Fluid analysis of spatio-temporal properties of agents in a population model

We consider large stochastic population models in which heterogeneous agents are interacting locally and moving in space. These models are very common, e. g. in the context of mobile wireless networks, crowd dynamics, traffic management, but they are typically very hard to analyze, even when space is discretized in a grid. Here we consider individual agents and look at their properties, e. g. quality of service metrics in mobile networks. Leveraging recent results on the combination of stochastic approximation with formal verification, and of fluid approximation of spatio-temporal population processes, we devise a novel mean-field based approach to check such behaviors, which requires the solution of a low-dimensional set of Partial Differential Equation, which is shown to be much faster than simulation. We prove the correctness of the method and validate it on a mobile peer-to-peer network example.