# Some remarks about the duality relation in queues

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## Abstract

The dual of a queue is derived by inter-changing the arrival and service processes. In this paper some general relations relating the dual queues to the parent queues have been brought out. The queue considered is of type GI/G/1.

## Keywords

General Relation Service Process Duality Relation Dual Queue Parent Queue
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## References

- [1]P. D. Finch, The effect of the size of the waiting room on a simple queue,
*J. Roy. Statist. Soc.***B****20**(1958), pp. 182–186.Google Scholar - [2]P. D. Finch, A probability limit theorem with application to a generalization of a queueing theory,
*Acta Math. Acad. Sci. Hung.*,**10**(1959), pp. 317–326 (see also*Acta Math. Acad. Sci. Hung.*,**10**(1959), pp. 327–336).Google Scholar - [3]P. D. Finch, Deterministic customer impatience in the queueing system GI/M/1,
*Biometrika*,**47**, (1960), pp. 45–62.Google Scholar - [4]
- [5]
- [6]J. Keilson, The ergodic queue length distribution for queueing with finite capacity.
*J. Roy. Statist. Soc.*,**B 28**(1966), pp. 190–201.Google Scholar - [7]D. G. Kendall, Some problems in the theory of queues,
*J. Roy. Statist. Soc.*,**B 13**(1951), pp. 151–185.Google Scholar - [8]J. F. C. Kingman, The heavy traffic approximation in the theory of queues,
*Proceedings of the Symposium on Congestion Theory, Univ. of North Carolina*, 1966, pp. 137–169.Google Scholar - [9]D. V. Lindley, Theory of queues with a single server,
*Proc. Camb. Phil. Soc.*,**48**(1952), pp. 277–289.Google Scholar - [10]R. M. Loynes, On a property of the random walks describing simple queues and dams,
*J. Roy. Statist. Soc.*,**B 27**(1965), pp. 125–129.Google Scholar - [11]N. U. Prabhu, Elementary methods for some waiting time problems,
*Opns. Res.*,**10**(1962), pp. 599–606.Google Scholar - [12]R. Syski, Markovian queues, (Chap. 7),
*Proceedings of the Symposium on Congestion Theory Univ. of North Carolina*, 1966, pp. 170–223.Google Scholar

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© Akadémiai Kiadó 1968