Estimation of probabilistic processes in wireless networks of 802.11 standard

Abstract

The article analyzes mechanisms of collision in a wireless 802.11 network with competitive access to a radio channel. The calculated relationships for determining the probabilities of collisions in the network as a whole in the presence of N active stations with a saturated load, and also for one station when implementing the binary exponential mechanism of increasing the competitive window are presented. The graphs, which illustrate the proposed equations, are given in this article too. An equation is also proposed for determining the probability of successful transmission of a data frame depending on the number of active stations and the initial value of the competitive window. The equations are obtained using the concept of a virtual competitive window.It was shown that in the case, where the number of active stations is one third of the contention window, the probability of collisions is about 0.25. This means that in the network with such number of active stations, each station will experience the collision at every fourth attempt to transmit a frame of data in average. The next attempt to transmit frame of data will be carried out by using the larger contention window. Collisions will cause the increase of transmitting time duration and its irregularity.It was analyzed the efficacy of application of binary exponential law for the change of the contention window for active stations, caught in a conflict when trying to access the channel.The equation for estimate the changes in the probability of collision and the number of competing stations in the access cycle was obtained by taken into account that it will take place when a quasi-stationary mode of operation of wireless networks is established. It was shown that the most effectively this mechanism is triggered in the early stages of repeated access to radio channel. Those stations that carry out the 5-th and 6-th attempts to access channel have a little impact on the probability of collisions on the network. Such result may be explained because every station after successful transmit the data frame will begin a new attempt from the initial meaning of contention window. So, if the initial number of active stations in the wireless network approximately equal to the value of contention window, in steady state of saturated network the effective number of active stations will be twice less due to application of binary exponential law for the change of the competitive window. If the initial number of active stations will be only 30% from the value of contention window, the effective number of active stations will be less twice too.It was gave the estimation of the overall probability of collisions in a saturated 802.11 network with competitive access to the radio channel. The threat of collisions increases quickly in comparison with the increase of number of active stations in the networkFrom the analysis of the received equations and graphs it follows that for the normal operation of the wireless network, it is necessary that the number of active stations that simultaneously compete for access to the radio channel does not exceed a third of the initial value of the contention window used in this network. In this case, the probability of successful transmission will be more than 0.85.Ref. 10, fig. 7.