Effects of service disciplines inG/GI/s queueing systems

Abstract

Transient extremal properties of some service disciplines are established in the G/GI/s queuing system for the minimization and maximization of the expectations of the schur convex functions, convex symmetric functions and the sums of convex functions of the waiting times, response times, lagtimes, and latenesses. When resequencing is required in the system, the FCFS and LCFS disciplines are shown to minimize and maximize, respectively, the expectations of any increasing functions of the end-to-end delays. All of these results are presented in terms of stochastic orderings. The paper concludes with extensions of the results of the steady state and to the queuing networks.