The Annals of Probability

Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue

Douglas R. Miller and F. Dennis Sentilles

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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.

Article information

Source
Ann. Probab., Volume 3, Number 3 (1975), 424-439.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996350

Digital Object Identifier
doi:10.1214/aop/1176996350

Mathematical Reviews number (MathSciNet)
MR402975

Zentralblatt MATH identifier
0311.60053

JSTOR
links.jstor.org

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60B10: Convergence of probability measures 60K05: Renewal theory

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

Citation

Miller, Douglas R.; Sentilles, F. Dennis. Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue. Ann. Probab. 3 (1975), no. 3, 424--439. doi:10.1214/aop/1176996350. https://projecteuclid.org/euclid.aop/1176996350


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