Strongly asymptotically optimal design and control of production and service systems

In this paper we consider production and service systems that can be modele d as single or multiple stage queueing networks. We provide a formal defini tion of strong asymptotic optimality in the context of design and control o f such queueing systems. We describe a simple approach to obtain strongly a symptotically optimal design and control policies for these systems. We ill ustrate our approach through some examples. In particular we obtain a stron gly asymptotically optimal workload allocation for a multiple center servic e system modeled by the open Jackson network. The objective here is to mini mize the expected total holding cost. A simple counter example shows that t he much celebrated balanced workload allocation is not even asymptotically optimal for minimizing the expected number of jobs in the system. We show t hat an index policy is strongly asymptotically optimal for the scheduling c ontrol problem in a single stage (G/GI/1) service system. We also obtain a strongly asymptotically optimal allocation of classes of customers to a mul tiple center service system. This allocation agrees with the traditional wi sdom of forming service stations to process similar tasks that reduce fluct uations in processing times. Suggestions for further work on this topic are summarized as well.