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Analysis of two parallel queues by common exit service and infinite queue size

Published online by Cambridge University Press:  01 July 2016

C. Atkinson  and
M. E. Thompson
C. Atkinson*
Affiliation:
Imperial College, London
M. E. Thompson*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Mathematics, Imperial College, Huxley Building, Queen's Gate, London SW7 2B2, U.K.
∗∗Postal address: Department of Statistics, Faculty of Mathematics, University of Waterloo, Waterloo, Ont, N2L 3G1, Canada.
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Abstract

A system of two parallel queues is considered, where each customer must leave after service through a common gate G. It is assumed that service times at the two stations I and II are independent and identically distributed, and that exit service takes a fixed length of time. A I-customer may be served at station I only if the previous I-customer has completed exit service. Integral equations are formulated from which the distribution of the total service time may be obtained when the two queue sizes are infinite. These equations are solved for exponential and generalized erlangian service times. Extensions to the case of k parallel queues and to the case of Poisson arrivals and finite queue sizes are discussed briefly.

Keywords

MANY SERVER QUEUESTANDEM QUEUESINTERFERENCEDIRECT ACCESS STORAGE DEVICEINTEGRAL EQUATIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 1 , March 1981 , pp. 147 - 166
Copyright
Copyright © Applied Probability Trust 1981 

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References

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