The majority of analytical work on the performance of IEEE 802.11 [1] focuses on predicting the throughput and the mean delay of only the medium access, although higher layer applications and protocols are interested in the total performance of the MAC layer. Seen in this perspective, surprisingly little focus has been on predicting the queueing delay. The main contribution of this paper opposed to other works is that it presents the full delay distribution through the z-transform. As a result, the mean medium access delay is found by the first order moment of the transform, and the mean queueing delay by the second order moment. Together this gives the average total delay associated with the MAC layer. The z-transform is derived 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 [2]. EDCA provides class-based differentiated Quality of Service (QoS) to IEEE 802.11 WLANs, and distinguishes between four different traffic classes – called Access Categories (AC). By setting the number of ACs to one, and by using an appropriate parameter setting, the results presented are also applicable to the legacy 802.11 Distributed Coordination Function (DCF) [1]. The model predictions are calculated numerically and validated against simulation results. A good match between the analytical predictions and simulations was observed.