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A queuing-theoretic anomaly

Published online by Cambridge University Press:  14 July 2016

P. J. Burke
P. J. Burke*
Affiliation:
Bell Telephone Laboratories
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Abstract

The equilibrium delay distribution for a system with finite-source input, constant service time, and s > 1 servers, as determined by simulation, showed the existence of values of t such that the probability of delay greater than t is a non-monotone function of the input intensity. Since repeated efforts to remove this counter-intuitive result by debugging failed, a simple case was attacked by analytical and numerical methods; and the same anomaly was revealed. The method of analysis is described and an explanation of the result is offered.

Keywords

QUEUESCONSTANT SERVICE TIMEFINITE SOURCESDELAY DISTRIBUTIONSNON-MONOTONE DELAYSTWO-SERVER QUEUESANOMALOUS QUEUESANOMALOUS DELAYS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 373 - 383
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Durnan, C. J. (1967) Estimates of the delay distributions for queuing systems with constant server holding time and random order of service. Fifth International Teletraffic Congress, Preprints of Technical Papers (unpublished) 96–106.Google Scholar
[2] Durnan, C. J. and Weber, J. H. (1961) Traffic studies — finite queues with constant service time. Unpublished memorandum, Bell Telephone Laboratories.Google Scholar