Performance Analysis of the IEEE 802.11e Enhanced Distributed
  Coordination Function using Cycle Time Approach
Performance Analysis of the IEEE 802.11e
Enhanced Distributed Coordination Function using
Cycle Time Approach †
Inanc Inan, Feyza Keceli, and Ender Ayanoglu
Center for Pervasive Communications and Computing
Department of Electrical Engineering and Computer Science
The Henry Samueli School of Engineering
University of California, Irvine, 92697-2625
Email: {iinan, fkeceli, ayanoglu}@uci.edu
Abstract
The recently ratified IEEE 802.11e standard defines the Enhanced Distributed Channel Access (EDCA) function
for Quality-of-Service (QoS) provisioning in the Wireless Local Area Networks (WLANs). The EDCA uses Carrier
Sense Multiple Access with Collision Avoidance (CSMA/CA) and slotted Binary Exponential Backoff (BEB)
mechanism. We present a simple mathematical analysis framework for the EDCA function. Our analysis considers
the fact that the distributed random access systems exhibit cyclic behavior where each station successfully transmits
a packet in a cycle. Our analysis shows that an AC-specific cycle time exists for the EDCA function. Validating
the theoretical results via simulations, we show that the proposed analysis accurately captures EDCA saturation
performance in terms of average throughput, medium access delay, and packet loss ratio. The cycle time analysis
is a simple and insightful substitute for previously proposed more complex EDCA models.
I. INTRODUCTION
The IEEE 802.11e standard [1] specifies the Hybrid Coordination Function (HCF) which enables
prioritized and parameterized Quality-of-Service (QoS) services at the MAC layer. The HCF combines
a distributed contention-based channel access mechanism, referred to as Enhanced Distributed Channel
Access (EDCA), and a centralized polling-based channel access mechanism, referred to as HCF Con-
trolled Channel Access (HCCA). We confine our analysis to the EDCA scheme, which uses Carrier
† This work is supported by the Center for Pervasive Communications and Computing, and by Natural Science Foundation under Grant No.
0434928. Any opinions, findings, and conclusions or recommendations expressed in this material are those of authors and do not necessarily
reflect the view of the Natural Science Foundation.
http://arxiv.org/abs/0704.1838v1
Sense Multiple Access with Collision Avoidance (CSMA/CA) and slotted Binary Exponential Backoff
(BEB) mechanism as the basic access method. The EDCA defines multiple Access Categories (AC) with
AC-specific Contention Window (CW) sizes, Arbitration Interframe Space (AIFS) values, and Transmit
Opportunity (TXOP) limits to support MAC-level QoS and prioritization.
We evaluate the EDCA performance for the saturation (asymptotic) case. The saturation analysis
provides the limits reached by the system throughput and protocol service time in stable conditions
when every station has always backlogged data ready to transmit in its buffer. The analysis of the
saturation provides in-depth understanding and insights into the random access schemes and the effects
of different contention parameters on the performance. The results of such analysis can be employed in
access parameter adaptation or in a call admission control algorithm.
Our analysis is based on the fact that a random access system exhibits cyclic behavior. A cycle time is
defined as the duration in which an arbitrary tagged user successfully transmits one packet on average [2].
We will derive the explicit mathematical expression of the AC-specific EDCA cycle time. The derivation
considers the AIFS and CW differentiation by employing a simple average collision probability analysis.
We will use the EDCA cycle time to predict the first moments of the saturation throughput, the service
time, and the packet loss probability. We will show that the results obtained using the cycle time model
closely follow the accurate predictions of the previously proposed more complex analytical models and
simulation results. Our cycle time analysis can serve as a simple and practical alternative model for EDCA
saturation throughput analysis.
II. EDCA OVERVIEW
The IEEE 802.11e EDCA is a QoS extension of IEEE 802.11 Distributed Coordination Function (DCF).
The major enhancement to support QoS is that EDCA differentiates packets using different priorities and
maps them to specific ACs that are buffered in separate queues at a station. Each ACi within a station
(0 ≤ i ≤ imax, imax = 3 in [1]) having its own EDCA parameters contends for the channel independently
of the others. Following the convention of [1], the larger the index i is, the higher the priority of the AC
is. Levels of services are provided through different assignments of the AC-specific EDCA parameters;
AIFS, CW, and TXOP limits.
If there is a packet ready for transmission in the MAC queue of an AC, the EDCA function must sense
the channel to be idle for a complete AIFS before it can start the transmission. The AIFS of an AC is
determined by using the MAC Information Base (MIB) parameters as AIFS = SIFS+AIFSN ×Tslot,
where AIFSN is the AC-specific AIFS number, SIFS is the length of the Short Interframe Space, and
Tslot is the duration of a time slot.
If the channel is idle when the first packet arrives at the AC queue, the packet can be directly transmitted
as soon as the channel is sensed to be idle for AIFS. Otherwise, a backoff procedure is completed following
the completion of AIFS before the transmission of this packet. A uniformly distributed random integer,
namely a backoff value, is selected from the range [0,W ]. The backoff counter is decremented at the slot
boundary if the previous time slot is idle. Should the channel be sensed busy at any time slot during AIFS
or backoff, the backoff procedure is suspended at the current backoff value. The backoff resumes as soon
as the channel is sensed to be idle for AIFS again. When the backoff counter reaches zero, the packet is
transmitted in the following slot.
The value of W depends on the number of retransmissions the current packet experienced. The initial
value of W is set to the AC-specific CWmin. If the transmitter cannot receive an Acknowledgment (ACK)
packet from the receiver in a timeout interval, the transmission is labeled as unsuccessful and the packet
is scheduled for retransmission. At each unsuccessful transmission, the value of W is doubled until the
maximum AC-specific CWmax limit is reached. The value of W is reset to the AC-specific CWmin if the
transmission is successful, or the retry limit is reached thus the packet is dropped.
The higher priority ACs are assigned smaller AIFSN. Therefore, the higher priority ACs can either
transmit or decrement their backoff counters while lower priority ACs are still waiting in AIFS. This
results in higher priority ACs facing a lower average probability of collision and relatively faster progress
through backoff slots. Moreover, in EDCA, the ACs with higher priority may select backoff values from
a comparably smaller CW range. This approach prioritizes the access since a smaller CW value means a
smaller backoff delay before the transmission.
Upon gaining the access to the medium, each AC may carry out multiple frame exchange sequences as
long as the total access duration does not go over a TXOP limit. Within a TXOP, the transmissions are
separated by SIFS. Multiple frame transmissions in a TXOP can reduce the overhead due to contention.
A TXOP limit of zero corresponds to only one frame exchange per access.
An internal (virtual) collision within a station is handled by granting the access to the AC with the
highest priority. The ACs with lower priority that suffer from a virtual collision run the collision procedure
as if an outside collision has occured.
III. RELATED WORK
In this section, we provide a brief summary of the studies in the literature on the theoretical DCF and
EDCA function saturation performance analysis.
Three major saturation performance models have been proposed for DCF; i) assuming constant collision
probability for each station, Bianchi [3] developed a simple Discrete-Time Markov Chain (DTMC) and the
saturation throughput is obtained by applying regenerative analysis to a generic slot time, ii) Cali et al. [4]
employed renewal theory to analyze a p-persistent variant of DCF with persistence factor p derived from
the CW, and iii) Tay et al. [5] instead used an average value mathematical method to model DCF backoff
procedure and to calculate the average number of interruptions that the backoff timer experiences. Having
the common assumption of slot homogeneity (for an arbitrary station, constant collision or transmission
probability at an arbitrary slot), these models define all different renewal cycles all of which lead to
accurate saturation performance analysis.
These major methods (especially [3]) are modified by several researchers to include the extra features of
the EDCA function in the saturation analysis. Xiao [6] extended [3] to analyze only the CW differentiation.
Kong et al. [7] took AIFS differentiation into account. On the other hand, these EDCA extensions miss the
treatment of varying collision probabilities at different AIFS slots due to varying number of contending
stations. Robinson et al. [8] proposed an average analysis on the collision probability for different
contention zones during AIFS. Hui et al. [9] unified several major approaches into one approximate average
model taking into account varying collision probability in different backoff subperiods (corresponds to
contention zones in [8]). Zhu et al. [10] proposed another analytical EDCA Markov model averaging the
transition probabilities based on the number and the parameters of high priority flows. Inan et al. [11]
proposed a 3-dimensional DTMC which provides accurate treatment of AIFS and CW differentiation.
Another 3-dimensional DTMC is proposed by Tao et al. [12] in which the third dimension models the
state of backoff slots between successive transmission periods. The fact that the number of idle slots
between successive transmissions can be at most the minimum of AC-specific CWmax values is considered.
Independently, Zhao et al. [13] had previously proposed a similar model for the heterogeneous case where
each station has traffic of only one AC. Banchs et al. [14] proposed another model which considers varying
collision probability among different AIFS slots due to a variable number of stations. Lin et al. [15]
extended [5] in order to carry out mean value analysis for approximating AIFS and CW differentiation.
Our approach is based on the observation that the transmission behavior in the 802.11 WLAN follows a
pattern of periodic cycles. Previously, Medepalli et al. [2] provided explicit expressions for average DCF
cycle time and system throughput. Similarly, Kuo et al. [16] calculated the EDCA transmission cycle
assuming constant collision probability for any traffic class. On the other hand, such an assumption leads
to analytical inaccuracies [7]-[15]. The main contribution is that we incorporate accurate AIFS and CW
differentiation calculation in the EDCA cycle time analysis. We show that the cyclic behavior is observed
on a per AC basis in the EDCA. To maintain the simplicity of the cycle time analysis, we employ averaging
on the AC-specific collision probability. The comparison with more complex and detailed theoretical and
simulation models reveals that the analytical accuracy is preserved.
IV. EDCA CYCLE TIME ANALYSIS
In this section, we will first derive the AC-specific average collision probability. Next, we will calculate
the AC-specific average cycle time. Finally, we will relate the average cycle time and the average collision
probability to the average normalized throughput, EDCA service time, and packet loss probability.
A. AC-specific Average Collision Probability
The difference in AIFS of each AC in EDCA creates the so-called contention zones or periods as shown
in Fig. 1 [8],[9]. In each contention zone, the number of contending stations may vary. We employ an
average analysis on the AC-specific collision probability rather than calculating it separately for different
AIFS and backoff slots as in [11]-[14]. We calculate the AC-specific collision probability according to
the long term occupancy of AIFS and backoff slots.
We define pci,x as the conditional probability that ACi experiences either an external or an internal
collision given that it has observed the medium idle for AIFSx and transmits in the current slot (note
AIFSx ≥ AIFSi should hold). For the following, in order to be consistent with the notation of [1],
we assume AIFS0 ≥ AIFS1 ≥ AIFS2 ≥ AIFS3. Let di = AIFSNi − AIFSN3. Following the slot
homogeneity assumption of [3], assume that each ACi transmits with constant probability, τi. Also, let
the total number ACi flows be Ni. Then, for the heterogeneous scenario in which each station has only
one AC
pci,x = 1−
i′≤dx
(1− τi′)
(1− τi)
. (1)
We only formulate the situation when there is only one AC per station, therefore no internal collisions
can occur. Note that this simplification does not cause any loss of generality, because the proposed model
can be extended for the case of higher number of ACs per station as in [7],[11].
We use the Markov chain shown in Fig. 2 to find the long term occupancy of the contention zones.
Each state represents the nth backoff slot after the completion of the AIFS3 idle interval following a
transmission period. The Markov chain model uses the fact that a backoff slot is reached if and only if
no transmission occurs in the previous slot. Moreover, the number of states is limited by the maximum
idle time between two successive transmissions which is Wmin = min(CWi,max) for a saturated scenario.
The probability that at least one transmission occurs in a backoff slot in contention zone x is
ptrx = 1−
i′:di′≤dx
(1− τi′)
Ni′ . (2)
Note that the contention zones are labeled with x regarding the indices of d. In the case of an equality in
AIFS values of different ACs, the contention zone is labeled with the index of AC with higher priority.
Given the state transition probabilities as in Fig. 2, the long term occupancy of the backoff slots b′n can
be obtained from the steady-state solution of the Markov chain. Then, the AC-specific average collision
probability pci is found by weighing zone specific collision probabilities pci,x according to the long term
occupancy of contention zones (thus backoff slots)
pci =
∑Wmin
n=di+1
pci,xb
∑Wmin
n=di+1
where x = max
y | dy = max
(dz | dz ≤ n)
which shows x is assigned the highest index value within
a set of ACs that have AIFSN smaller than or equal to n+AIFSN3. This ensures that at backoff slot n,
ACi has observed the medium idle for AIFSx. Therefore, the calculation in (3) fits into the definition of
pci,x .
B. AC-Specific Average Cycle Time
Intuitively, it can be seen that each user transmitting at the same AC has equal cycle time, while the
cycle time may differ among ACs. Our analysis will also mathematically show this is the case. Let Ei[tcyc]
be average cycle time for a tagged ACi user. Ei[tcyc] can be calculated as the sum of average duration for
i) the successful transmissions, Ei[tsuc], ii) the collisions, Ei[tcol], and iii) the idle slots, Ei[tidle] in one
cycle.
In order to calculate the average time spent on successful transmissions during an ACi cycle time, we
should find the expected number of total successful transmissions between two successful transmissions
of ACi. Let Qi represent this random variable. Also, let γi be the probability that the transmitted packet
belongs to an arbitrary user from ACi given that the transmission is successful. Then,
n=di+1
psi,n/Ni
psj,n
where
psi,n =
(1− τi)
i′:di′≤n−1
(1− τi′)Ni′ , if n ≥ di + 1
0, if n < di + 1.
Then, the Probability Mass Function (PMF) of Qi is
Pr(Qi = k) = γi(1− γi)
k, k ≥ 0. (6)
We can calculate expected number of successful transmissions of any ACj during the cycle time of
ACi, STj,i, as
STj,i = NjE[Qi]
1− γi
. (7)
Inserting E[Qi] = (1 − γi)/γi in (7), our intuition that each user from ACi can transmit successfully
once on average during the cycle time of another ACi user, i.e., STi,i = Ni, is confirmed. Therefore, the
average cycle time of any user belonging to the same AC is equal in a heterogeneous scenario where each
station runs only one AC. Including the own successful packet transmission time of tagged ACi user in
Ei[tsuc], we find
Ei[tsuc] =
STj,iTsj (8)
where Tsj is defined as the time required for a successful packet exchange sequence. Tsj will be derived
in (16).
To obtain Ei[tcol], we need to calculate average number of users that involve in a collision, Ncn , at the
nth slot after last busy time for given Ni and τi, ∀i. Let the total number of users transmitting at the n
th slot
after last busy time be denoted as Yn. We see that Yn is the sum of random variables, Binomial(Ni, τi),
∀i : di ≤ n− 1. Employing simple probability theory, we can calculate Ncn = E[Yn|Yn ≥ 2]. After some
simplification,
Ncn =
i:di≤n−1
(Niτi − psi,n)
i:di≤n−1
(1− τi)Ni −
i:di≤n−1
psi,n
If we let the average number of users involved in a collision at an arbitrary backoff slot be Nc, then
b′nNcn . (10)
We can also calculate the expected number of collisions that an ACj user experiences during the cycle
time of an ACi, CTj,i, as
CTj,i =
1− pcj
STj,i. (11)
Then, defining Tcj as the time wasted in a collision period (will be derived in (17),
Ei[tcol] =
CTj,iTcj . (12)
Given pci , we can calculate the expected number of backoff slots Ei[tbo] that ACi waits before attempting
a transmission. Let Wi,k be the CW size of ACi at backoff stage k [11]. Note that, when the retry limit
ri is reached, any packet is discarded. Therefore, another Ei[tbo] passes between two transmissions with
probability prici
Ei[tbo] =
pk−1ci (1− pci)
. (13)
Noticing that between two successful transmissions, ACi also experiences CTi,i collisions,
Ei[tidle] = Ei[tbo](CTi,i/Ni + 1)tslot. (14)
As shown in [9], the transmission probability of a user using ACi,
Ei[tbo] + 1
. (15)
Note that, in [9], it is proven that the mean value analysis for the average transmission probability as
in (15) matches the Markov analysis of [3].
The fixed-point equations (1)-(15) can numerically be solved for τi and pci , ∀i. Then, each component
of the average cycle time for ACi, ∀i, can be calculated using (4)-(14).
C. Performance Analysis
Let Tpi be the average payload transmission time for ACi (Tpi includes the transmission time of MAC
and PHY headers), δ be the propagation delay, Tack be the time required for acknowledgment packet (ACK)
transmission. Then, for the basic access scheme, we define the time spent in a successful transmission
Tsi and a collision Tci for any ACi as
Tsi =Tpi + δ + SIFS + Tack + δ + AIFSi (16)
Tci =Tp∗i + ACK Timeout+ AIFSi (17)
where Tp∗
is the average transmission time of the longest packet payload involved in a collision [3]. For
simplicity, we assume the packet size to be equal for any AC, then Tp∗
= Tpi . Being not explicitly specified
in the standards, we set ACK Timeout, using Extended Inter Frame Space (EIFS) as EIFSi −AIFSi.
Note that the extensions of (16) and (17) for the RTS/CTS scheme are straightforward [3].
The average cycle time of an AC represents the renewal cycle for each AC. Then, the normalized
throughput of ACi is defined as the successfully transmitted information per renewal cycle
NiTpi
Ei[tsuc] + Ei[tcol] + Ei[tidle]
. (18)
The AC-specific cycle time is directly related but not equal to the mean protocol service time. By
definition, the cycle time is the duration between successful transmissions. We define the average protocol
service time such that it also considers the service time of packets which are dropped due to retry limit.
On the average, 1/pi,drop service intervals correspond to 1/pi,drop − 1 cycles. Therefore, the mean service
time µi can be calculated as
µi = (1− pi,drop)Ei[tcyc]. (19)
Simply, the average packet drop probability due to MAC layer collisions is
pi,drop = p
. (20)
V. NUMERICAL AND SIMULATION RESULTS
We validate the accuracy of the numerical results by comparing them to the simulation results obtained
from ns-2 [17]. For the simulations, we employ the IEEE 802.11e HCF MAC simulation model for ns-2.28
[18]. This module implements all the EDCA and HCCA functionalities stated in [1].
In simulations, we consider two ACs, one high priority (AC3) and one low priority (AC1). Each station
runs only one AC. Each AC has always buffered packets that are ready for transmission. For both ACs,
the payload size is 1000 bytes. RTS/CTS handshake is turned on. The simulation results are reported for
the wireless channel which is assumed to be not prone to any errors during transmission. The errored
channel case is left for future study. All the stations have 802.11g Physical Layer (PHY) using 54 Mbps
and 6 Mbps as the data and basic rate respectively (Tslot = 9 µs, SIFS = 10 µs) [19]. The simulation
runtime is 100 seconds.
In the first set of experiments, we set AIFSN1 = 3, AIFSN3 = 2, CW1,min = 31, CW3,min = 15,
m1 = m3 = 3, r1 = r3 = 7. Fig. 3 shows the normalized throughput of each AC when both N1 and N3
are varied from 5 to 30 and equal to each other. As the comparison with a more detailed analytical model
[11] and the simulation results reveal, the cycle time analysis can predict saturation throughput accurately.
Fig. 4 and Fig. 5 display the mean protocol service time and packet drop probability respectively for
the same scenario of Fig. 3. As comparison with [11] and the simulation results show, both performance
measures can accurately be predicted by the proposed cycle time model. Although not included in the
figures, a similar discussion holds for the comparison with other detailed and/or complex models of
[12]-[14].
In the second set of experiments, we fix the EDCA parameters of one AC and vary the parameters
of the other AC in order to show the proposed cycle time model accurately captures the normalized
throughput for different sets of EDCA parameters. In the simulations, both N1 and N3 are set to 10.
Fig. 6 shows the normalized throughput of each AC when we set AIFSN3 = 2, CW3,min = 15, and vary
AIFSN1 and CW1,min. Fig. 7 shows the normalized throughput of each AC when we set AIFSN1 = 4,
CW1,min = 127, and vary AIFSN3 and CW3,min. As the comparison with simulation results show, the
predictions of the proposed cycle time model are accurate. We do not include the results for packet drop
probability and service time for this experiment. No discernable trends toward error are observed.
VI. CONCLUSION
We have presented an accurate cycle time model for predicting the EDCA saturation performance
analytically. The model accounts for AIFS and CW differentiation mechanisms of EDCA. We employ a
simple average collision probability calculation regarding AIFS and CW differentiation mechanisms of
EDCA. Instead of generic slot time analysis of [3], we use the AC-specific cycle time as the renewal cycle.
We show that the proposed simple cycle time model performs as accurate as more detailed and complex
models previously proposed in the literature. The mean saturation throughput, protocol service time and
packet drop probability are calculated using the model. This analysis also highlights some commonalities
between approaches in EDCA saturation performance analysis. The simple cycle time analysis can provide
invaluable insights for QoS provisioning in the WLAN.
REFERENCES
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Transmission/
Collision period
AIFSN
AIFSN
AIFSN
AIFSN
No Tx Zone 3 Zone 2 Zone 1
AC3 in Backoff
AC2 in Backoff
AC1 in Backoff
AC0 in Backoff
Fig. 1. EDCA backoff after busy medium.
1 2 d2 d2+1 d1 d1+1
tr 1-p
tr 1-p
Fig. 2. Transition through backoff slots in different contention zones for the example given in Fig.1.
5 10 15 20 25 30
Number of AC
 and AC
Cycle−AC
Cycle−AC
Cycle−total
[11]−AC
[11]−AC
[11]−total
Sim−AC
Sim−AC
Sim−total
Fig. 3. Analyzed and simulated normalized throughput of each AC when both N1 and N3 are varied from 5 to 30 and equal to each other
for the cycle time analysis. Analytical results of the model proposed in [11] are also added for comparison.
5 10 15 20 25 30
Number of AC
 and AC
Cycle−AC
Cycle−AC
[11]−AC
[11]−AC
Sim−AC
Sim−AC
Fig. 4. Analyzed and simulated mean protocol service time of each AC when both N1 and N3 are varied from 5 to 30 and equal to each
other for the proposed cycle time analysis and the model in [11].
5 10 15 20 25 30
Number of AC
 and AC
Cycle−AC
Cycle−AC
[11]−AC
[11]−AC
Sim−AC
Sim−AC
Fig. 5. Analyzed and simulated mean packet drop probability of each AC when both N1 and N3 are varied from 5 to 30 and equal to
each other for the proposed cycle time analysis and the model in [11].
0 50 100 150 200 250
1,min
A=0−AC
A=0−AC
A=1−AC
A=1−AC
A=2−AC
A=2−AC
sim−AC
sim−AC
Fig. 6. Analytically calculated and simulated performance of each AC when AIFSN3 = 2, CW3,min = 15, N1 = N3 = 10, AIFSN1
varies from 2 to 4, and CW1,min takes values from the set {15, 31, 63, 127, 255}. Note that AIFSN1 − AIFSN3 is denoted by A.
0 20 40 60 80 100 120
3,min
A=0−AC
A=0−AC
A=1−AC
A=1−AC
A=2−AC
A=2−AC
sim−AC
sim−AC
Fig. 7. Analytically calculated and simulated performance of each AC when AIFSN1 = 4, CW1,min = 127, N1 = N3 = 10, AIFSN3
varies from 2 to 4, and CW3,min takes values from the set {15, 31, 63, 127}. Note that AIFSN1 − AIFSN3 is denoted by A.
	Introduction
	EDCA Overview
	Related Work
	EDCA Cycle Time Analysis
	AC-specific Average Collision Probability
	AC-Specific Average Cycle Time
	Performance Analysis
	Numerical and Simulation Results
	Conclusion
	References
