Discrete-time buffer systems with session-based arrival streams

The paper considers a discrete-time buffer system with an infinite storage capacity and one single output channel. Users can start and end sessions during which they are active and send packets to the buffer system. In this paper we study a simple model for the resulting session-based arrival process: we assume that each active user generates a random but strictly positive number of packets per time slot. Furthermore it is assumed that the time (expressed in slots) needed to transmit a packet is geometrically distributed. The distribution of the session lengths is also geometrical. This model can be applied to study the traffic of a file server, where one file download by a user is considered to be one session. The probability generating functions of the steady-state number of active sessions, the buffer occupancy and the packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. Furthermore, an expression for the mean session delay is obtained. This allows us to study the influence of the different system parameters: some examples are presented. We end by applying the model to a web server, based on actual web traffic.