Abstract-In this paper, we analyse the MAC access delay of the IEEE 802.11e EDCA mechanism under saturation. We develop a detailed analytical model to evaluate the influence of all EDCA differentiation parameters, namely AIFS, CWmin, CWmax and TXOP limit, as well as the backoff multiplier β. We derive explicit expressions for the mean, standard deviation and generating function of the access delay distribution. By applying numerical inversion on the generating function, we are able to efficiently compute values of the distribution. Through comparison with simulation, we confirm the accuracy of our analytical model over a wide range of operating conditions. Using the model, we derive simple asymptotics and approximations for the mean and standard deviation of the access delay, which reveal the salient model parameters for performance under different differentiation mechanisms. We also use the model to study the characteristics of CWmin, AIFS, TXOP, and β differentiation. We find that, though rejected during the standardization process, β differentiation is an effective differentiation mechanism that has some advantages over the other mechanisms.