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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.
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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 

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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