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Sample-path derivations of the excess, age, and spread distributions

Published online by Cambridge University Press:  14 July 2016

Ronald W. Wolff
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
∗Postal address: College of Engineering, Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

The familiar limiting distributions of excess, age, and spread are derived on sample paths, where these distributions are fractions of time. Similar results are obtained for the distribution of remaining service at a queue. For stochastic processes, where specified limits exist as finite constants with probability 1, the derived sample-path results are shown to imply that the same limiting distributions hold, where in a stochastic setting, these distributions may be defined in a more conventional way.

Keywords

LIMITING DISTRIBUTIONSREMAINING SERVICETIME AVERAGEQUEUE
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 432 - 436
Copyright
Copyright © Applied Probability Trust 1988 

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References

Green, L. (1982) A limit theorem on subintervals of interrenewal times. Operat. Res. 30, 210–216.Google Scholar
Heyman, D. P. and Stidham, S. Jr. (1980) The relation between customer and time averages in queues. Operat. Res. 28, 983–994.CrossRefGoogle Scholar
Miller, D. R. (1972) Existence of limits in regenerative processes. Ann. Math. Statist. 43, 1275–1282.CrossRefGoogle Scholar
Stidham, S. Jr. (1974) A last word on L = ?W . Operat. Res. 22, 417–421.Google Scholar
Stidham, S. Jr. (1982) Sample-path analysis of queues. Applied Probability — Computer Science: The Interface , Volume II, ed. Disney, R. L. and Ott, T. J., Birkhauser, Boston, 41–70.Google Scholar