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HITTING PROBABILITIES AND HITTING TIMES FOR STOCHASTIC FLUID FLOWS: THE BOUNDED MODEL

Published online by Cambridge University Press:  13 November 2008

Nigel G. Bean ,
Małgorzata M. O'Reilly  and
Peter G. Taylor
Nigel G. Bean
Affiliation:
Applied Mathematics, University of Adelaide, SA 5005, Australia
Małgorzata M. O'Reilly
Affiliation:
School of Mathematics, University of Tasmania, Tas 7001, Australia E-mail: [email protected]
Peter G. Taylor
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Vic 3010, Australia
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Abstract

We consider a Markovian stochastic fluid flow model in which the fluid level has a lower bound zero and a positive upper bound. The behavior of the process at the boundaries is modeled by parameters that are different than those in the interior and allow for modeling a range of desired behaviors at the boundaries. We illustrate this with examples. We establish formulas for several time-dependent performance measures of significance to a number of applied probability models. These results are achieved with techniques applied within the fluid flow model directly. This leads to useful physical interpretations, which are presented.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 1 , January 2009 , pp. 121 - 147
Copyright
Copyright © Cambridge University Press 2009

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