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A solvable model for a finite-capacity queueing system

Published online by Cambridge University Press:  14 July 2016

V. Giorno ,
C. Negri  and
A. G. Nobile
V. Giorno*
Affiliation:
Università di Salerno
C. Negri*
Affiliation:
Università di Salerno
A. G. Nobile*
Affiliation:
Università di Salerno
*
∗ Postal address: Dipartimento di Informatica e Applicazioni, Università di Salerno, 84100 Salerno, Italy.
∗ Postal address: Dipartimento di Informatica e Applicazioni, Università di Salerno, 84100 Salerno, Italy.
∗ Postal address: Dipartimento di Informatica e Applicazioni, Università di Salerno, 84100 Salerno, Italy.
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Abstract

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

Keywords

ADAPTIVE QUEUEING PROCESSESINTERARRIVAL TIMESSERVICE TIMESEFFECTIVE DISTRIBUTIONSWAITING TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 903 - 911
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Work performed under CNR-JSPS Scientific Cooperation Programme, Contracts 83.00032.01 and 84.00227.01 and under M.P.I. financial support.

References

[1] Chan, J. and Conolly, B. W. (1978) Comparative effectiveness of certain queueing systems with adaptive demand and service mechanisms. Comput. Operat. Res. 5, 187–196.CrossRefGoogle Scholar
[2] Conolly, B. W. (1975) Queueing Systems. Ellis Horwood, Chichester.Google Scholar
[3] Conolly, B. W. and Chan, J. (1977) Generalised birth and death queueing processes: recent results. Adv. Appl. Prob. 9, 125–140.Google Scholar
[4] Iosifescu, M. and Tautu, P. (1973) Stochastic Processes and Applications in Biology and Medicine. II. Models. Springer-Verlag, Heidelberg.Google Scholar