An analytical model is proposed to describe the priority schemes of the Enhanced Distributed Channel Access (EDCA) mechanism of the IEEE 802.11e standard. EDCA provides class-based differentiated Quality of Service (QoS) to IEEE 802.11 WLANs. The main contribution of this paper opposed to other works is that the model predicts the full delay distribution through its z-transform. Furthermore, the mean delay, throughput and frame dropping probabilities of the different traffic classes are found in the whole range from a lightly loaded, non-saturated channel to a heavily congested, saturated medium. Moreover, the model describes differentiation based on different Arbitration Inter-Frame Space (AIFS) values, in addition to the other adjustable parameters (i.e. window-sizes, retransmission limits, transmission opportunity (TXOP) lengths etc.) also encompassed by previous models. AIFS differentiation is described by a simple equation that enables access points to predict at which traffic loads starvation of a traffic class will occur. The model is calculated numerically and validated against simulation results. We observed a good match between the analytical model and simulations.