Conditioned Response-Time Distribution for a Large Closed Processor-Sharing System with Multiple Classes in Very Heavy Usage

Abstract

A large closed processor-sharing system with multiple job-classes is considered. The system consists of a bank of terminals grouped according to job-classes, where the class structure allows for distinctions in the user’s behavior in the terminal, and in the service requirements from the central processing unit. Our earlier results for the single-class system in very heavy usage are extended to the multiple-class systems. For large systems, asymptotic approximations to the distribution of the equilibrium response time, conditioned on the required service time $\tau $, are derived. The first order correction term to the leading normal approximation, which leads to a skewness of the distribution, is shown to have the same structure as the single-class system. Equations are obtained for determining the asymptotic approximations to the mean, variance, and skewness of the response time as functions of the required service time $\tau $.