Geometrical Optics Approach to Markov-Modulated Fluid Models

Details Geometrical Optics Approach to Markov-Modulated Fluid Models Geometrical Optics Approach to Markov-Modulated Fluid Models

2003-06-17

arxiv.org/abs/math/0306262v1

Mathematics

Analysis of PDEs

Scientific paper

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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