Introduction

This thesis studies dynamic flows comprised of infinitesimally small agents (=flow particles) travelling through a network while continuously adapting their choice of route based on the current state of the network as determined by the flow up to the current time. The main motivation for such models comes from the study of large-scale road traffic wherein individual drivers try to get as fast as possible from their starting point to their destination and adjust their routes on-the-fly whenever they get new information about current congestion events (e.g. via traffic radio or navigational devices). To make this idea clearer, we start with a small, slightly informal example.