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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

Conolly, B. W. and Good, I. J. (1977) A table of discrete Fourier transform pairs. SIAM J. Appl. Math. 32, 810–822.CrossRefGoogle Scholar
Flatto, L. and Mckean, H. P. (1977) Two queues in parallel. Comm. Pure Appl. Math. 30, 255–263.Google Scholar
Haight, F. A. (1958) Two queues in parallel. Biometrika 45, 401–410.Google Scholar
Kingman, J. F. C. (1961) Two similar queues in parallel. Ann. Math. Statist. 32, 1314–1323.CrossRefGoogle Scholar
Mccrea, W. H. and Whipple, F. J. W. (1940) Random paths in two and three dimensions. Proc. R. Soc. Edinburgh 60, 281–298.Google Scholar
Morse, P. M. (1958) Queues, Inventories, and Maintenance. Wiley, New York.Google Scholar
Spitzer, F. (1964) Principles of Random Walk. Van Nostrand, Princeton.Google Scholar
Weber, R. R. (1978) On the optimal assignment of customers to parallel servers. J. Appl. Prob. 15, 406–413.Google Scholar
Winston, W. (1977) Optimality of the shortest line discipline. J. Appl. Prob. 14, 181–189.Google Scholar