Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T13:05:25.373Z Has data issue: false hasContentIssue false
  • English
  • Français

A queuing-theoretic anomaly

Published online by Cambridge University Press:  14 July 2016

P. J. Burke
P. J. Burke*
Affiliation:
Bell Telephone Laboratories
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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 Fifth International Teletraffic Congress, Preprints of Technical Papers (unpublished) 96–106.Google Scholar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 Unpublished memorandum, Bell Telephone Laboratories.Google Scholar