A discrete-time queueing system with correlated arrivals and geometric service times

A discrete-time single-server queueing system with infinite buffer size, geometric service times and a two-state correlated traffic source is considered. The source states are assumed to have geometrically distributed sojourn times. The arrival process is dependent on the source state, but arbitrary. The behavior of the queueing system is studied analytically by means of a generating-functions approach. This results in closed-form expressions for the mean values and the tail distributions of the buffer contents and the packet delay. Some numerical examples are given to illustrate the analysis.