Moments of the conditioned waiting time in 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 = O(1), where p is a 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 tau, are derived for: normal usage, rho 1; heavy usage, rho-1 = O(N(-1/2)); and very heavy usage, rho> 1. Singular perturbation techniques are used, and the matching of the heavy-usage approximations with both the normal and very heavy-usage approximations is investigated. Numerical results are presented.