Some Problems of Optimisation in Queueing Systems

Abstract

Compared with the abundance of literature devoted to the study of queues, there is relatively little treating their optimisation. However if it is certain that the study of their properties (waiting time, state probabilities, busy periods, etc.) is important, in order to determine the characteristics of the systems in which they are incorporated, it is equally important to carefully estimate their costs. One often attempts to realise systems in which the waiting times are sufficiently short not to loose customers or simply in order to integrate the service point in a production line. On the other hand, if one wishes to ensure ever shorter waiting times for each customer, the associated costs will in general be ever increasing. Thus for each system, there is a balance to be struck between cost and advantages. The problems that one may encounter in this particular class of optimisation models are very varied. First of all, we will try to expose the crux of these models by giving a brief survey of the most widely known methods (2). There exists more substantial works, for example that of Crabill et al. [1]. We will then develop a constrained static optimisation model (3).