Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-17T23:39:28.646Z Has data issue: false hasContentIssue false
  • English
  • Français

On queues in which customers are served in random order

Published online by Cambridge University Press:  24 October 2008

J. F. C. Kingman
J. F. C. Kingman
Affiliation:
Statistical LaboratoryCambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The queue M |G| l is considered in the case in which customers are served in random order. A formal solution is obtained for the waiting time distribution in the steady state, and is used to consider the exponential decay of the distribution. The moments of the waiting time are examined, and the asymptotic form of the distribution in heavy traffic is found. Finally, the problem is related to those of the busy period and the approach to the steady state.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 1 , January 1962 , pp. 79 - 91
Copyright
Copyright © Cambridge Philosophical Society 1962

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bartlett, M. S.Stochastic processes (Cambridge, 1956).Google Scholar
(2)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Tables of integral trans-forms, vol. 1 (New York, 1954).Google Scholar
(3)Kendall, D. G.J. Roy. Statist. Soc. Ser. B, 13 (1952), 151.Google Scholar
(4)Kendall, M. G. and Stuart, A.The advanced theory of statistics, vol. 1 (London, 1958).Google Scholar
(5)Kingman, J. F. C.Proc. Cambridge Philos. Soc. (to appear).Google Scholar
(6)Mellor, S. D.Post Office Elect. Engrs', J. 35 (1942), 53.Google Scholar
(7)Riordan, J.Bell System Tech. J. 32 (1953), 100.CrossRefGoogle Scholar
(8)Vaulot, E.Ann. Télécommun. 9 (1954), 9.CrossRefGoogle Scholar