Abstract
Many of the queueing-processes which are to be observed in the world do not consist of a single service stage. It is quite common to find systems in which the output from one queueing-process, or part of it, is the input to another. This is illustrated in Fig. 5.1. These are called
Illustration of two-stage serial queue
serial queueing-processes: or, are called systems with queues in tandem, or in series. When the ends are joined to form a loop, so that customers rotate through the system, the system is called a cyclic queueing system. In this chapter we shall consider models of these two special types of queueing-process very briefly. The length of the exposition does not reflect the importance of serial and cyclic queues, but only the paucity of theory concerning them and the rarity of examples of their use in operational research literature.
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Notes on Sources and References
Jackson, J. R. Networks of Waiting Lines (1957), Operat. Res., 5, No. 4.
Burke, P. J. The Output of a Queueing System (1956), Operat. Res., 4, pp. 699–704.
An interesting paper which relates to a genuine and important practical problem is: Taylor, J. and Jackson, R. R. P. An Application of the Birth-and-Death Process to the Provision of Spare Machines (1954), Operat. Res. Quart., 5, pp. 95–108.
Koenigsberg, E. Cyclic Queues (1958), Operat. Res. Quart., 9, No. 1.
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© 1966 Alec M. Lee
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Lee, A.M. (1966). Models of Serial and Cyclic Processes. In: Applied Queueing Theory. Studies in Management. Palgrave, London. https://doi.org/10.1007/978-1-349-00273-3_5
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