Density Flow over Networks: A Mean-field Game Theoretic Approach

A distributed routing control algorithm for dynamicnetworks has recently been presented in the literature.The networks were modeled using time evolution of densityat network edges and the routing control algorithm allowededge density to converge to a Wardrop equilibrium, which wascharacterized by an equal traffic density on all used paths.We borrow the idea and rearrange the density model to recastthe problem within the framework of mean-field games. Thecontribution of this paper is three-fold. First, we provide amean-field game formulation of the problem at hand. Second,we illustrate an extended state space solution approach. Third,we study the stochastic case where the density evolution isdriven by a Brownian motion.