Kavita Ramanan, Brown University
Authors: Rami Atar, Weining Kang, Haya Kaspi, Kavita Ramanan,
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs

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.

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