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

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

2005-05-30

arxiv.org/abs/math/0505658v1

Mathematics

Analysis of PDEs

38 pages, 3 figures

Scientific paper

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.

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