A PROCESSOR-SHARED QUEUE THAT MODELS SWITCHING TIMES - HEAVY USAGE ASYMPTOTICS

A closed processor-sharing queueing model that corresponds to M termin als in series with a central processing unit (CPU) is considered under heavy usage conditions. The effects of switching times between the CP U and the individual jobs are included by assuming that the effective service rate that the CPU provides is a decreasing function of the ins tantaneous number of jobs being processed. Using perturbation methods, asymptotic expansions are constructed for the first two moments of a customer's response (sojourn) time, conditioned on that customer's tot al required service from the CPU. The asymptotic limit assumes that th e number of terminals M is large (M much greater than 1), that the rat e at which the CPU provides service is fast (O(M)), and that the durat ion of a typical switching time is small compared to the time the CPU actually spends servicing the individual jobs. Extensive numerical com parisons show the quality of our asymptotic approximations.