4 papers
Ray solution of a singularly perturbed elliptic PDE with applications to communications networks
Diego Dominici, Charles Knessl
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 switche…
Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model
Diego Dominici, Charles Knessl
We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an…
Geometrical Optics Approach to Markov-Modulated Fluid Models
Diego Dominici, Charles Knessl
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 a Small Elliptic Perturbation of a Backward-Forward Parabolic Problem, with Applications to Stochastic Models
Diego Dominici, Charles Knessl
We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backwar…