Analysis of a Task Oriented Multipriority Queueing System

Abstract

This paper presents closed form expressions for average delay in a class of work conserving single server queueing systems suggested by, but not limited to, the behavior of heavily I/O oriented computing systems. Jobs arrive at the system according to a Poisson process, and each job consists of a set of tasks which must be accomplished in a prescribed order. The tasks with index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> have a general service time distribution G <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> and a priorityP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> which.is arbitrary but prescribed. Tasks are serviced within composite priority groups in a preemptive resume fashion and in the order in which, the tasks reached a ready-for-service status. Such queue behavior would be characteristic, for example, of a front end processor or a terminal controller in a communications environment. A design example is presented which illustrates the usefulness of the model to compare alternatives in communications systems design and other areas as well.