An Analytical Model of the Virtual Collision Handler of
802.11e
Paal E. Engelstad
Olav N. Østerbø
Telenor R&D/ UniK
1331 Fornebu, Norway
Tel: +47-41633776
Telenor R&D
1331 Fornebu, Norway
Tel: +47-48212596
paal.engelstad@telenor.com
olav-norvald.osterbo@telenor.com
ABSTRACT
A number of analytical models have been proposed to describe
the priority schemes of the Enhanced Distributed Channel Access
(EDCA) mechanism of the IEEE 802.11e standard. EDCA
provides a class-based differentiated Quality of Service (QoS) to
IEEE 802.11 WLANs. Many have used a multiple number of
nodes to study the differentiation behaviour of the model.
However, in many real-life usage scenarios Internet traffic is
often asymmetric with much downlink traffic from the access
point to the stations and little traffic in the reverse direction.
Hence, most of the overall traffic differentiation will happen in
the Virtual Collision Handler (VCH) of the access point. If the
access point uses EDCA, it should know the characteristics of the
VCH to be able to control the differentiation of the downlink
traffic. The main contribution of this paper opposed to other
works is that it demonstrates how a generic channel model of
802.11e can be modified to predict the behaviour of the VCH
with a remarkably good accuracy. In doing so, we first introduce
virtual collision handling into the generic model. We observe
good match between the analytical model and simulations.
Categories and Subject Descriptors
C.2.5 [Computer-Communication Networks]: Local and WideArea Networks; C.4 [Performance of Systems]: Modeling
techniques, Performance attributes, Reliability, availability, and
serviceability.
General Terms
Performance, Reliability, Theory, Verification.
Keywords
802.11e, Virtual Collision Handler, Performance Analysis,
EDCA, Non-Saturation, AIFS, Starvation.
1. INTRODUCTION
In daily life, IEEE 802.11 WLAN [1] is mainly used for Internet
access or for access to a wired Local Area Network (LAN)
infrastructure. In both cases, the wireless station (STA) is often a
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that
copies bear this notice and the full citation on the first page. To copy
otherwise, or republish, to post on servers or to redistribute to lists,
requires prior specific permission and/or a fee.
Conference’04, Month 1–2, 2004, City, State, Country.
Copyright 2004 ACM 1-58113-000-0/00/0004…$5.00.
client that retrieves a large amount of information from the wired
network (e.g. video streaming from a server on the Internet). In
other words, traffic patterns are normally asymmetric, with little
uplink traffic from the STAs, but a large amount of downlink
traffic from the Access Point (AP).
The new IEEE 802.11 amendment [2] provides 802.11 with
mechanisms for Quality of Service (QoS). Since traffic patterns
normally are asymmetric, ensuring QoS and appropriate
differentiation of the downlink traffic is therefore of utmost
importance when 802.11e is being used.
We point out that the majority of other works that do analytical
performance evaluations, empirical simulations and/or validations
between analytical numerical results and simulations, seem to
focus on the uplink traffic problem. They present results with a
number of STAs contending for the channel, and with fairly equal
shares of traffic allocated to each station and to each AC. The
situation where the majority of traffic is downlink traffic from the
QoS-enabled Access Point (QAP) to the QoS-enabled STAs
(QSTAs) is of higher practical interest.
This paper focuses on situations where the mandatory Enhanced
Distributed Channel Access (EDCA) of 802.11e is being used.
EDCA works as an extension to the Distributed Coordination
Function (DCF) of legacy 802.11. EDCA enhances DCF by
allowing four different access categories (ACs) at each station and
a transmission queue associated with each AC. Each AC at a
station has a conceptual module responsible for channel access for
each AC and in this paper the module is referred to as a ”backoff
instance”.
A key point is that the different backoff instances in a station do
not access the channel completely independently, due to the
virtual collision handling between the queues in the station. If two
or more backoff instances on the same station try to access the
channel in the same timeslot, the station attempts to transmit the
frame of the highest priority AC, while the lower priority frames
will enter backoff.
When EDCA is being used, a QAP will be interested in ensuring
appropriate QoS of all traffic it is transmitting. Not only is it
important to ensure appropriate QoS on the wireless channel. The
QAP must also somehow control the performance of the Virtual
Collision Handler (VCH), which performs the virtual collision
handling internally in the node. With the analytical model
presented in this paper, the QAP can predict how the VCH
responds to different traffic patterns and different parameters
settings of each AC.
http://folk.uio.no/paalee/
Needless to say, being able to predict and control the performance
of the VCH can be useful not only for a QAP, but also for any
QSTA using EDCA. As such, the results presented in this paper
can be useful for any QSTA, although this paper primarily
focuses on the VCH of a QAP.
When modelling the behaviour of the VCH, we assume for
simplicity the extreme situation where all traffic is downlink
traffic from the QAP - in contrast to most other relevant work.
Then, the VCH is always free to use the wireless channel, and
will not experience collision from any other station. This actually
means that all traffic contention will occur in the VCH. The VCH
represents a “virtual” traffic channel, and we can use analytical
models that incorporate virtual collision handling to derive the
performance of the VCH.
In this paper we extend the model presented extensively in [3] and
show how it can be used to model the behaviour of the VCH of
e.g. a QAP. The reader is encouraged to consult [3] for more
details and explanations of the model used in this paper.
This model is capable of predicting the performance not only in
the saturated case, but in the whole range from a non-saturated
medium to a fully saturated channel. It also describes the use of
AIFSN as a differentiating parameter, in addition to the other
differentiation parameters encompassed by other works. A simple
closed-form equation that predicts with satisfactory accuracy the
starvation point (or ”freeze point”) of each traffic class is also
provided. The only prerequisite for a station (e.g. a QAP) to
determine that starvation of an AC has occurred, is to know the
access parameters (such as the AIFSN values of each AC
i, AIFSN [i] ]) and the traffic load on the channel. Hence, the QAP
can simply predict from the downlink traffic load that it pours into
the transmission queues, whether any AC will face starvation
when the traffic is handled by the VCH.
In order to predict the behaviour of the VCH, this paper first
introduces virtual collision handling into the aforementioned
model.
The remaining part of the paper is organized as follows: The next
section incorporates virtual collision handling into the generic
model presented in [3] and demonstrates how it can be used to
model the behaviour of a VCH (e.g. on a QAP). Then, Section 3
shows how this adaptation influences on the expression of the
throughput. In Section 4 the model is validated against
simulations. Concluding remarks follow in Section 5.
2. ANALYTICAL MODEL
2.1 Markov Model
The Markov model for the transmission process of a backoff
instance of priority class i under non-saturation and saturation
conditions is presented and explained in detail in [3]. For each
AC, i (i = 0., , ,.3) on a QSTA, the transmission probability, τ i ,
is expressed as:
τ i = bi ,0,0
1 − piL +1 ,
1 − pi
where bi , 0, 0 is given as:
i
1
bi ,0,0
Wi , j − k
Li 
Wi , j − k  j 1 − ρ i 1 − (1 − qi∗ )Wi , 0
(Wi ,0 − 1)qi pi .
1
= ∑ 1 +
(1 +
)
 pi +
∗ ∑
∗
1
1
−
−
2(1 − pi )
p
W
q
W
q
j =0 
k
0
=

i
i
j
,
i
,
0
i
i


(2)
Like in [3], Wi, j here denotes the contention window size in the
j -th backoff stage i.e. after the j -th unsuccessful transmission,
and Li is the retry limit. We refer to [3] for the calculations of the
traffic parameters ρi , qi and q i∗ .
According to [3], the countdown blocking probability, pi∗ , which
occurs in Eq. (2), is defined as:
pi∗ = min(1, pi +
( AIFSN [i ] − 2) pb ,
)
1 −τi
According to [3], the AP can in fact use this expression to predict,
from the traffic load that it pours into the transmission queues,
whether any AC will face starvation when the traffic is handled
by the VCH.
An expression for pb appearing in Eq. (3) will be provided below
[see Eq. (9)]. The only remaining parameter in Eqs. (1)-(3) is the
collision probability, p i , which will be affected by the virtual
collision handling. Expressions for p i will be derived below.
2.2 Collision Probabilities without Virtual
Collision Handling
The probability of unsuccessful transmission, p i , from one
specific backoff instance is given when at least one of the other
backoff instances does transmit in the same slot:
pi = 1 −
N −1
∏ (1 − τ
c
)n .
c
(4)
c =0,c ≠i
Here, ni denotes the number of backoff instances contending for
channel access in each priority class i , and N denotes the total
number of classes.
2.3 Collision Probabilities with Virtual
Collision Handling
It is possible to make modifications to take virtual collisions into
account in the analytical model. Consider for example a situation
with n stations, and four active transmission queues on each
station. A backoff instance can transmit packets if other backoff
instances don’t transmit, except the backoff instances of the lower
priority ACs on the same QSTA. The reason for this exception is
that the virtual collision handling mechanism ensures that upon
virtual collision the higher priority AC will be attempted for
transmission while the colliding lower priority traffic goes into
backoff. This can be generalized by the expression:
(1)
N −1
pi = 1 −
∏ (1 − τ
c =0
i
c
)n
∏ (1 − τ c )
c =0
http://www.unik.no/personer/paalee
(3)
c
.
(5)
If this expression replaces our original expression in Eq. (4),
virtual collisions are correctly incorporated in the model.
2.4 Collision Probabilities within the Virtual
Collision Handler (VCH)
With virtual collisions incorporated in the model, one may in fact
use it to study the behaviour of the Virtual Collision Handler
(VCH). Here the VCH represents the channel, while there are
only N (typically four) queues contending for access, i.e. one
queue per AC i. Hence, one may model the throughput of the
VCH by setting ni = 1 for all i. In this case, Eq. (4) is simply
replaced by:
pi = 1 −
N −1
∏ (1 − τ
c
) .
Here, we note that the highest priority class will correctly have
p N −1 = 0 , which means that it is never blocked and never
experiences a collision when it tries to access the channel for
transmission.
According to the original model in [3], the probability that a
packet from any of the backoff instances of class i is transmitted
successfully in a time slot, p i , s , is:
(7)
p i , s Ti , MSDU
(1 − p b )Te + p s Ts + ( p b − p s )Tc
,
(8)
where Te , Ts and Tc are 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. TMDSDU
is the average real-time required to transmit the MSDU part of a
data packet.
p b , which occurs both in Eq. (3) and in Eq. (8), denotes the
probability that the channel is busy (i.e. at least one backoff
instance transmits during a slot time):
N −1
p b = 1 − ∏ (1 − τ i ) .
.
(10)
If there is one transmission queue of each AC on each station, on
the contrary, there will be virtual collision handling between the
queues on each station. Then, higher priority traffic does not need
to take into account transmission of lower-priority queues on the
same station. Their transmission probabilities will not affect the
throughput of the higher priority AC. Thus, Eq. (7) above must be
replaced by:
N −1
pi,s
nτ
= i i
(1 − τ i )
(1 − τ c ) n
∏
c =0
i
∏ (1 − τ c )
c
.
(11)
c =0
Using this expression for p i , s , p s is calculated as before using
3.3 Throughput of the Virtual Collision
Handler (VCH)
One can use Eq. (11) to look at the throughput of a VCH within
one station by setting ni = 1 for all i. Then, we get:
pi , s = τ i (1 − pi ) .
(12)
Using this new expression for p i , s , both p s and S i of the VCH
Then, the throughput of class i , S i , can be written as the
average real-time duration of successfully transmitted packets by
the average real-time duration of a contention slot that follows the
special time scale of our model:
Si =
i, s
i =0
the summation in Eq. (10), and S i is calculated using Eq. (8)
above.
3. THROUGHPUT
3.1 Throughput without Virtual Collision
Handling
n iτ i N −1
∏ (1 − τ c ) nc .
(1 − τ i ) c = 0
N −1
∑p
3.2 Throughput with Virtual Collision
Handling
(6)
c = i +1
pi,s =
ps =
(9)
i =0
Finally, p s is the probability that a packet from any class is
transmitted successfully in a time slot:
are calculated as earlier, i.e. using Eq. (8) and Eq. (10).
4. VALIDATIONS
We compared numerical computations of the model with
simulations. Mathematica was used for the computations and the
TKN implementation of 802.11e for ns-2 [4] was used for the ns2 simulations. We selected 802.11b [5] with the mandatory long
preamble [5] and used the default 802.11e values summarized in
Table 1 of [3]. We use Poisson distributed traffic consisting of
1024 bytes packets sent at 11 Mbps without the optional
RTS/CTS
mechanism.
The
corresponding
values
for Te , Ts , Tc and TMDSDU are calculated in [3]. For simplicity,
we assumed that the QAP generated the same amount of downlink
traffic for each of the four ACs.
role is only to acknowledge all MAC frames that the QAP
successfully transmit on the channel. This corresponds to the
downlink scenarios presented in the frequently cited paper by
Mangold et al. [6], except that here we consider 802.11b instead
of 802.11a.
QAP
QSTA 1
Figure 2 compares numerical calculations of the analytical model
with the actual simulation results. We observe that our analytical
model of the VCH, which describes the performance on the full
range from a non-saturated (finite queues) to a saturated (infinite
queues) system, gives a good match when compared with
simulations.
QSTA 5
QSTA 2
QSTA 4
QSTA 3
Figure 1. Simulation setup to validate numerical results of
downlink traffic.
We consider a scenario with a QAP that implements a VCH and
uses four transmission queues. This configuration is depicted in
Figure 1. Here, the QSTAs are not actively initiating traffic. Their
In Figure 3 we repeat the validations using different values for the
contention window. Here we have doubled all minimum and
maximum contention windows compared to the recommended
values given in Table I. We have also shown the results on a
larger scale (up till 20000 Kbps per AC) to illustrate the
remarkably good accuracy between model and simulation results
in the saturation part of the figure.
802.11b/802.11e: Analysis vs. Simulation of the Virtual Collision Handler
Throughput per AC [Kb/s]
6000
5000
AC[0]: Simulations
AC[1]: Simulations
AC[2]: Simulations
AC[3]: Simulations
AC[0]: Numerical
AC[1]: Numerical
AC[2]: Numerical
AC[3]: Numerical
4000
3000
2000
1000
0
-1000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Traffic generated per AC [Kb/s]
Figure 2. Comparison between analytical results and simulation results using Recommended 802.11e parameter settings.
802.11b/802.11e: Analysis vs. Simulation of the Virtual Collision Handler (Doubled CW
values)
Throughput per AC [Kb/s]
5000
4500
4000
AC[0]: Simulations
AC[1]: Simulations
AC[2]: Simulations
AC[3]: Simulations
AC[0]: Numerical
AC[1]: Numerical
AC[2]: Numerical
AC[3]: Numerical
3500
3000
2500
2000
1500
1000
500
0
-500
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
Traffic generated per AC [Kb/s]
Figure 3. Comparison between analytical results and simulation results (using doubled CWmin values).
802.11b/802.11e: Analysis vs. Simulation of the Virtual
Collision Handler (Small Scale)
5000
4500
Throughput per AC [Kb/s]
4000
3500
AC[0]: Simulations
AC[1]: Simulations
AC[2]: Simulations
AC[3]: Simulations
AC[0]: Numerical
AC[1]: Numerical
AC[2]: Numerical
AC[3]: Numerical
3000
2500
2000
1500
1000
500
0
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Traffic generated per AC [Kb/s]
Figure 4. Comparison between analytical results and
simulation results (on a small scale).
However, there are ranges of Figure 2 and Figure 3 where there
are noticeable discrepancies between the curves. For Figure 3, this
range is expanded and shown on a smaller scale in Figure 4. Here,
we observe that the model – probably the AIFS-approximation - is
a little too rough on the lowest priority AC, AC[0]. Due to the fact
that AC[0] and partly also AC[1] are underestimated here, the
model incorrectly gives a throughput of AC[3] that exceeds the 1to-1 linear line. This would mean that AC[3] transmits more
traffic than is generated, which is obviously not correct. It is
indeed possible to do some improvements of the model in this
region, although one must keep in mind that the model is
approximate, and a complete match might be difficult to find
without adding considerable complexity to the model.
5. CONCLUSIONS
This paper shows how virtual collision handling can be
incorporated into an analytical model that covers the full range
from a non-saturated to a fully saturated channel.
Using a model that encompasses virtual collision handling, we
demonstrate that it is also possible to describe the behaviour of a
Virtual Collision Handler internally on a node, such as on an
Access Point. The Virtual Collision Handler is treated as a
"virtual" channel.
An access point that uses EDCA for massive downlink traffic is
therefore able to predict the levels of QoS that the data traffic it is
transmitting will obtain by its own Virtual Collision Handler. In
this way it is to a larger extent in control of the QoS of the traffic
it is sending. (Needless to say, any station – whether it is an
access point or not – may benefit from predicting the behaviour of
the Virtual Collision Handler, although we anticipate that the
model will be mostly appreciated by the access points.)
The model is calculated numerically and validated against
simulations, using 802.11b and variations of the default parameter
settings for 802.11e. The analytical model of the Virtual Collision
Handler corresponds well with our simulations.
6. REFERENCES
[1] IEEE 802.11 WG, "Part 11: Wireless LAN Medium Access
Control (MAC) and Physical Layer (PHY) specification",
IEEE 1999.
[2] 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.
[3] Engelstad, P.E. and Østerbø, O.N, "Non-Saturation and
Saturation Analysis of IEEE 802.11e EDCF with Starvation
Prediction", Proceedings of the Eighth ACM/IEEE
International Symposium on Modeling, Analysis and
Simulation of Wireless and Mobile Systems (MSWiM‘05),
Montreal, Canada, Oct. 10-13, 2005.
[4] 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.
[5] 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.
[6] Mangold, S., Choi, S., Hiertz, G., Klein, O. and Walke, B.,
"Analysis of IEEE 802.11e for QoS support in wireless
LANs", IEEE Wireless Comm, Dec. 2003, pp. 40-50.