A stochastic model for a hysteresis based priority queueing strategy for ATM networks with batch arrivals-theory

In this paper, we study a non-preemptive delay priority queueing system with a hysteresis mechanism for priority control in ATM networks. We consider a single server queue with two buffers of finite capacity, one for the real-time traffic such as voice and video and the other buffer for the non-real time traffic like data. ATM cells from real-time traffic are given higher priority over non-real-time ATM traffic. The real-time traffic is modeled using a batch Markovian arrival process (BMAP) and the non-real-time traffic is modeled as a Poisson process. We approximate the constant service time of the multiplexer by an Erlang distribution of very high order. This enables us to study the model in the context of matrix analytic methods. The ATM cells are scheduled for service according to a hysteresis-based priority control scheme. This scheme serves as a generalization of previous delay priority mechanisms like 1-limited discipline, fixed priority discipline and queue length threshold scheme. The queueing model is studied as a Markov chain with a large state space. Efficient algorithmic procedures for computing various performance measures of the model are also presented.