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A comparison of convergence rates for three models in the theory of dams

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Robert Lund  and
Walter Smith
Robert Lund*
Affiliation:
The University of Georgia
Walter Smith*
Affiliation:
The University of North Carolina
*
∗Postal address: Department of Statistics, The University of Georgia, Athens, GA 30602–1952, USA.
∗∗Postal address: Department of Statistics, The University of North Carolina, Chapel Hill, NC 275993260, USA.
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Abstract

This paper compares the convergence rate properties of three storage models (dams) driven by time-homogeneous jump process input: the infinitely high dam, the finite dam, and the infinitely deep dam. We show that the convergence rate of the infinitely high dam depends on the moment properties of the input process, the finite dam always approaches its limiting distribution exponentially fast, and the infinitely deep dam approaches its limiting distribution exponentially fast under very general conditions. Our methods make use of rate results for regenerative processes and several sample path orderings.

Keywords

STORAGE MODELCONVERGENCE RATESMARKOV PROCESSPOISSON PROCESSEXPONENTIAL ERGODICITYSTORAGE EQUATION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 74 - 83
Copyright
Copyright © Applied Probability Trust 1997 

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