Abstract In this paper we study the effect of session-based arrival streams on the behavior of a discrete-time queueing system with infinite storage capacity and a single output line. These session-based arrival streams are a new and realistic approach for modelling traffic generated by users in a telecommunication network. Users from an infinite population can start and end sessions during which they are active and send packets to the queueing system. Each active user generates a random, yet strictly positive number of packets per time slot. There are T different sessions types, each characterized by their own general session-length, session-incidence and bandwidth distribution. The corresponding discrete-time queueing model is analyzed by a generating-functions approach with infinite-dimensional state description. We derive the steady-state probability generating functions of the buffer content and the packet delay. From these, we obtain the mean buffer content as well as the mean packet delay and even the mean session delay. Finally, some numerical examples illustrate the influence of various parameters on the buffer behavior.