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On the service time distribution and the waiting time process of a potentially infinite capacity queueing system

Published online by Cambridge University Press:  14 July 2016

Nasser Hadidi
Nasser Hadidi*
Affiliation:
University of Oslo
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Abstract

In [1] the authors dealt with a particular queueing system in which arrivals occurred in a Poisson stream and the probability differential of a service completion was μσn when the queue contained n customers. Much of the theory could not be carried out further analytically for a general σn, which is a purely n-dependent quantity. To carry the analysis further to the extent of finding the “effective” service time and the waiting time distribution when σn is a linear function of n, (which is considered to be rather general and sufficient for practical purposes), constitutes the subject matter of this paper.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 594 - 603
Copyright
Copyright © Applied Probability Trust 

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References

[1] Hadidi, N. and Conolly, B. W. (1969) On the improvement of the operational characteristics of single server queues by the use of a queue length dependent service mechanism. Appl. Statist. 18, (in press).CrossRefGoogle Scholar
[2] Conolly, B. W. and Hadidi, N. (1969) A correlated queue. J. Appl. Prob. 6, 122–136.CrossRefGoogle Scholar
[3] Conolly, B. W. and Hadidi, N. (1969) A comparison of the operational features of the conventional M/M/1, D/M/1 and M/D/1 queues with those of a self regulating system. Appl. Statist. 18, 41–53.CrossRefGoogle Scholar