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Journal of Applied Probability Journal of Applied Probability

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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
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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 PARALLEL FINITE BOUNDARY-VALUE PROBLEM TWO-DIMENSIONAL RANDOM WALK OPERATIONAL COMPARISON WITH ALTERNATIVE SYSTEMS DISCIPLINE AUTOSTRADA TOLL BOOTHS HARMONIC 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.CrossRefGoogle Scholar
Haight, F. A. (1958) Two queues in parallel. Biometrika 45, 401–410.CrossRefGoogle 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.CrossRefGoogle Scholar
Morse, P. M. (1958) Queues, Inventories, and Maintenance. Wiley, New York.Google Scholar
Spitzer, F. (1964) Principles of Random Walk. Van Nostrand, Princeton.CrossRefGoogle Scholar
Weber, R. R. (1978) On the optimal assignment of customers to parallel servers. J. Appl. Prob. 15, 406–413.CrossRefGoogle Scholar
Winston, W. (1977) Optimality of the shortest line discipline. J. Appl. Prob. 14, 181–189.CrossRefGoogle Scholar

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