Geometrical Optics Approach to Markov-Modulated Fluid Models

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We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. Here there are N identical sources that turn "on" and "off", and when "on" they generate fluid at unit rate into a buffer, which process the fluid at a rate c < N. In the steady state limit, the joint probability distribution of the buffer content and the number of active sources satisfies a system of N + 1 ODEs, that can also be viewed as a differential-difference equation analogous to a backward/forward parabolic PDE. We use singular perturbation methods to analyze the problem for N large with appropriate scalings of the two state variables. In particular, the ray method and asymptotic matching are used.

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Analysis of PDEs, Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/67816

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306262
 http://arxiv.org/abs/math/0306262

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arXiv