2003/06/17 by Diego Dominici, Dominici, Diego, Charles Knessl +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.AP #math.PR
paper · pdf · doi:10.48550/arxiv.math/0306262
arxiv created 2003/06/17 · openalex publication_date 2003/06/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.