The mean dynamics of many stochastic processing networks in which jobs with general service distributions are routed in a network of multiple servers are often described by nonlinearly coupled systems of measure-valued partial differential equations. These have some similarities with partial differential equations that describe age-structured population models, but require rather different tools for the analysis of their long-time behavior due to the presence of nonlinear couplings. I will describe these equations, explaining where they arise and why they are challenging to analyze, then present results on their long-time behavior and end with some open questions.
Long-time behavior of nonlinearly coupled measure-valued partial differential equations
Kavita Ramanan, Brown UniversityAuthors: Rami Atar, Weining Kang, Haya Kaspi, Kavita Ramanan,
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs