Conditioned response-time distribution for a large closed processor- sharing system with multiple classes in very heavy usage.

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 for the single-class system.