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June, 1975 Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue
Douglas R. Miller, F. Dennis Sentilles
Ann. Probab. 3(3): 424-439 (June, 1975). DOI: 10.1214/aop/1176996350

Abstract

Some ideas from the theory of weak convergence of probability measures on function spaces are modified and extended to show that the queue-length of the GI/G/s system converges in distribution as time passes, for the case of atomless interarrival and service distributions. The key to this result is the concept of the uniform $\sigma$-additivity of certain sets of renewal measures on a space endowed with incompatible topology and $\sigma$-field.

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Douglas R. Miller. F. Dennis Sentilles. "Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue." Ann. Probab. 3 (3) 424 - 439, June, 1975. https://doi.org/10.1214/aop/1176996350

Information

Published: June, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0311.60053
MathSciNet: MR402975
Digital Object Identifier: 10.1214/aop/1176996350

Subjects:
Primary: 60K25
Secondary: 60B10 , 60K05

Keywords: GI/G/s queue , Renewal process , uniform $\sigma$-additivity , weak convergence of measures on nonseparable metric spaces

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 3 • June, 1975
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