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The autostrada queueing problem

Published online by Cambridge University Press:  14 July 2016

B. W. Conolly
B. W. Conolly*
Affiliation:
Chelsea College, London
*
∗ Postal address: Department of Mathematics, Chelsea College, University of London, 552 Kings Road, London SW10 OUA, U.K.
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Abstract

The model considered in this note has been referred to by Haight (1958), Kingman (1961) and Flatto and McKean (1977) as two queues in parallel. Customers choose the shorter of the two queues which are otherwise independent. This system is known to be inferior to a single queue feeding the two servers, but how much? Some elementary considerations provide a fresh perspective on this awkward boundary-value problem. A procedure is proposed for the solution in the context of finite waiting-room size and some comparisons are made with the single-queue system and an independent two-queue system.

Keywords

QUEUES IN PARALLELFINITE BOUNDARY-VALUE PROBLEMTWO-DIMENSIONAL RANDOM WALKOPERATIONAL COMPARISON WITH ALTERNATIVE SYSTEMSDISCIPLINEAUTOSTRADA TOLL BOOTHSHARMONIC REPRESENTATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 394 - 403
Copyright
Copyright © Applied Probability Trust 1984 

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References

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