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A singular property of multiserver systems with constant service time

Published online by Cambridge University Press:  14 July 2016

S. Halfin
S. Halfin*
Affiliation:
Bell Laboratories, Holmdel, N.J.
*
∗Postal address: Bell Laboratories, Holmdel, N.J. 07733, U.S.A.
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Abstract

The behavior of queuing systems with two servers and one waiting room is investigated. It is shown that if the service time is constant, then the difference between the times to service completion of the two servers (phase difference) tends to a constant, for increasing input intensities. This phenomenon holds for a wide class of arrival processes, but not when the service time has even a small variability. These results imply that the delay is not stochastically monotone in the input intensity. In general, we conjecture that the behavior of the phase differences, and delays, depends on whether the size of the waiting room is even or odd.

Keywords

QUEUING THEORYMULTI-SERVER QUEUESCONSTANT SERVICE TIMELIMIT PROPERTIESFINITE WAITING ROOMNON-MONOTONE DELAYS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 362 - 372
Copyright
Copyright © Applied Probability Trust 1979 

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References

Burke, P. J. (1979) A queueing-theoretic anomaly. J. Appl. Prob. 16, 373–383.Google Scholar
Durnan, C. J. and Weber, J. H. (1961) Traffic studies — finite queues with constant service time. Unpublished memorandum, Bell Telephone Laboratories.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York.Google Scholar