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

Abstract

The service of an interactive computer system is characterized by the random, response (waiting) time perceived by users. The system consists of a bank of user terminals, each of which asynchronously alternates between “thinking” and waiting for service from a central processing unit (CPU) which operates under the processorsharing discipline. It is assumed that there are $( N + 1 )$ terminals, where N is large, and that $\rho = Np = O( 1 )$, where p is the ratio of the mean required service time by the CPU to the mean think time. Asymptotic approximations to the distribution of the equilibrium response time, conditioned on the required service time $\tau $, are derived in the very heavy-usage case $\rho > 1$. The first order correction term to the leading normal approximation is obtained, and leads to a skewness of the distribution. Numerical comparisons with simulated results show that the correction term provides a significant improvement.

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