The delay distribution of IEEE 802.11e EDCA and 802.11 DCF

A number of works have focused on the mean delay performance of IEEE 802.11. The main contribution of this paper is that it provides a method to obtain the full distribution of the delay, and not only mean values or higher order moments. Hence, any desirable delay percentiles can be found. The distribution is found by inverting the z-transform of the delay numerically. The trapezoidal rule is used with a configurable error bound (- in this paper set to 10^-14). The z-transform was derived in our previous works from an analytical model that works in the whole range from a lightly loaded, non-saturated channel to a heavily congested, saturated medium. The model describes the priority schemes of the enhanced distributed channel access (EDCA) mechanism of the IEEE 802.11e standard. By setting the number of traffic classes (access categories) to one, and by using an appropriate parameter setting, the results presented are also applicable to the legacy 802.11 distributed coordination function (DCF)