In this talk I will discuss an important example of complex networks, namely road traffic networks. I start by giving an overview of the existing literature, distinguishing between microscopic models (describing the stochastic evolution of the position of individual vehicles) and macroscopic models (built around deterministic continuous flows, represented as partial differential equations). Then I argue that the “optimal" model is a compromise between these: we aim at a stochastic model with enough aggregation to make sure that explicit limiting analysis can be performed. The underlying dynamics are consistent with the macroscopic fundamental diagram that describes the functional relation between the vehicle density and velocity. Discretizing space, the model can be phrased in terms of a spatial population process, thus allowing the application of a classical scaling approach. More specifically, it follows that under a diffusion scaling, the vehicle density process can be approximated by an appropriate Gaussian process. This Gaussian approximation can be used to evaluate the travel time distribution between a given origin and destination.
Joint work with Jaap Storm (VU University Amsterdam).
Joint at https://meet.google.com/hdv-zcxa-zvw