In this paper we propose a model of the IEEE 802.11 Enhanced Distributed Coordination Function (EDCF) which can build different access priorities for different classes of traffic. These priorities are obtained using different inter frame spacings called Arbitration Inter Frame Spacings (AIFSs) to differentiate the access of different classes of traffic. When a node has a pending packet it must first wait for the channel to become idle for a given number A of mini-slots σ before starting to decrement its back-off; this interval of A mini-slots σ is called the AIFS. If the channel becomes busy before this back-off expires, then the node will have to to wait for another A mini-slots before starting to decrement its back-off again. The nodes can also use different back-off windows to further differentiate between different classes of traffic. The model we propose is much simpler than previous models , ,  and handles the more general case of a Poisson arrival for the traffic. Moreover, the model presented here is designed for broadcast traffic whereas most models handle point-to-point IEEE 802.11 transmission. When we have two classes of traffic, the model leads to two coupled non-linear equations involving the transmission rates in each class of traffics. These equations can be easily solved using simple numerical methods. The model then allows the successful rate or the throughput for each class of traffic to be computed in a straightforward manner. Numerical examples derived from VANET scenarios show the direct and positive influence of the Arbitration Inter Frame Spacings on the performance of each class of traffic.