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The actual waiting time of each customer in a GI/G/1 queue

Published online by Cambridge University Press:  14 July 2016

Do Le Minh
Do Le Minh*
Affiliation:
The New South Wales Institute of Technology
*
∗Postal address: School of Mathematical Sciences, The New South Wales Institute of Technology, P.O. Box 123, Broadway, N.S.W. 2007, Australia.
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Abstract

This paper studies a generalization of the GI/G/1 queueing system in which the inter-arrival times are not necessarily identically distributed and there is a random set-up time for customers who arrive when the server is idle. A recursive scheme is derived to obtain the distribution of the actual waiting time of each customer in the system.

Keywords

QUEUEINGDISCRETE TIMEGI/G/1SET-UP TIMESNON-IDENTICAL INTER-ARRIVAL TIMESIDLENESS PROBABILITIESACTUAL WAITING TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 910 - 916
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Bhat, U. N. (1964) On the busy period of a single server bulk queue with a modified service mechanism. Calcutta Statist. Assoc. Bull. 13, 163–171.Google Scholar
[2] Finch, P. D. (1959) A probability limit theorem with application to a generalization of queueing theory. Acta Math. Acad. Sci. Hungar. 10, 317–325.Google Scholar
[3] Keilson, J. and Kooharian, A. (1962) On the general time dependent queue with a single server. Ann. Math. Statist. 33, 767–791.CrossRefGoogle Scholar
[4] Lemoine, A. J. (1974) Limit theorems for generalised single server queues. Adv. Appl. Prob. 6, 159–174.CrossRefGoogle Scholar
[5] Lemoine, A. J. (1975) Limit theorems for generalised single server queues: the exceptional system. SIAM J. Appl. Math. 28, 596–606.Google Scholar
[6] Minh, D. L. (1978) The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution. J. Appl. Prob. 15, 590–601.Google Scholar
[7] Pakes, A. G. (1972) A GI/M/1 queue with a modified service mechanism. Ann. Inst. Statist. Math. 24, 589–597.Google Scholar
[8] Pakes, A. G. (1973) On the busy period of the modified GI/G/1 queue. J. Appl. Prob. 10, 192–197.CrossRefGoogle Scholar
[9] Rossberg, H. J. and Siegel, G. (1974) The GI/G/1 model with warming-up time. Zast. Mat. XIV, 17–26.Google Scholar
[10] Welch, P. D. (1964) On a generalised M/G/1 queueing process in which the first customer of each busy period receives exceptional service. Opns Res. 12, 736–752.Google Scholar
[11] Yeo, G. F. (1962) Single server queues with modified service mechanisms. J. Austral. Math. Soc. 3, 499–507.Google Scholar