A discrete time queueing analysis of ATM systems with phase-type distributed talk spurts traffic sources

A discrete time queueing model for the performance of an ATM system is analyzed using matrix analytic methods. Time is segmented into slots with each slot equal to the transmission time of one ATM cell. The ATM system is modeled as a single server queue with Markovian arrivals and service time equal to one slot. The arrival process includes as a special case the superposition of on-off sources, possibly heterogeneous. The queueing model is of the “M/G/1 type”. By exploring the structure of the “M/G/1 type” Markov chain the complexity of the solution to the problem is reduced to only the inversion of a 2×2 matrix irrespective of the size of the Markov chain. This simplification allows us to solve problems of large sizes. In this paper, we generalize this basic model without losing much of the computational simplifications to the case where there are multiple states corresponding to k (k⩾1) arrivals in a time slot (as opposed to a one-to-one mapping between the number of arrivals and the number of states in the Markov chain) providing a semi-Markov model for the number of arrivals