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Time and customer processes in queues with stationary inputs

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Tokyo Institute of Technology, Japan
*
*Now at Science University of Tokyo, Noda City, Chiba, Japan.
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Abstract

Two types of processes occurring in queues with stationary inputs are considered. They are called ‘time processes’ and ‘customer processes’. Sufficient conditions for the convergence of sample averages and the existence of limiting distributions for each type of processes are given. The results generalize those of Loynes (1962). The results are applied to three queueing processes and the Little's formula L = λW is obtained under rather general conditions.

Keywords

QUEUESSTATIONARY INPUTSPOINT PROCESSERGODIC PROPERTYCONVERGENCE OF SAMPLE AVERAGESEXISTENCE OF LIMITING DISTRIBUTIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977, pp. 349 - 357
Copyright
Copyright © Applied Probability Trust 1977 

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References

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