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The expected wet period of finite dam with exponential inputs

Authors
Lee, EYKinateder, KKJ
Issue Date
Nov-2000
Publisher
ELSEVIER SCIENCE BV
Keywords
queue; finite queue; busy period; martingales; dam; finite dam; capacity
Citation
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, v.90, no.1, pp.175 - 180
Journal Title
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume
90
Number
1
Start Page
175
End Page
180
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/16730
DOI
10.1016/S0304-4149(00)00034-X
ISSN
0304-4149
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. (C) 2000 Elsevier Science B.V. All rights reserved.
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