Effects of service disciplines inG/GI/s queueing systems

Transient extremal properties of some service disciplines are established in theG/GI/s queueing 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, lag times 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 to the stationary regime and to tandem as well as general queueing networks.This work was supported in part by the National Science Foundation under grant ASC 88-8802764.The work of this author was also partially supported by CEC DG-XIII under the ESPRIT-BRA grant QMIPS.