State of The ART

Since the first IEEE 802.11 standard in 1997 [1], research laboratories kept on trying to model the behavior of access mechanisms to the medium. In-deed, it is difficult to model the distributed coordination function (DCF), particularly due to the number of parameters that change during the trans-mission. A relevant and efficient model would constitute a key to assist the deployment of wireless networks, which is currently done in a quasi empir-ical way. As far as we know, there exists no software to evaluate the exact capacity of a cell where users have very different requirements in quality of service (QoS); taking into account the overhead induced by the contention

Figure 2.6: AIFS prioritization mechanism of EDCA

process; and the collision. Thus, it is necessary to calculate the probabil-ity of collision, errors over the channel, and also the average time spent in contention period.

2.2.1 Seminal Models

We distinguish two main categories of models. Since 1996, the CSMA/CA mechanism used by the DCF and its performances were studied by Bianchi [17] . This model which is based onMarkov chains was published in 1998 [15]-[16] . In parallel, Cali et al. [18] developed a model based ongeometric distributions.

The Bianchi model is based on a two dimensional Markov chain. The first dimension s(t) indicates the backoff stage which represents the number of transmission attempts which failed. The second dimension b(t), indicates the value of the backoff timer, which corresponds to the number of time slots to wait before being able re-initialize a transmission after a failure.

This model is a good fit for a saturated medium because it assumes that the STA always has data to transmit. This implies that the results represent the maximum throughput offered by a WiFi cell. However, this model uses several approximations. Firstly, the channel is supposed to be ideal, i.e., it does not introduce any error. Moreover, the limited number of retransmis-sions allowed in the standard is not taken into account in the model. The

stations. Besides delay is not derived.

Cali’s model also allows to compute the maximum flow offered in sat-urated mode for the DCF, but this time, the backoff time is evaluated as the average of a geometric distribution. Although both Cali’s and Bianchi’s models use the same approximations,a major difference between those two models lies in the way of computing the probability for a station transmitting at a time t (the computation being easier in Cali’s model).

2.2.2 DCF models

In order to enrich these two models, several papers were published that tried to improve one of the approximations listed previously.

[72] developed a model with an error-prone channel based on Cali’s model. We notice that the maximum attempt of retransmissions is not taken into account. This model leads to a finite load of the network, thus it can be considered as a non saturated model. It is based on geometric distribution [73] and relies essentially on the work of Tobagi [65] who used matrices to represent the state variations of the network. Each node of the network is in a ”thinking” state if it’s either waiting for a packet to transmit or has already succeed to transmit a packet in the first attempt. Other-wise the node is in ”backlogged” state where the packet is still waiting in the buffer or being transmitted by the station. The matrices account for the transition probabilities from a system of ibacklogged nodes andM −i thinking nodes to kand M−k respectively.

Several improvements of Bianchi’s model have also been proposed. Among the refinements, one is due to [75] aiming to capture the freezing of backoff counters when the broadcast channel is sensed busy by a station. How-ever an inaccuracy in the model affecting sHow-everal important measures was reported later, and corrected in [32]. [22] derives the delay but still in the saturated mode with ideal channel assumptions. The assumptions is that the average backoff time that a station wait in the contention period equal to half of the contention windows, in the same way of Cali [18]. However the probability that a station transmit is derived in the same way as Bianchi [15] which leads us to consider this model as an extention of the Bianchi’s model. [29] improves Bianchi’s model by taking into account an error prone channel, but still with the saturation assumption. The error probability is not integrated in the markov chain but directly in the calculation of the collision probability.

[20] examined unsaturated networks, by introducing an additional state into the Markov chain. This state takes into account the possibility of having

an empty buffer after a transmission. The model deals with an additional problem, which is that of the multi-rate STA. It is achieved by taking into account the rate of each of the stations in the derivation of the transmission time of data. However, this work was carried out within the framework of an ideal channel, and does not take into account several significant charac-teristics of the DCF such as the frozen time when the channel is busy.It ’s worth to mention that the model was compared against real measurements from a 802.11b testbed developed for this purpose. A similar treatment of finite load can be found also in [10].

Some other models were used to derive performance of the DCF. For example we can mention [40] based on stochastic peri nets.

2.2.3 EDCA models

The IEEE 802.11e standard [4] including mechanisms for QoS management, has also been studied, in saturated mode [48], [57], [30], [55].These models are both based on Markov chains and extend the Bianchi’s model. They assume that the system is in saturated mode and that the channel is ideal.

It’s worth to remind that all the mentioned models including our model presented further deal only with the infrastructure mode of the IEEE 802.11 (i.e. single hop). Ad-hoc mode or multi-hop is not considered. [49] also extends the Bianchi’s model but without introducing a new state in the Markov chain. Instead, it deals with the multiple access categories directly in the computation of the collision probability.

In [13], a model to analyze the delay behavior of the EDCA mechanism is presented. The collision probability is computed with the assumption of Cali’s model [19] that backoff times follow a geometric distribution. Delay derivation following the Bianchi’s model is computed in [14] and is a direct extension of [55].

An interesting approach is found in [42], which presents a unified model based on three different seminal models [15],[18],[64].( the two first were ex-plained in 2.2.1). Backoff stages are still accounted for by using a bidimensional-state Markov Chain as in [16] but in order to account for the effect of dif-ferent AIFS values, we did not introduce further dimension(s) to the state space. Instead they used multiple bidimensional chains which easier to ap-ply beacuse reducing the complexity of Markov chains, what the authors claimed.

Performance Metric Protocol Assumption Validation Type Delay Throughput DCF EDCA

Non-Saturated

Saturated Error Prone

Error Free

Simulation Experiment Cali Bianchi Other

[16] X X X X X X

[18] X X X X X X

[57] X X X X X X

[20] X X X X X X X

[73] X X X X X X X

[48] X X X X X X X

[29] X X X X X X

[49] X X X X X X

[10] X X X X X X

[40] X X X X X X

[30] X X X X X X X

[42] X X X X X X X X X

[55] X X X X X X

[14] X X X X X X

[13] X X X X X X

Our model

X X X X X X X X X X

Table 2.1: State of the art summary and comparaison of DCF and EDCA Stochastic models

69

Chapter 3

Frequency Allocation to