Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T17:01:12.215Z Has data issue: false hasContentIssue false
  • English
  • Français

The busy period of the queueing system M/G/∞

Published online by Cambridge University Press:  14 July 2016

Wolfgang Stadje
Wolfgang Stadje*
Affiliation:
Universität Osnabrück
*
∗Postal address: Universität Osnabrück, Fachbereich Mathematik, 45 Osnabrück, Postfach 4469, Albrechtstr. 28, West Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

For the queueing system M/G/∞ some distributions connected with the associated busy periods are derived.

Keywords

QUEUES WITH UNLIMITED SERVICE
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 697 - 704
Copyright
Copyright © Applied Probability Trust 1985 

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] Brown, M. and Ross, S. M. (1969) Some results for infinite server Poisson queues. J. Appl. Prob. 6, 604–611.CrossRefGoogle Scholar
[2] Daley, D. J. (1976) Queueing output processes. J. Appl. Prob. 8, 395–415.CrossRefGoogle Scholar
[3] Eckler, A. R. (1969) A survey of coverage problems associated with point and target area. Technometrics 11, 561–589.CrossRefGoogle Scholar
[4] Feller, W. (1971) An Introduction to Probability Theory and its Applications, volume II. Wiley, New York.Google Scholar
[5] Glaz, J. and Naus, J. (1979) Multiple coverage of the line. Ann. Prob. 7, 900–906.CrossRefGoogle Scholar
[6] Kaplan, N. (1975) Limit theorems for a GI/G/8 queue. Ann. Prob. 3, 780–789.CrossRefGoogle Scholar
[7] Purdue, P. and Linton, D. (1981) An infinite server queue subject to an extraneous phase process and related models. J. Appl. Prob. 18, 236–244.CrossRefGoogle Scholar
[8] Robbins, H. (1944/45) On the measure of a random set, I. Ann. Math. Statist. 15, 70–74; II. Ann. Math. Statist. 16, 342–347.CrossRefGoogle Scholar
[9] Santaló, L. A. (1976) Integral Geometry and Geometric Probability. Addison-Wesley, Reading, Mass.Google Scholar
[10] Shepp, L. (1972) Covering the circle with random arcs. Israel J. Math. 11, 328–345.CrossRefGoogle Scholar
[11] Siegel, A. F. (1979) Asymptotic coverage distributions on the circle. Ann. Prob. 7, 651–661.CrossRefGoogle Scholar
[12] Siegel, A. F. and Holst, L. (1982) Covering the circle with random arcs of random sizes. J. Appl. Prob. 19, 373–381.CrossRefGoogle Scholar
[13] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[14] Votaw, D. F. (1946) The probability distribution of the measure of a random linear set. Ann. Math. Statist. 17, 240–244.CrossRefGoogle Scholar