Ray solution of a singularly perturbed elliptic PDE with applications to communications networks

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We analyze a second order, linear, elliptic PDE with mixed boundary conditions. This problem arose as a limiting case of a Markov-modulated queueing model for data handling switches in communications networks. We use singular perturbation methods to analyze the problem. In particular we use the ray method to solve the PDE in the limit where convection dominates diffusion. We show that there are both interior and boundary caustics, as well as a cusp point where two caustics meet, an internal layer, boundary layers and a corner layer. Our analysis leads to approximate formulas for the queue length (or buffer content) distribution at the switch.
38 pages, 3 figures

Keywords

Analysis of PDEs, MSC-class: 34E20 (Primary) 60J20 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/75356

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505658
 http://arxiv.org/abs/math/0505658

Collections

arXiv