Hitting probabilities and hitting times for stochastic fluid flows the bounded model
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(Published version)
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2009
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Bean, N.
O'Reilly, M.
Taylor, P.
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Probability in the Engineering and Informational Sciences, 2009; 23(1):121-147
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Nigel G. Bean, Małgorzata M. O'Reilly and Peter G. Taylor
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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.
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Copyright © Cambridge University Press 2009