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On a certain type of network of queues

Published online by Cambridge University Press:  14 July 2016

K. C. Madan
K. C. Madan*
Affiliation:
National Council of Educational Research and Training, New Delhi
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Abstract

The paper studies a network of queues in which units arrive singly in a Poisson stream at a service channel S from which they branch out into k parallel channels S1, S2, …, Sk. After having been serviced at S1, S2, … Sk, the units converge again into a single channel S′. The service times of units at each of the channels are assumed to be exponential. Units finally serviced at S’ may leave the system or may again join S. This has been considered by taking two models denoted as Model A and Model B. Steady-state probabilities giving the number of units present in the system have been obtained explicitly for both the models. The expressions for mean queue lengths have also been arrived at.

Keywords

NETWORK OF QUEUESMULTICHANNEL ARRAY OF PARALLEL CHANNELS LINKED IN SERIES ON EITHER SIDE WITH A SINGLE CHANNELINFINITE QUEUEING SPACE BEFORE EACHCHANNELSTEADY-STATE SOLUTIONAVERAGE NUMBER OF UNITS IN THE SYSTEM

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 195 - 200
Copyright
Copyright © Applied Probability Trust 1975 

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References

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[4] Saaty, T. L. (1961) Elements of Queueing Theory. McGraw-Hill, New York.Google Scholar