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Generalized state-dependent Erlangian queues: Speculations about calculating measures of effectiveness

Published online by Cambridge University Press:  14 July 2016

B. W. Conolly
B. W. Conolly*
Affiliation:
Chelsea College, University of London
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Abstract

The provision of easily calculable measures of effectiveness for generalised Erlang queues (state-dependent parameters λn and μn of arrival and of service) motivates speculation about the applicability of renewal theory. The application envisaged is justified by known results for certain models and its extension to an operationally more promising system is proposed. Use of the formula ‘L = λW' with ‘effective’ λ calculated by foregoing methods is likewise shown to be justified by known results for certain models and hence its wider applicability is conjectured. Mechanisms are discussed which may provide improved models, and investigation is made of choices of λn and μn which may lead to time dependent solutions having a prescribed form. The example of panic buying is considered as an example.

Keywords

ADAPTIVE QUEUEING SYSTEMSSTATE-DEPENDENT ERLANGIAN QUEUESNUMERICAL ASSESSMENT OF QUEUEING SYSTEMSPANIC-BUYING MODELTRANSIENT SOLUTION OF QUEUEING SYSTEMSEQUIVALENT RENEWAL THEORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 358 - 363
Copyright
Copyright © Applied Probability Trust 1975 

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References

Conolly, B. W. (1974) The generalised state-dependent Erlangian queue: the busy period. J. Appl. Prob. 11, 618–623.CrossRefGoogle Scholar
Little, J. D. C. (1961) A proof for the queueing formula L = ?W. Operat. Res. 9, 383.CrossRefGoogle Scholar