theoretically infinite, resulting in buffer overflow in practical
situations. At this point the medium access delay, Di , equals
DiSAT , because the post-backoff delay must always be taken into
account under saturation conditions. The size of the medium
access delay when the queueing starvation occurs depends on
the size of the traffic intensity λi . Since the medium access
delay, Di , is finite in this situation, while it is infinite under
medium access starvation, it is safe to say that the queueing
starvation normally occurs before the medium access
starvation occurs.
The queueing starvation is therefore the limiting factor on
the usability of 802.11. As a consequence, model-based
admission control should try to configure the system to ensure
that the MAC delay matches the admitted rate of the traffic of
each
EDCAF.
If
the
utilization
factor
SAT
of
an
EDCAF
of
AC
i
equals
1, the
ρ EDCAF = min(1, λ EDCAF Di )
admitted traffic of the EDCAF does not get the resources it
should be granted. In other words, the admission control must
avoid that admitted traffic of an EDCAF is subject to queueing
starvation. This will be explored in follow-up work.
ACKNOWLEDGMENTS
This work has been supported by the OBAN project, which
is funded by the European Commissions 6th Framework
Program. However, the information in this document is
provided as is, and no guarantee is given that the information is
fit for any purpose. Other OBAN partners are not committed
under any circumstances by its content.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
IEEE 802.11 WG, "Part 11: Wireless LAN Medium Access Control
(MAC) and Physical Layer (PHY) specification", IEEE 1999.
IEEE 802.11 WG, "Draft Supplement to Part 11: Wireless Medium
Access Control (MAC) and physical layer (PHY) specifications:
Medium Access Control (MAC) Enhancements for Quality of Service
(QoS)", IEEE 802.11e/D13.0, Jan. 2005.
Bianchi, G., "Performance Analysis of the IEEE 802.11 Distributed
Coordination Function", IEEE J-SAC Vol. 18 N. 3, Mar. 2000, pp. 535547.
Ziouva, E. and Antonakopoulos, T., "CSMA/CA performance under
high traffic conditions: throughput and delay analysis", Computer
Communications, vol. 25, pp. 313-321, Feb. 2002.
Xiao, Y., "Performance analysis of IEEE 802.11e EDCF under
saturation conditions", Proceedings of ICC, Paris, France, June 2004.
Engelstad, P.E., Østerbø O.N., "Non-Saturation and Saturation Analysis
of IEEE 802.11e EDCA with Starvation Prediction", Proceedings of the
Eighth ACM International Symposium on Modeling, Analysis &
Simulation of Wireless and Mobile Systems (ACM MSWiM 2005),
Montreal,
Canada,
Oct.
10-13,
2005.
(See
also:
http://www.unik.no/~paalee/research.htm.)
Engelstad, P.E., Østerbø O.N., "Delay and Throughput Analysis of IEEE
802.11e EDCA with AIFS Differentiation under Varying Traffic Loads",
Proceedings of the Fifth International IEEE Workshop on Wireless
Local Networks (WLN ’05), Sydney, Australia, Nov. 15-17, 2005. (See
also: http://www.unik.no/~paalee/PhD.htm.)
Engelstad, P.E. and Østerbø O.N., "Queueing Delay Analysis of 802.11e
EDCA", Proceedings of The Third Annual Conference on Wireless On
demand Network Systems and Services (WONS 2006), Les Menuires,
France, Jan. 18-20, 2006. (See also: http://hal.inria.fr/inria-00001016 or
http://hal.inria.fr/view_by_stamp.php?label=WONS2006&langue=en&a
ction_todo=view&id=inria-00001016&version=1 .)
[9]
[10]
[11]
[12]
[13]
Engelstad, P.E. and Østerbø O.N., "The Delay Distribution of IEEE
802.11e EDCA and 802.11 DCF", Proceedings of the 25th IEEE
International Performance Computing and Communications Conference
(IPCCC'06), Phoenix, Arizona, April 10 - 12, 2006. (See also:
http://www.unik.no/~paalee/research.htm.)
Engelstad, P.E., Østerbø O.N., "Differentiation of the Downlink 802.11e
Traffic in the Virtual Collision Handler", Proceedings of the Fifth
International IEEE Workshop on Wireless Local Networks (WLN ’05),
Sydney,
Australia,
Nov.
15-17,
2005.
(See
also:
http://www.unik.no/~paalee/PhD.htm.)
Kleinrock, L., “Queuing Systems,Vol. I”, John Wiley, 1975.
Wietholter, S. and Hoene, C., "Design and verification of an IEEE
802.11e EDCF simulation model in ns-2.26", Technische Universitet at
Berlin, Tech. Rep. TKN-03-019, November 2003.
IEEE 802.11b WG, "Part 11: Wireless LAN Medium Access Control
(MAC) and Physical Layer (PHY) specification: High-speed Physical
Layer Extension in the 2.4 GHz Band, Supplement to IEEE 802.11
Standard", IEEE, Sep. 1999.
APPENDIX
i
It is clear that the expression for Dstate
( z) should reflect the
Markov model chosen. This paper uses the model of Xiao i
with the expression for Dstate
( z) found in Eq. (17) - primarily
because it easily incorporates AIFS differentiation into the
model through Eq. (8). Secondarily, the TKN module used for
simulation of 802.11e EDCA in ns-2 implements the draft
version 4 of the standard, where this model is adequate.
With the model of Bianchi, on the contrary, there is no
countdown blocking [expressed by Eq. (6)], and the weighted
average delay associated with the countdown of the backoff
counter can be written Te (1 − pb ) + Ts ps + Tc ( pb − ps ) . Hence, the
corresponding z-transform is simply:
i , BIANCHI
Dstate
( z) = (1 − pb ) zTe + ps zTs + ( pb − ps ) zTc .
(40)
The first order moment of this countdown delay DiBIANCHI , state is
found as:
DiBIANCHI , state = (1 − p b )Te + p s Ts + ( p b − p s )Tc ,
(41)
while the second order moment, DiBIANCHI ,state 2 , can be
determined by:
2
DiBIANCHI , state = (1 − p b )Te2 + p s Ts2 + ( p b − p s )Tc2 .
(42)