# Performance analysis and enhancement of IEEE 802.11e EDCA networks under fading channels and unsaturated traffic conditions

Djamil Aïssani, Lina Bachiri, Nassima Abdi, Kahina Aroul

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Djamil Aïssani, Lina Bachiri, Nassima Abdi, Kahina Aroul. Performance analysis and enhancement of IEEE 802.11e EDCA networks under fading channels and unsaturated traffic conditions. 2024. [hal-04469942v2](https://hal.science/hal-04469942v2)

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# Performance analysis and enhancement of IEEE 802.11e EDCA networks under fading channels and unsaturated traffic conditions.

Djamil AÏSSANI*¹, Lina BACHIRI², Nassima ABDI³, Kahina AROUL⁴

¹, ²BEJAIA University, Research Unit LaMOS, Algeria

³, ⁴BEJAIA University, Algeria

*E-mail: djamil.aissani@univ-bejaia.dz

DOI: 10.46298/arima.idpermanent

Submitted on Day Month-in-full-text Year - Published on Day Month-in-full-text Year

Volume: N - Year: YYYY

Special Issue: Title

Editors: First name-1 Last name-1, First name-2 Nom-2,...

## Abstract

IEEE 802.11e standard is the enhanced version of the IEEE 802.11 to provide Quality of Service of Wireless Network. In IEEE 802.11e, the fundamental Medium Access Control (MAC) protocol is Enhanced Distributed Channel Access (EDCA), which provides a priority scheme by differentiating the Arbitration Inter Frame Space (AIFS), minimum and maximum Contention Window size values (CWmin, CWmax) and Transmission Opportunity limit (TXOPlimit). In this paper, we propose a modification to the IEEE 802.11e EDCA, called Enhanced EDCA (A-EDCA) to reduce unnecessary retransmissions in the case of transmission failure due to channel error. then, we present an analytical model for the performance analysis of A-EDCA under fading channel and unsaturated conditions. This model captures all the major QoS specific features, namely AIFS, minimum contention window size, maximum contention window size, virtual collision and TXOPlimit. We compare the performance of EDCA with the performance of A-EDCA.

## Keywords

EEE 802.11e; EDCA; Fading channel; Unsaturated traffic; Throughput; Markov chain.

# I INTRODUCTION

The IEEE 802.11 standard is currently one of the most popular wireless access technologies. One of the channel access mechanisms in IEEE 802.11 is Distributed Coordination Function (DCF). DCF does not support any type of priority access to the wireless medium. As a consequence, DCF provides only best effort service, and there is no mechanism to provide better service for real time traffic. As a remedy to this problem, the 'IEEE 802.11 Task Group E' has proposed a new MAC layer standard, namely IEEE 802.11e. In IEEE 802.11e, EDCA is the fundamental mechanism.
Many research efforts have been done to study the IEEE 802.11e EDCA performance, by both of analysis and simulation. Most of them assumed the ideal channel condition, which means that the packet corruptions are only due to collisions. In the following, we provide a brief summary of the proposed models for DCF and EDCA functions in the available literature.

Bianchi [1], proposed a simple analytic model to compute saturation throughput. To drive a saturation delay Ziouva and Antonakopoulous [25] extended the Bianchi's model. In [15], the authors proposed a new backoff method to enhance the performance of IEEE 802.11 DCF. In [3], the authors provide an extended model for IEEE 802.11 wireless local area networks under noisy channel.

The authors in [2], proposed a new model analytic to analysis the performance of EDCA. In [4], the authors modified the Ziouva and Antonakopoulous model [25] and extend the model to support EDCA. In [5, 6], authors analyzed IEEE 802.11e EDCA under non saturation condition. In [7, 8], the authors studied the efficiency of burst transmissions with block acknowledgements. In [9, 10, 11], the authors proposed an analytical model to study the effect of burst transmissions. In [12], an analytical model is proposed to evaluate the performance of the 802.11e in the saturated case. The authors in [13] analyze the timing behavior of the EDCA function, when it is used to support real time traffic. In [14], the authors evaluate, through simulations, the benefits derived from the adoption of the IEEE 802.11e standard in delivering multimedia over WLANs. In [16, 17], the authors studies the influence of transmission error on the MAC layer performance. In [19], the authors mathematically analyze the throughput and delay performance of the IEEE 802.11e block ACK scheme in an erroneous channel environment. In [20], Based on this previous work, our proposal summarizes Xiao model [12] and Kong model [2] the authors proposed a Markov chain model for the EDCA analysis. The proposed developed model reflects the backoff and access procedures accurately by taking account of the backoff timer freeze that includes the external collision time, the transmission time, AIFS and CW parameters. In [21], the authors In this paper, first we develop an analytical model to derive an average delay and loss estimate for 802.11e over fading channel. As the second contribution, an adjustment for the maximum number of retransmissions is proposed to maintain the QoS requirements of the realtime traffic sources. In [22], under ideal channel the authors propose an analytical model for EDCA. In [23], the authors studied the Effect of transmission opportunity limit on transmission time. The authors in [30], the authors studied the performance of IEEE 802.11p EDCA. In [31], the authors investigates the influence of the access categories communication protocol 802.11p EDCA under fading channel.

In this paper, we propose a modification to the IEEE 802.11e EDCA, called Enhanced EDCA (A-EDCA) to reduce unnecessary retransmissions in the case of transmission failure due to channel error. Then, we presents an analytical model for the performance analysis of A-EDCA under fading channel and unsaturated conditions.

## II OVERVIEW OF DCF AND EDCA

### 2.1 Distributed Coordination Function (DCF)

DCF is the fundamental MAC protocol proposed in IEEE 802.11 standard [28]. The media access is controlled by the use of interframe spaces, or IFS (Inter-Fram Spacing), which correspond to the time interval between the transmission of two frames. IFS intervals are periods of inactivity on the support transmission. In the DCF a station with a frame to transmit must sense
the channel idle for a duration, called distributed inter frame space (DIFS), and an additional backoff time. The station can initiate the transmission when the channel remains idle during all this period. The backoff time is uniformly chosen in the range (0,CW), CW is initially set to CWmin and doubled after each unsuccessful transmission until a maximum backoff window size value, CWmax is reached. For each slottime the backoff counter is decreased by one. The station transmits a frame when its backoff time reaches zero. After the successful reception of the frame, the destination station sends back an ACK immediately after a Short Inter Frame Space (SIFS). The source will retransmit the frame if it does not receive the ACK within a specified ACKtimeout. Each station maintains a retry conter that is increased by one after each retransmissions. The frame is dropped if the retry counter reaches the retrylimit. An optional mechanism named RTS/CTS is defined in DCF to reduce collisions caused by hidden terminals.

## 2.2 Enhanced Distributed Channel Access (EDCA)

EDCA is based on DCF. A set of EDCA parameters, namely Arbitration Inter Frame Space (AIFS), minimum and maximum Contention Window size values ($CW_{min}$ and $CW_{max}$), and TXOPlimit [24]. In EDCA, for a given station traffic is mapped into four different Access Categorie (AC) in the MAC layer as shown in tab1. The user priority value is defined in the IEEE802.11D bridge specification [27]. EDCA defines the following four AC for each station: AC\_VO (voice) with highest priority, AC\_VI (video), AC\_BE (best effort) and AC\_BK (background) with the lowest priority. Each AC within a station behaves like a virtual station. When a collision occurs among different $AC_i$ within the same station, the higher priority AC can transmit, while the lower priority AC suffers from a virtual collision, which is similar to real collision outside the station.

<table><caption>Table 1: Mapping between user priorities and access categories.</caption><thead><tr><th>Priority</th><th>User priority</th><th>802.11D designation</th><th>Access Category</th><th>802.11e</th><th>Designation</th></tr></thead><tbody><tr><td rowspan="6">Lowest</td><td>1</td><td>BK</td><td>AC_BK</td><td></td><td>Background</td></tr><tr><td>2</td><td>-</td><td>AC_BK</td><td></td><td>Background</td></tr><tr><td>0</td><td>BE</td><td>AC_BE</td><td></td><td>Best effort</td></tr><tr><td>3</td><td>EE</td><td>AC_BE</td><td></td><td>Best effort</td></tr><tr><td>4</td><td>CL</td><td>AC_VI</td><td></td><td>Video</td></tr><tr><td>5</td><td>VI</td><td>AC_VI</td><td></td><td>Video</td></tr><tr><td rowspan="2">Highest</td><td>6</td><td>VO</td><td>AC_VO</td><td></td><td>Voice</td></tr><tr><td>7</td><td>NC</td><td>ACVO</td><td></td><td>Voice</td></tr></tbody></table>

## III COLLISION AND TRANSMISSION ERRORS

In order to detect if a collision occurs in the transmission channel, the station simultaneously checks whether the signal sent is identical to that present on the transmission medium. If the message is not identical then another station is transmitting at the same time. On the other hand, transmission errors are managed by the data link layer.

## IV ENHANCEMENT OF EDCA FUNCTION (A-EDCA)

In IEEE 802.11e EDCA function, a node does not differentiate between the media access collision and the channel failure. The behavior of an AC after a collision or a transmission error is the same, it doubles the contention window. When AC doubles its contention window is to avoid collisions. So if the packet is lost due to transmission errors, doubling the contention
window is not necessary. To improve EDCA, we propose to treat the transmission errors before
the collision. So our solution is based on the separation of transmission errors and collisions.
In the case of transmission errors, not doubling the contention window in collisions, doubling
the contention window, named A-EDCA (Enhanced EDCA). In what follows, we present the
analytical model of A-EDCA.

V ANALYTICAL MODEL

In this section, we propose a four dimensional discrete time Markov chain for A-EDCA know-
ing that we used a model proposed in [29] with the introduction of transmission errors. We
assume a fixed number of stations N and each station has four ACᵢ, able to estimate the per-
formance metrics in the conditions of non-saturation. The analysis is conducted under fading
channel and non saturation conditions.

**5.1 Discrete time Markov chain model for A-EDCA**

In our model, time is slotted and each state represents an AC in a time slot. At the end of each
time slot, an event triggers a transition to another state [26]. Because each AC within a station
behaves like a virtual station and invokes its own backoff procedure individually.

We assume for a given $AC_i(i = 0, 1, 2, 3)$, $s(i, t)$ is defined as the stochastic process repre-
senting the backoff stage j, where $0 \le j \le m$ and m is the maximum backoff stage, $p(i, t)$
is defined as the stochastic process representing the state of $AC_i$, and $b(i, t)$ is defined as the
stochastic process that denote the value of the backoff at time t. The value of the backoff counter
is uniformly chosen from $[0, W_{i,j}]$, where $W_{i,j}$ depends on the retransmission backoff stage and
satisfies $W_{i,j+1} = 2W_{i,j} + 1$. So, the process $(s(i, t), b(i, t), p(i, t))$ is a discrete time Markov
chain under the assumption that $P_{coli}$ the transition probabilities are constant. At each time
slot, the state of each $AC_i$ is described by $(d, i, j, k)$, where d=B the $AC_i$ decrements its back-
off time slot, d=T the $AC_i$ transmits its packet and d=E for error of transmission, i is just an
index standing for the priority class, j stands for the backoff stage and takes values $(0, 1, ..., m)$,
and k stands for the backoff delay and takes values $(0, 1, ..., W_{i,j} - 1)$.
<figure><img src="image_2.png" /><figcaption>Figure 1: Markov chain model of A-EDCA function</figcaption></figure>

### 5.1.1 Transition probabilities

The transition probabilities in this model are described as follows

$$ 
\left\{
\begin{array}{ll}
p\{B, i, j, k | B, i, j, (k+1)\} = 1, & 0 \le j \le m, 0 \le k \le (w_{i,j} - 1) \\
p\{B, i, 0, k | B, i, j, 0\} = q(1-P_i)/w_{i,0}, & 0 \le j \le m, 0 \le k \le (w_{i,0} - 1) \\
p\{B, i, j, k | B, i, j-1, 0\} = P_{\text{coli}}/w_{i,j}, & 0 \le j \le m, 0 \le k \le (w_{i,j} - 1) \\
p\{B, i, m, k | B, i, m, 0\} = P_{\text{coli}}/w_{i,m}, & 0 \le k \le (w_{i,m} - 1) \\
p\{B, i, 0, k | I\} = q/w_{i,0}, & 0 \le k \le (w_{i,0} - 1) \\
p\{B, i, 1, k | T, i, 0, -1\} = P_{\text{coli}}/w_{i,1}, & 0 \le k \le (w_{i,1} - 1) \\
p\{E, i, 0, k | E, i, 0, (k+1)\} = P_E, & 0 \le k \le (w_{i,0} - 1) \\
p\{E, i, 0, k | T, i, 0, -1\} = P_e(1-P_{\text{coli}}), & 0 \le k \le (w_{i,0} - 1) \\
p\{E, i, 0, k | B, i, j, 0\} = P_e(1-P_{\text{coli}}), & 0 \le j \le m, 0 \le k \le (w_{i,j} - 1) \\
p\{E, i, 0, 0 | E, i, 0, 0\} = P_E, \\
p\{I | T, i, 0, -1\} = (1-q)(1-P_i), & 0 \le k \le (w_{i,j} - 1) \\
p\{I | B, i, j, 0\} = (1-q)(1-P_i), \\
p\{T, i, 0, -1 | E, i, 0, 0\} = 1-P_E, \\
p\{I | I\} = 1-q,
\end{array}
\right.
\quad (1)
$$
### 5.1.2 Stationary probabilities

Let $b_{i,j,k}$ be the steady probability of state $(i, j, k)$.

$$ egin{cases} b_{B,i,j,0} = P_{\text{coli}}^{j-1}(P_{\text{coli}}b_{B,i,j,0} + P_{\text{coli}}(1-P_E)b_{E,i,0,0}), & 0 \le j \le m; \\ b_{B,i,m,0} = \frac{P_{\text{coli}}^{m-1}}{1-P_{\text{coli}}}(P_{\text{coli}}b_{B,i,j,0} + P_{\text{coli}}(1-P_E)b_{E,i,0,0}), & \\ \sum_{j \ge 0} b_{B,i,j,0} = \frac{b_{B,i,j,0} + P_{\text{coli}}(1-P_E)b_{E,i,0,0}}{1-P_{\text{coli}}}, & \end{cases} \quad (2) $$

$$ b(I) = \frac{b_{E,i,0,0}}{q} \left[ \frac{(1-q)(1-P_i)(1-P_E)^{2W_{i,0}}}{P_e(1-P_{\text{coli}})(1-P_E^{W_{i,0}})} \right] \quad (3) $$

By using the normalizing condition, we obtain

$$ 1 = \sum_{j=0}^{m} \sum_{k=0}^{W_{i,j-1}} b_{B,i,k,0} + \sum_{k=0}^{W_{i,0}-1} b_{E,i,k,0} + b_{T,i,0-1} + b_I \quad (4) $$

$$ b_{E,0,0,0} = \left[ 1 + \frac{W_{i,0}(W_{i,0} + 1)}{2} \left[ \frac{(1-P_E)^2}{P_e(1-P_E^{W_{i,0}})} \right] + \left[ \frac{W_{i,0}P_{\text{coli}}(1-P_E)^2}{P_e(1-P_E^{W_{i,0}})} \right] \right. \\ \left. \left[ \frac{1}{2(1-P_{\text{coli}})} \left[ 1 + \frac{2W_{i,0}(1-P_{\text{coli}}-P_{\text{coli}}(2P_{\text{coli}})^{m-1})}{(1-2P_{\text{coli}})} \right] \right] + \right. \\ \left. \frac{(1-q)(1-P_i)(1-P_E)^2 W_{i,0}}{qP_e(1-p_{\text{coli}})(1-P_E^{W_{i,0}})} \right]^{-1} \quad (5) $$

#### Transmission probability of access categories $\tau_i$:

The probability that an $AC_i$ accesses the medium in randomly chosen time slot is expressed as

$$ \begin{aligned} \tau_i &= \sum_{j \ge 0} b_{B,i,0,0} + (1-P_E)b_{E,i,0,0} \\ &= b_{E,i,j,0} \left[ \frac{W_{i,0}(1-P_E)^2}{p_e(1-P_E^{W_{i,0}})(1-P_{\text{coli}})} \right] \\ &= \left[ 1 + \frac{W_{i,0}(W_{i,0} + 1)}{2} \left[ \frac{(1-P_E)^2}{P_e(1-P_E^{W_{i,0}})} \right] + \left[ \frac{W_{i,0}P_{\text{coli}}(1-P_E)^2}{P_e(1-P_E^{W_{i,0}})} \right] \right. \\ & \quad \left. \left[ \frac{1}{2(1-P_{\text{coli}})} \left[ 1 + \frac{2W_{i,0}(1-P_{\text{coli}}-P_{\text{coli}}(2P_{\text{coli}})^{m-1})}{(1-2P_{\text{coli}})} \right] \right] + \right. \\ & \quad \left. \frac{(1-q)(1-P_i)(1-P_E)^2 W_{i,0}}{qP_e(1-p_{\text{coli}})(1-P_E^{W_{i,0}})} \right]^{-1} \left[ \frac{W_{i,0}(1-P_E)^2}{p_e(1-P_E^{W_{i,0}})(1-P_{\text{coli}})} \right] \end{aligned} \quad (6) $$
• Transmission probability $\tau$ :

The probability that the station accesses the channel is, therefore

$$ \tau = 1 - \prod_{i=0}^{3} (1 - \tau_i) \qquad (7) $$

• Error Probability $P_e$ :

$$ P_e = 1 - (1 - BER)^{paquet} $$

• Error Probability $P_E$ :

The probability that there is a transmission error on the channel is expressed as

$$ P_E = (N - 1)\tau(1 - \tau)^{(N-2)}P_e \qquad (8) $$

• Probability of failure $P_i$ :

The probability of transmission failure is expressed as

$$ P_i = 1 - (1 - p_{\text{coli}})(1 - P_e) \qquad (9) $$

• Collision probability :

A collision occurs when a station transmits and another of $(N - 1)$ other stations also tries to convey. So $P_{\text{coli}}$ is expressed as follows

$$ P_{\text{coli}} = 1 - (1 - \tau^{N-1}) \prod_{i>i'} (1 - \tau_i') P_e \qquad (10) $$

• Probability that there is a packet in the file is given by :

$$ q = 1 - e^{-\lambda T} \qquad (11) $$

## 5.2 Normalized throughput

The normalized throughput of a given $AC_i$ is calculated as the ratio of time occupied by the transmitted information to the interval between two consecutive transmissions [3]. The throughput of each $AC_i$, $S_i$ is expressed as

$$ S_i = \frac{P_{tr} P_{si} (1 - P_e) E[P]}{(1 - P_{tr}) \delta + P_{tr} \sum_{i=0}^{3} P_{si} (1 - P_e) T_s + P_{tr} (1 - \sum_{i=0}^{3} P_{si}) T_c + P_{tr} \sum_{i=0}^{3} P_{si} P_e T_e} \qquad (12) $$

$E[P]$ is the payload size, $T_s$ is the average successful transmission, $T_c$ is the collision time and $T_e$ is the error time. $T_s$, $T_c$ and $T_e$ in basic mode can be written as
$$ egin{cases} T_s = AIFS + H + P + SIFS + ASK \\ T_{TXOP_i} = Nb_i T_s \\ T_c = H + P + SIFS \\ T_e = AIFS + RTS + SIFS + CTS + H + P + SIFS + ACK_{timeout} \end{cases} \quad (13) $$

$Nb_i = TXOP_i / T_s$, $Nb_i$ is the number of the packets transmitted in burst for each $AC_i$.

### Transmission probability for N stations:

$P_{tr}$ is the probability that at least one station transmits in a time slot, and can be obtained by

$$ P_{tr} = 1 - (1 - \tau)^N \quad (14) $$

### Probability of successful transmission:

An $AC_i$ frame can be transmitted successfully only when no other higher priority AC in the same station and no other station of the remaining $(N-1)$ transmits. Therefore, the conditional successful transmission probability $P_{si}$, can be obtained by

$$ P_{si} = \frac{N \cdot \tau_i \cdot (1 - \tau)^{(N-1)} \cdot \prod_{i'>i} (1 - \tau_{i'})}{P_{tr}} \quad (15) $$

## VI RESULTS AND DISCUSSION

In this section, we present the numerical results of our model. The following analytical results have been obtained assuming the parameters listed in Table 2.
<table><caption>Table 2: Parameters of the PHY layer and the MAC layer of the IEEE 802.11e</caption><thead><tr><td>Parameter</td><td>Numerical value</td></tr></thead><tbody><tr><td>Propagation Delay</td><td>64μs</td></tr><tr><td>Payload Size</td><td>1000 bytes</td></tr><tr><td>Phy Header(including preamble)</td><td>192 bits</td></tr><tr><td>Mac Header(including CRC bits)</td><td>272 bits</td></tr><tr><td>RTS Frame</td><td>Phy Header+160 bits</td></tr><tr><td>CTS Frame</td><td>Phy Header+112 bits</td></tr><tr><td>ACK Frame</td><td>Phy Header+112 bits</td></tr><tr><td>CTS-timeout</td><td>DIFS+CTS</td></tr><tr><td>ACK-timeout</td><td>DIFS+ACK</td></tr><tr><td>Data Rate</td><td>11 Mbps</td></tr><tr><td>Basic Rate</td><td>2 Mbps</td></tr><tr><td>Time slot</td><td>20μs</td></tr><tr><td>SIFS</td><td>1 Time slot</td></tr><tr><td>AIFS[AC3]</td><td>7 Time slot</td></tr><tr><td>AIFS[AC2]</td><td>3 Time slot</td></tr><tr><td>AIFS[AC1]</td><td>2 Time slot</td></tr><tr><td>AIFS[AC0]</td><td>2 Time slot</td></tr><tr><td>CW[AC3]</td><td>{7,15,31,63}</td></tr><tr><td>CW[AC2]</td><td>{15,31,63,127}</td></tr><tr><td>CW[AC1]</td><td>{31,63,127,255}</td></tr><tr><td>CW[AC0]</td><td>{31,63,127,255}</td></tr></tbody></table>

Figure (2) shows the variation of normalized throughput according to the number of stations. In figure (a), there is a degradation of the normalized throughput compared with the increase in the number of stations. The decrease of normalized throughput which depends on the access categories is explained by the fact that there are more stations in the network, more collision is high. The differentiation with TXOPlimit gives more priority to AC3 which reaches its maximum at almost 0.45 bit/s, because it has a priority to transmit multiple frames in bursts than others (AC1, AC2, AC0), which are authorized with to transmit a small number of frames.

While the figure (b) shows the reduction in the normalized throughput compared to the increase in the number of stations of categories AC0, AC1, AC2 and a light degradation for AC3 which does not exceed 0.4 bit/s without using TXOPlimit.

Figure (3) represents the variation of total throughput compared to the increase in the number of stations. We always observe a decrease in the total throughput compared to the increase in the number of stations, this is explained by the fact that there are more stations in the network, more collision is high and it can reach a maximum value nearly equal to 0.9 bit/s using TXOPlimit as illustrated in figure (c) and not exceeding 0.8 bit/s without using TXOPlimit like illustrates it in figure (d).
<figure><img src="image_3.png" /><figcaption>Figure 2: Normalized throughput according to the number of station.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3: Total throughput according to the number of station.</figcaption></figure>

Figure (4) represents the variation of normalized throughput of each access category according to the bit error rate (BER). This figure shows that when the bit error rate increases, the normalized throughput for each AC decreases slightly until it reaches the value equal to $10^{-5}$, because the error rate is negligible and when the bit error rate (BER) exceeds $10^{-5}$, the normalized throughput of all access categories diverge towards the same value (which is equal to 0). This can be explained by the probability of error is very large.
<figure><img src="image_5.png" /><figcaption>Figure 4: Normalized throughput according to the bit error rate (BER).</figcaption></figure>

## VII CONCLUSION

Enhanced Distributed Channel Access EDCA is the fundamental medium access control MAC scheme in the IEEE 802.11e protocol. In this paper, to enhance the 802.11e performance, we have proposed a new treatment for channel failures called A-EDCA. We have presented an accurate analytical model to evaluate the performance of A-EDCA under fading channel and non saturated conditions. The results obtained show that A-EDCA is better performance than basic EDCA. We conclude that the proposed modified method gives better throughput performance than the presently existing IEEE 802.11e EDCA.

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