0000000000951705
AUTHOR
Antonis Papachristodoulou
Density flow over networks: A mean-field game theoretic approach
A distributed routing control algorithm for dynamic networks has recently been presented in the literature. The networks were modeled using time evolution of density at network edges and the routing control algorithm allowed edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We borrow the idea and rearrange the density model to recast the problem within the framework of mean-field games. The contribution of this paper is three-fold. First, we provide a mean-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 …
Density Flow in Dynamical Networks via Mean-Field Games
Current distributed routing control algorithms for dynamic networks model networks using the time evolution of density at network edges, while the routing control algorithm ensures edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We rearrange the density model to recast the problem within the framework of mean-field games. In doing that, we illustrate an extended state-space solution approach and we study the stochastic case where the density evolution is driven by a Brownian motion. Further, we investigate the case where the density evolution is perturbed by a bounded adversarial disturbance. For both the stochastic a…