Routing on Traffic Networks Incorporating Past Memory up to Real-Time Information on the Network State

In this review, we discuss routing algorithms for the dynamic traffic assignment (DTA) problem that assigns traffic flow in a given road network as realistically as possible. We present a new class of so-called routing operators that route traffic flow at intersections based on either real-time information about the status of the network or historical data. These routing operators thus cover the distribution of traffic flow at all possible intersections. To model traffic flow on the links, we use a well-known macroscopic ordinary delay differential equation. We prove the existence and uniqueness of the solutions of the resulting DTA for a broad class of routing operators. This new routing approach is required and justified by the increased usage of real-time information on the network provided by map services, changing the laws of routing significantly. Because these map and routing services have a huge impact on the infrastructure of cities, a more precise mathematical description of the emerging new traffic patterns and effects becomes crucial for understanding and improving road and city conditions.