Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-06-02T02:20:29.521Z Has data issue: false hasContentIssue false
  • English
  • Français

A low traffic approximation for queues

Published online by Cambridge University Press:  14 July 2016

P. Bloomfield  and
D. R. Cox
P. Bloomfield
Affiliation:
Imperial College, London
D. R. Cox*
Affiliation:
Imperial College, London
*
*Now at Princeton University.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general procedure is outlined for obtaining lower bounds and approximations to the amount of congestion in queues with low traffic. Some detailed formulae are given for a number of single-server systems and compared with exact solutions where available. Results are also given for a discrete time system in which departures clash with new arrivals.

Keywords

SINGLE-SERVER QUEUEAPPROXIMATION TO QUEUEING-TIMELIGHT TRAFFICUN PUNCTUALITY SYSTEMREGULAR ARRIVALSPOISSON ARRIVALSBUSY-PERIOD DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 832 - 840
Copyright
Copyright © Applied Probability Trust 1972 

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

Cox, D. R. (1955) The statistical analysis of congestion. J. R. Statist. Soc. A, 118, 324–335.CrossRefGoogle Scholar
Cox, D. R. and Hinkley, D. V. (1970) Some properties of multiserver queues with appointments. J. R. Statist. Soc. A, 133, 1–13.CrossRefGoogle Scholar
Kendall, D. G. (1953) Stochastic processes occuring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math. Statist. 24, 338–354.CrossRefGoogle Scholar
Kingman, J. F. C. (1965) The heavy traffic approximation in the theory of queues. In Proc. Symp. on Congestion Theory, eds. Smith, W. L. and Wilkinson, W., 137–159. Univ. of N. Carolina Press, Chapel Hill.Google Scholar
Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.CrossRefGoogle Scholar
Winsten, C. B. (1959) Geometric distributions in the theory of queues. J. R. Statist. Soc. B, 21, 1–35.Google Scholar