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The generalised state-dependent queue: the busy period Erlangian

Published online by Cambridge University Press:  14 July 2016

B. W. Conolly
B. W. Conolly*
Affiliation:
SACLANT ASW Research Centre, La Spezia, Italy
*
Now at Chelsea College University of London.
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Abstract

A continued fraction representation is presented of the Laplace transform of the generating function of the fundamental joint probability and density of busy period length measured in customers served and duration in time. The setting is the single server Erlang queueing system where the parameters of negative exponentially distributed arrival and service times have a general dependence on instantaneous system state.

Keywords

STATE-DEPENDENTQUEUEING THEORYBUSY PERIOD
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 618 - 623
Copyright
Copyright © Applied Probability Trust 1974 

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References

Callaert, H. and Keilson, J. (1972) On exponential ergodicity and spectral structure for birth-death process. Report CSS 72–01, Center for System Science, University of Rochester, Rochester, New York.Google Scholar
Conolly, B. W. (1959) The busy period in relation to the queueing process GI/M/1. Biometrika 46, 246–251.Google Scholar
Cox, D. R. and Smith, W. L. (1961) Queues. Methuen, London.Google Scholar
Hadidi, N. (1974) Busy period of Poisson queues with state dependent arrival and service rates. J. Appl. Prob. 11, No. 4. To appear.CrossRefGoogle Scholar
Hadidi, N. and Conolly, B. W. (1969) On the improvement of the operational characteristics of single server queues by use of a queue length dependent mechanism. Appl. Statist. 18, 229–240.Google Scholar
Keilson, J. (1964) A review of transient behavior in regular diffusion and birth-death processes. J. Appl. Prob. 1, 247–266.CrossRefGoogle Scholar
Keilson, J. (1965) A review of transient behavior in regular diffusion and birth-death processes. II. J. Appl. Prob. 2, 405–428.Google Scholar
Natvig, B. (1974) A queueing model where potential customers are discouraged by queue length. Scard. J. Statist. 1, To appear.Google Scholar