Asymptotic analysis of the waiting-time distribution for a large closed processor-sharing system.

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 rho=Np=0 (1), where p is the ratio of the mean required service time to the mean think time. Asymptotic approximations to the equilibrium distribution of the waiting time are derived for: normal usage, rho1. Singular perturbation techniques are used, and the matching of the heavy-usage approximation with both the normal and very heavy-usage approximations is investigated. Numerical results are presented which indicate that the approximations are useful for N>=100.