Session-based arrival streams are a new approach for modelling the traffic generated by users in a telecommunication network. In this paper, we analyze the behavior of a discrete-time buffer with one output line, an infinite storage capacity and session-based arrivals. Users from an infinite user population can start and end sessions during which they are active and send packets to the buffer. Each active user generates a random but strictly positive number of packets per time slot. Unlike in previous work, there are
different session types and for each type, the session-length distribution is general. The resulting discrete-time queueing model is analyzed by means of an analytical technique, which is basically a generating-functions approach that uses an infinite-dimensional state description. Expressions are obtained for the steady-state probability generating functions of both the buffer content and the packet delay. From these, the mean values and the tail distributions of the buffer content and the packet delay are derived as well. Some numerical examples are shown to illustrate the influence of the session-based packet arrival process on the buffer behavior.