Approximations for time-dependent distributions in Markovian fluid models

Sarah Dendievel; Guy Latouche

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arXiv · 1409.4989

Approximations for time-dependent distributions in Markovian fluid models

Sarah Dendievel·Guy Latouche

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Abstract

In this paper we study the distribution of the level at time $\theta$ of Markovian fluid queues and Markovian continuous time random walks, the maximum (and minimum) level over $[0,\theta]$, and their joint distributions. We approximate $\theta$ by a random variable $T$ with Erlang distribution and we use an alternative way, with respect to the usual Laplace transform approach, to compute the distributions. We present probabilistic interpretation of the equations and provide a numerical illustration.

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Sarah Dendievel, Guy Latouche. 2014-09-17. Approximations for time-dependent distributions in Markovian fluid models. https://arxiv.org/abs/1409.4989

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