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A model for queues in series

Published online by Cambridge University Press:  14 July 2016

O. P. Sharma
O. P. Sharma*
Affiliation:
Indian Institute of Technology, Delhi
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Abstract

This paper studies the stationary behaviour of a finite space queueing model consisting of r queues in series with multi-server service facilities at each queue. Poisson input and exponential service times have been assumed. The model is suitable for phase-type service as well as service with waiting allowed before the different phases. In the case of single-server queues explicit expressions for certain probability distributions, parameters and a steady-state solution for infinite queueing space have been obtained.

Keywords

MULTI-SERVER SERVICE FACILITIESFINITE AND INFINITE QUEUEING SPACESSTEADY-STATE SOLUTIONSINGLE-SERVER QUEUESOCCUPATION TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 691 - 696
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research done while the author was visiting the University of Sheffield supported by a Technical Assistance Award from the Ministry of Overseas Development.

References

[1] Jackson, R. R. P. (1954) Queueing systems with phase type service. Operat. Res. Quart. 5, 109–120.10.1057/jors.1954.23Google Scholar
[2] Saaty, T. L. (1961) Elements of Queueing Theory. McGraw-Hill, New York.Google Scholar
[3] Prabhu, N. U. (1965) Queues and Inventories. John Wiley, New York.Google Scholar
[4] Arya, Krishan Lal (1972) Study of a network of serial and non-serial servers with phase type service and finite queueing space. J. Appl. Prob. 9, 198–201.10.2307/3212649Google Scholar