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An embedded level crossing technique for dams and queues

Published online by Cambridge University Press:  14 July 2016

P. H. Brill
P. H. Brill*
Affiliation:
University of Toronto
*
∗Presently with Department of Quantitative Methods, University of Illinois, Chicago, IL 60680, U.S.A. This work was sponsored by the National Research Council of Canada under Grants # A4374 and # A2796.
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Abstract

The new concept of embedded level crossings is combined with the old principle of stationary set balance to produce an alternative approach for obtaining the steady-state distribution of the level in a dam with general release rule. The method yields the steady state distribution of the customer waiting time in the GI/G/1 queue as a special case. Results for a dam in which the instantaneous release rate is proportional to the level, and for the M/G/1, GI/M/1, Ek/M/1 and D/M/1 queues are derived using the new technique.

Keywords

LEVEL CROSSINGSEMBEDDED STOCHASTIC PROCESSSTATIONARY SET BALANCEDAMSQUEUES
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 174 - 186
Copyright
Copyright © Applied Probability Trust 1979 

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References

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