Analysis of Discrete-Time Server Queues with Bursty Markovian Inputs

We study a discrete-time deterministic server queue with infinite buffer and with packet arrivals that depend on a multidimensional Markov process. Using the generating functions approach we give a means for obtaining the boundary conditions vector for the case where the value zero is a multiple eigenvalue of the problem. We also derive recursive form expressions for the direct determination of the moments of the queue length. These expressions do not require the knowledge of the steady state probabilities of the combined source-queue process. Finally our method is applied to two queueing problems related to data transmission through an ATM switch with a queue of infinite length. Closed form expressions for the first two moments of the corresponding queue lengths are obtained.