Geometrical Optics Approach to Markov-Modulated Fluid Models
| dc.creator | Dominici, Diego | |
| dc.creator | Knessl, Charles | |
| dc.date | 2003-06-17 | |
| dc.date.accessioned | 2026-07-07T04:59:01Z | |
| dc.date.available | 2026-07-07T04:59:01Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0306262 | |
| dc.identifier | http://arxiv.org/abs/math/0306262 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67816 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Probability | |
| dc.title | Geometrical Optics Approach to Markov-Modulated Fluid Models | |
| dc.type | text |