## Geometrical Optics Approach to Markov-Modulated Fluid Models (2008)

Citations: | 2 - 2 self |

### BibTeX

@MISC{Dominici08geometricaloptics,

author = {Diego Dominici and Charles Knessl},

title = {Geometrical Optics Approach to Markov-Modulated Fluid Models},

year = {2008}

}

### OpenURL

### Abstract

We analyze asymptotically a differential-difference equation, that arises in a Markovmodulated 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 → ∞, with appropriate scalings of the two state variables. In particular, the ray method and asymptotic matching are used. 1