Technical Report CS0572

Title: Exptected Waiting Times in Cyclic Service Systems Under Priority Disciplines
Authors: L. Fournier and Z. Rosberg
Abstract: In this paper, we analyse a service system which consists ofseveral queues (stations) polled by a single server in a cyclic order with arbitrary switchover times. Customers from several priority classes arrive into each of the queues according to independent Poisson processes and require arbitrary distributed service times. We consider the system under various priority service disciplines: head-of-the-line priority limited to one and semi-exhaustive, head-of-theline priority limited to one with background customers, and global priority limited to one. For the first two disciplines we derive a pseudo conservation law. For the third discipline, we obtain the expected waiting time of a customer from any given priority class and for the last discipline we find the expected waiting time of a customer from the highest priority class. The principal tool for our analysis is the stochastic decomposItion law for a single server system with vacations.

Keywords: Polling systems, loop systems, single-server-queue, priorities, pseudo conservation law.

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