In this paper we propose analytic model for computing the delay of the slotted ALOHA protocol with Binary Exponential Backoff (BEB) with multiple priorities as a collision resolution algorithm in mobile information systems. If a packet which tries to reserve a channel collides times, it chooses one of the next 2n frames with equal probabilities and attempts the reservation again. We derive the expected access delay until an arbitrary packet reserves a channel in any cell. Then the expected transmission delays for packets of calls with multiple priorities are calculated analytically. Proposed analytic model is checked against simulation.