A discrete time queueing analysis of ATM systems with heterogeneous 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 extend the model to the heterogeneous case with L types of traffic sources and demonstrate that the solution to the model now involves the inversion of an L+1 by L+1 matrix. Derivations of the steady-state solutions and numerical analysis are given for the case of L=2