Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T14:01:25.277Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical approximations for compound geometric distributions with applications in queueing theory

Published online by Cambridge University Press:  14 July 2016

L. E. N. Delbrouck
L. E. N. Delbrouck*
Affiliation:
Bell-Northern Research, Ottawa, Ontario
Get access Rights & Permissions [Opens in a new window]

Abstract

A two-step procedure is described to approximate first come first served delay distributions in M/G/1 and GI/G/1 systems. The procedure consists in formulating a coarse initial approximation for the distribution sought, and then correcting this approximation by means of a suitable integral transformation. Examples are displayed.

Keywords

DELAY DISTRIBUTIONSQUEUESPOLLACZEK FORMULAWIENER-HOPF EQUATIONEXPONENTIAL APPROXIMANTSASYMPTOTIC BEHAVIORTWO-STEP COMPUTATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 202 - 208
Copyright
Copyright © Applied Probability Trust 1978 

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] Borovkov, A. A. (1970) Factorization identities and properties of the distribution of the supremum of sequential sums. Theory Prob. Appl. 15, 359–402.Google Scholar
[2] Delbrouck, L. E. N. (1975) Convexity properties, moment inequalities, and asymptotic exponential approximations for delay distributions in GI/G/1 systems. Stoch. Proc. Appl. 3, 193–207.Google Scholar
[3] Kühn, P. (1976) Tables on Delay Systems. Institute of Switching and Data Technics, Stuttgart.Google Scholar
[4] Lindley, D. V. (1952) Theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.Google Scholar
[5] Marchal, W. G. and Harris, C. M. (1976) A modified Erlang approach to approximating GI/G/1 queues. J. Appl. Prob. 13, 118–126.Google Scholar
[6] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar