Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T13:17:46.607Z Has data issue: false hasContentIssue false
  • English
  • Français

The transient state probabilities for a queueing model where potential customers are discouraged by queue length

Published online by Cambridge University Press:  14 July 2016

Erik A. Van Doorn
Erik A. Van Doorn*
Affiliation:
Twente University of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Exact expressions are derived for the transition probabilities of the birth-death process with parameters and which serves as a queueing model where potential customers are discouraged by queue length.

Keywords

BIRTH-DEATH PROCESSBIRTH–DEATH QUEUEING MODELEXPONENTIAL ERGODICITYSPECTRAL REPRESENTATIONSTOCHASTIC MONOTONICITYTRANSITION PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 499 - 506
Copyright
Copyright © Applied Probability Trust 

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.)

Footnotes

∗

Present address: Netherlands Postal and Telecommunications Services, Dr. Neher-Laboratories, P.O. Box 421, 2260 AK Leidschendam, The Netherlands.

References

Callaert, H. (1974) On the rate of convergence in birth-and-death processes. Bull. Soc. Math. Belg. XXVI, 173–184.Google Scholar
Conolly, B. (1975) Lecture Notes on Queueing Systems. Ellis Horwood Limited, Chichester.Google Scholar
Hadidi, N. (1975) A queueing model with variable arrival rates. Period. Math. Hung. 6, 39–47.Google Scholar
Karlin, S. and McGregor, J. L. (1957a) The differential equations of birth-and-death processes and the Stieltjes moment problem. Trans. Amer. Math. Soc. 85, 489–546.Google Scholar
Karlin, S. and McGregor, J. L. (1957b) The classification of birth and death processes. Trans. Amer. Math. Soc. 86, 366–400.Google Scholar
Kendall, D. G. and Reuter, G. E. H. (1957) The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states. Acta Math. 97, 103–144.Google Scholar
Natvig, B. (1974) On the transient state probabilities for a queueing model where potential customers are discouraged by queue length. J. Appl. Prob. 11, 345–354.Google Scholar
Natvig, B. (1975) On a queueing model where potential customers are discouraged by queue length. Scand. J. Statist. 2, 34–42.Google Scholar
Van Doorn, E. A. (1980) Stochastic monotonicity of birth-death processes. Adv. Appl. Prob. 12, 59–80.Google Scholar
Widder, D. V. (1946) The Laplace Transform. Princeton University Press, Princeton, NJ.Google Scholar