A Taylor series expansions approach to queues with train arrivals

We assess the performance of a discrete-time queueing system with train arrivals. Arrivals at the queue stem from a number of active sessions, each generating a packet in a slot with fixed probability q. Since an exact analysis is not feasible for q ≠ 1, we rely on Taylor-series expansions around q = 0 of the joint probability generating functions of the number of active sessions and the queue content. These expansions are then either combined with the known generating function for q = 1 if the system is stable for q = 1, or with heavy-traffic results if this is not the case. In both cases, we obtain expressions for the moments of queue content and packet delay and assess the accuracy of our approximations by means of simulation.

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