An Empirical Analysis on Queue Network Models of Production Techniques |
In this paper we review open queue network models ofProduction Techniques. The paper consists of two parts. We discuss design andplanning problems arising in manufacturing. In doing so we focus on thoseproblems that are best addressed by queue network models. We describe the developments in queue networkmethodology. We are primarily concerned with features such as general servicetimes, deterministic product routings, and machine failures - features that areprevalent in manufacturing settings. Since these features have eluded exactanalysis, approximation procedures have been proposed. In the second part ofthis paper we review the developments in approximation procedures and highlightthe assumptions that underlie these approaches. A significant development in the study of queue networkmodels is the discovery (empirical) that under conditions that are not veryrestrictive in practice: (i) equilibrium expected queue lengths behave as ifthey are convex functions of the processing rate of the server, and (ii)altering the processing rate at one station has minimal effect on theequilibrium expected queue lengths at other stations in the network. As aresult researchers have been able to approximate some of the optimal designproblems by convex programs. In the second part of this paper we describe thesedevelopments.