The Erlangization method for Markovian fluid flows. (English) Zbl 1140.60357

Summary: For applications of stochastic fluid models, such as those related to wildfire spread and containment, one wants a fast method to compute time dependent probabilities. Erlangization is an approximation method that replaces various distributions at a time \(t\) by the corresponding ones at a random time with Erlang distribution having mean \(t\). Here, we develop an efficient version of that algorithm for various first passage time distributions of a fluid flow, exploiting recent results on fluid flows, probabilistic underpinnings, and some special structures. Some connections with a familiar Laplace transform inversion algorithm due to Jagerman are also noted up front.


60K40 Other physical applications of random processes
60K25 Queueing theory (aspects of probability theory)
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