Geometrical Optics Approach to Markov-Modulated Fluid Models
Analysis of PDEs
2007-05-23 v1 Probability
Abstract
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.
Cite
@article{arxiv.math/0306262,
title = {Geometrical Optics Approach to Markov-Modulated Fluid Models},
author = {Diego Dominici and Charles Knessl},
journal= {arXiv preprint arXiv:math/0306262},
year = {2007}
}