A Review of the Open Queueing Network Models

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe the developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches. A significant development in the study of queueing network models is the discovery (empirical) that under conditions that are not very restrictive in practice: (i) equilibrium expected queue lengths behave as if they are convex functions of the processing rate of the server, and (ii) altering the processing rate at one station has minimal effect on the equilibrium expected queue lengths at other stations in the network. As a result researchers have been able to approximate some of the optimal design problems by convex programs. In the second part of this paper we describe these developments. Inspite of the advances made in the analysis of open queueing networks, several of the problems described in the first part of the paper cannot be analyzed without further progress in