On Finite Capacity Processor-Shared Queues

Abstract

A processor-sharing queueing system is considered that can accommodate a finite number K of customers. In a processor-shared queue, every customer gets an equal fraction of the server (processor). The main quantity of interest in such a system is a customer’s response time (time spent in system) conditioned on that customer’s total required service and the number of other customers present at the arrival time. Using singular perturbation methods, we construct asymptotic expansions for the first two moments of the conditional response time for systems where the capacity K is large.

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