The dependence of computer system queues upon processing time distribution and central processor scheduling

Abstract

The stationary distribution of the number of jobs being served by a processor-sharing central server is independent of both the distribution of service times and the distribution of interarrival times when those distributions have rational Laplace-Stieltjes transforms. This result holds for both finite source and infinite source models. The steady state is identical to the steady state when all distributions are exponential. The expected response time, queue size, and central processor idle time of the finite source model under processor-sharing and FCFS scheduling are compared. These measures of system performance are all larger under processor-sharing for a class of central processor service time distributions with a coefficient of variation less than one. The measures are all smaller under processor-sharing for a class of distributions with a coefficient of variation greater than one. Experiments with data collected from actual computer systems indicate that these results extend to more general models and have practical applications in existing computer systems.