In this paper, we analyze the MAC access delay of the EDCA mechanism in the IEEE 802.11e standard under saturation. We model the effect of differentiation based on both contention window size and inter-frame spacing. Explicit expressions for the mean, the standard deviation and the generating function of the distribution of the access delay are obtained. By applying numerical inversion on the generating function, we are able to compute values of the distribution. We show that our analytical model is accurate through comparison with simulation.