Stephan Knapp

Theresa Dambach, Simone Göttlich, Stephan Knapp

This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at junctions that allow for the interpretation of roundabouts or on-ramps while the traffic dynamics is based on first-order macroscopic equations of Lighthill-Whitham-Richards (LWR) type. Trajectories for single drivers are then influenced by the surrounding traffic and can be tracked by appropriate numerical algorithms. The computational experiments show how the modeling framework can be used as navigation device.

Simone Göttlich, Stephan Knapp, Peter Schillen

We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of conservation law type. Therefore we use a kinetic mean-field equation and introduce a new problem-oriented closure function. Numerical experiments are presented to compare the above models and to show their similarities.