Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review

Abstract

The first paper to introduce the concept of a cyclic queue appeared in the Operational Research Quarterly in 1954. The paper dealt with the 'flow' of aircraft engines from operation to maintenance to available for operation. In 1958, the first paper analyzing the cyclic queue model appeared in the same journal. This paper was application of queue theory to underground coal mining. In 1965 it was shown that stochastic queue networks can be treated analytically in the same manner as cyclic queues with a small adjustment in the auxiliary parameters. Since then cyclic queue models have been applied not only to the problems mentioned above but also to many other production and service industry problems: computer design and control, ship operations, production processes, communications flow, ingot movements in a steel mill, to name but a few. In order for this to be possible, extension and advances in theory have been required and these have come from many nations and many fields of endeavour. This paper traces the development of the theory of cyclic queues and queue networks from 1954 to the present.