Moments of the conditioned waiting time in a large closed processor-sharing system

Abstract

The service of an interactive computer system is characterized by the random waiting (or response) time perceived by users. The system consists of a bank of terminals, each of which asynchronously alternates between “thinking” and waiting for service from a central processing unit which operates under the processor-sharing discipline. It is assumed that there are (N+1) terminals, where N is large, and that , where p is ratio of the mean required service time to the mean think time. Asymptotic approximations to the mean and variance of the equilibrium waiting time, conditioned on the required service time τ, are derived, by means of singular perturbation techniques, for: normal usage, ρ>1; heavy usageand very heavy usage, ρ>1. Numerical results are presented

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