Discrete time analysis of GI/G/1 priority queueing systems

Abstract

Discrete-time queueing systems have received greater attention in recent years due to their usefulness in modeling and analyzing various types of communication systems. Packet switched communication networks with point-to-point links between the nodes, where data packets are of fixed length, motivated most of these models, since the fixed packet length assumption induces their discrete-time nature. The main purpose of this paper is to analyze discrete-time priority queues with general independent arrivals and generally distributed service times. We consider three priority disciplines: nonpreemptive, preemptive resume and preemptive repeat with resampling. In each case, with the four dimensional embedded Markov chain method, we derive the (joint) probability generating functions of the numbers of customers of two priority types at various observation epochs and the (joint) probability generating functions of the unfinished works and the system times. In the cases of nonpreemptive and preemptive resume disciplines, we also obtain the probability generating function of the busy period. The results of this paper are applicable in the study of queueing phenomena in the area of digital communication systems.