<title>Three buffer-allocation schemes for a MAP/PH/1/K priority queue with vacations and an application to ATM networks</title>

Abstract

A discrete-time finite buffer capacity queueing system for a generic multimedia shared medium is studied in this paper. In such an environment, the arrival process at the aggregate level (e.g., frame arrival rather than cell arrival) can be captured using the Markovian arrival process and the service time can be represented by the phase type service. The quality of service can be increased through the assignment of priority and buffer allocation scheme. In this paper, we consider two types of priorities and three buffer allocation schemes. First, we consider priority service and non-priority buffer allocation, second, priority service and fixed buffer allocation, and third, priority service with priority buffer allocation with push-out and threshold. Our analysis leads to the queue length distribution and the blocking probability. In addition, we show that the throughput can be obtained as a Markov renewal process described by two sub-stochastic matrices derived by partitioning the transition matrix. Through several numerical examples, we show the effect of buffer allocation scheme on the throughput, and present some results for the average queue length, blocking probability, and the throughput.