In principle unrestricted processor sharing can be very useful when jobs with widely varying CPU requirements are competing for the same processor. Even if there are several processors available, processor sharing can be useful. However, in practice it must be implemented by round-robin, and there is an overhead cost (e.g., cache thrashing) to implementing this scheme. Furthermore, the overhead may depend on the number of jobs that are active, and can be significant. Therefore restricted processor sharing, which only allows a limited number of jobs to share the processors, may be a more appropriate strategy. In this paper we present a comprehensive analytic model to study the interplay among the number of parallel processors, the maximum degree of processor sharing, the overhead, and the job arrival rate. We examine how the CPU time distribution affects mean system time (or response time), under what conditions two slow processors are better than one double fast one, and when it pays to invoke restricted processor sharing.

Abstract—It has been observed in recent years that in many applications service time demands are highly variable. Without foreknowledge of exact service times of individual jobs, processor sharing is an effective theoretical strategy for handling such demands. In practice, however, processor sharing must be implemented by time-slicing with a round-robin discipline. In this paper, we investigate how round-robin performs with the consideration of job switching overhead. Because of recent results, we assume that the best strategy is for new jobs to preempt the one in service. By analyzing time-slicing with overhead, we derive the effective utilization parameter, and give a good approximation regarding the lower bound of time-slice under a given system load and overhead. The simulation results show that for both exponential and non-exponential distributions, the system blowup points agree with what the effective utilization parameter tells us. Furthermore, with the consideration of overhead, an optimum time-slice value exists for a particular environment. I.