Optimality of the Round Robin Routing Policy

In this paper we consider the problem of routing customers to identical servers, each with its own infinite capacity queue. Under the assumptions that i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and ii) state information is not available, we establish that the round robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues. Mathematics Subject Classification: primary: 60K25. secondary: 49K30, 49N30, 68M20, 90B22, 90B80. Keywords: Optimal Routing, Scheduling, Sample Path Analysis, Stochastic Ordering. This work was supported in part by the National Science Foundation under grant ASC 88-8802764 and NCR-9116183. y The work of this author was also partially supported by CEC DG-XIII under the ESPRIT-BRA grant QMIPS. 1 Introduction Consider a stream of customers arriving to a controller which immedi..

Optimal Load Balancing on Distributed Homogeneous Unreliable Processors

A common architecture for multiprocessor systems is the distributed architecture in which relatively autonomous processors..

Effects of Service Disciplines in G/GI/s Queueing Systems

Transient extremal properties of some service disciplines are established in the G=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. Keywords : Queueing System, Service Discipline, Stochastic Ordering, Sample Path Analysis, Lateness, End-to-End Delay. This work was supported in part by the National Science Foundation under grant ASC 88-8802764. y The work of this author was also partially supported by CEC DG-XIII u..

Stochastic Scheduling in In-Forest Networks

In this paper we study the extremal properties of several scheduling policies in an in-forest network consisting of multi-server queues. Each customer has a due date and we assume that service times at the different queues form mutually independent sequences of independent and identically distributed random variables independent of the arrival times and due dates. Furthermore, the network is assumed to consist of a mixture of nodes, some of which only permit non-preemptive service policies whereas the others permit preemptive resume policies. In the case of non-preemptive queues, service times may be generally distributed if there is only one server; otherwise the service times are required to be increasing in likelihood ratio (ILR). In the case of preemptive queues, service times are restricted to exponential distributions. Using stochastic majorizations and partial orders on permutations, we establish that, within the class of work conserving service policies, the stochastically smal..