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The expected wet period of finite dam with exponential inputs

Author

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  • Lee, Eui Yong
  • Kinateder, Kimberly K. J.

Abstract

We use martingale methods to obtain an explicit formula for the expected wet period of the finite dam of capacity V, where the amounts of inputs are i.i.d exponential random variables and the output rate is one, when the reservoir is not empty. As a consequence, we obtain an explicit formula for the expected hitting time of either 0 or V and a new expression for the distribution of the number of overflows during the wet period, both without the use of complex analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:90:y:2000:i:1:p:175-180
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    Cited by:

    1. Kinateder, Kimberly K.J., 2012. "Expected earnings of invested overflow strategies for M/M/1 queue with constrained workload," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2072-2081.
    2. 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.

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