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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 processes 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→∞ , with appropriate scalings of the two state variables. In particular, the ray method and asymptotic matching are used.
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Document Type: Research Article

Affiliations: 1: State University of New York at New Paltz 2: University of Illinois at Chicago

Publication date: January 1, 2005

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