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A Dam with seasonal input

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Robert B. Lund
Robert B. Lund*
Affiliation:
The University of North Carolina
*
∗ Present address: Department of Statistics, The University of Georgia, 204 Statistics Building, Athens, GA 30602–1952, USA.
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Abstract

This paper examines the infinitely high dam with seasonal (periodic) Lévy input under the unit release rule. We show that a periodic limiting distribution of dam content exists whenever the mean input over a seasonal cycle is less than 1. The Laplace transform of dam content at a finite time and the Laplace transform of the periodic limiting distribution are derived in terms of the probability of an empty dam. Necessary and sufficient conditions for the periodic limiting distribution to have finite moments are given. Convergence rates to the periodic limiting distribution are obtained from the moment results. Our methods of analysis lean heavily on the coupling method and a stochastic monotonicity result.

Keywords

PERIODIC QUEUEDAM THEORYCOUPLINGPERIODIC POISSON 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 31 , Issue 2 , June 1994 , pp. 526 - 541
Copyright
Copyright © Applied Probability Trust 1994 

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