Multiserver Queueing Models of Multiprocessing Systems

Abstract

Conventional time sharing and multiprogramming systems have been extensively modeled as single-server queues. In contrast, multiprocessing systems must be modeled as multiserver queueing systems. This paper investigates the effect of the scheduling strategy-a key parameter-on the performance of multiserver queues, under very general assumptions: arbitrary arrival process and arbitrary service times distribution. We distinguish two classes of queue disciplines: preemptive and nonpreemptive, and two types of arrival processes: dependent (on the state of the queue) and independent. The performance is evaluated in terms of global measures: the utilization factor of the servers, as a measure of internal efficiency, and the mean response time, as a measure of external (user-oriented) performance. It is shown that nonpreemptive disciplines leave both measures invariant, for given but arbitrary (dependent or not) arrival process and arbitrary service distribution. For preemptive disciplines, the utilization factor is invariant only if the arrival process is independent, while the mean response time depends on the discipline, whatever the arrival process. It is also shown that the exponential distribution is the only distribution for which the queue discipline does not affect the performance of the system, thus underlining the very peculiar nature of this standard assumption and preventing us from safely generalizing the conclusions reached under this assumption. A quantitative comparison of preemptive and nonpreemptive disciplines requires an analytical solution, for which a general technique is presented.