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The inter-arrival times of accepted customers in an M/G/1 queue with finite capacity

Published online by Cambridge University Press:  14 July 2016

Robert Gilchrist
Robert Gilchrist*
Affiliation:
Polytechnic of North London
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Abstract

This note draws attention to a practical problem of interest to physicists, namely the distribution of the inter-arrival times of those customers accepted by the M/D/1/K + 1 queue. The form of the distribution is found for all K and the generalisation to M/G/1/K + 1 is discussed. The approach follows the contour integral method described by Cohen.

Keywords

SINGLE-SERVER QUEUESFINITE CAPACITYPOISSON INPUTCONSTANT SERVICEGENERAL DISTRIBUTION OF SERVICEINTER-ARRIVAL TIMES OF ACCEPTED CUSTOMERSCOUNTERSDATA BUFFERS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 633 - 638
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Barton, J. C. (1976) Effect of a data buffer on the recorded distribution of time intervals for random events. Nuc. Instr. Meth. (To appear) Google Scholar
[2] Cohen, J. W. (1969) The Single Server Queue. North Holland, Amsterdam.Google Scholar
[3] Kleinrock, L. (1975) Queueing Systems. Volume 1: Theory. Wiley, New York.Google Scholar
[4] Overas, H. (1972) Dead time losses in a buffered data recording system. Nuc. Instr. Meth. 104, 85–91.Google Scholar