Sojourn time distribution in polling systems with processor-sharing policy

Abstract

We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service. One queue uses processor-sharing as a scheduling policy, and the customers in that queue have phase-type distributed service requirements. The other queues use any work conserving policy, and the customers in those queues have generally distributed service requirements. We derive a partial differential equation for the transform of the conditional sojourn time distribution of an arbitrary customer who arrives at the queue with processor sharing policy, conditioned on the service requirement. We also derive a partial differential equation for the transform of the unconditional sojourn time distribution. From these equations, we obtain the first and second moments of the conditional and unconditional sojourn time distributions. (C) 2017 Elsevier B.V. All rights reserved.