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First exit times for compound Poisson dams with a general release rule

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  • Jiyeon Lee

Abstract

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam. Copyright Springer-Verlag 2007

Suggested Citation

  • Jiyeon Lee, 2007. "First exit times for compound Poisson dams with a general release rule," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 169-178, February.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:1:p:169-178
    DOI: 10.1007/s00186-006-0111-3
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    References listed on IDEAS

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    1. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
    2. Lee, Eui Yong & Kinateder, Kimberly K. J., 2000. "The expected wet period of finite dam with exponential inputs," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 175-180, November.
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    Cited by:

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    2. Philipp Afèche & Adam Diamant & Joseph Milner, 2014. "Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks," Operations Research, INFORMS, vol. 62(5), pages 1179-1201, October.

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