Response times in M/M/1 time-sharing schemes with limited number of service positions

Abstract

Two service schemes for an M/M/1 time-sharing system with a limited number of service positions are studied. Both schemes possess the equilibrium properties of symmetric queues; however, in the first one, a preempted job is placed at the end of the waiting line; while in the second one, it is placed at the head of the line. Methods for calculating the Laplace transforms and moments of the response times are presented. The variances of the response times are then compared numerically to indicate that the first scheme is superior to the second scheme. It is also indicated that in both cases the response time variance decreases when the number of service positions increases.