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We analyze a second order, linear, elliptic PDE with mixed bound- ary conditions. This problem arose as a limiting case of a Markov- modulated queueing model for data handling switches in communica- tions networks. We use singular perturbation methods to analyze the problem. In particular we use the ray method to solve the PDE in the

Ray Solution of a Singularly Perturbed Elliptic PDE with Applications to Communications Networks