Delayed Traffic Models in Multiple Scales: New Macroscopic Models And Their Numerics.

Traffic becomes an ever more important topic in modern days, as it plays a vital role in economics, environmental issues and the daily life of most people. The simulation of traffic with mathematical models dates back to at least the 1950s. In that, microscopic models with explicit time delays, modeling the reaction times of both the driver and the car, are well known.
Starting from them, we derive new macroscopic traffic models, which keep this explicit time delay. This leaves us with part ...