Simulation and Optimization of Trajectories in a Congested Network

The subject of this article is twofold. Firstly it describes how a dynamic macroscopic network loading model can be used to simulate the movement of arbitrarily complex individual particles (agents) through a network without loss of the macroscopic model’s differentiability. Based on this result the problem of minimizing a given functional of the macroscopic model’s states by adjustment of individual agents’ trajectories is considered. A solution procedure is proposed, which is based on subsequent linearizations of the overall system dynamics and time variant best path calculations.