Conditioned response-time distribution for a large closed processor- sharing system in very heavy usage
01 January 1987
The service of an interactive computer system is characterized by the random 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 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 shows that the correction term provides a significant improvement.