Hitting probabilities and hitting times for stochastic fluid flows: The bounded model

Authors:
Nigel g. Bean;Małgorzata m. O'reilly;Peter g. Taylor
Affiliations:
Applied mathematics, university of adelaide, sa 5005, australia;School of mathematics, university of tasmania, tas 7001, australia e-mail: malgorzata.oreilly@utas.edu.au;Department of mathematics and statistics, university of melbourne, vic 3010, australia
Venue:
Probability in the Engineering and Informational Sciences
Year:
2009

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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.