Flows Over Time as Continuous Limits of Packet-Based Network Simulations

Transportation research procedia, vol. 52, pp. 123–130

Abstract

This study examines the connection between an agent-based transport simulation and Nash flows over time. While the former is able to represent many details of traffic and model large-scale, real-world traffic situations with a co-evolutionary approach, the latter provides an environment for provable mathematical statements and results on exact user equilibria. The flow dynamics of both models are very similar with the main difference that the simulation is discrete in terms of vehicles and time while the flows over time model considers continuous flows and continuous time. This raises the question whether Nash flows over time are the limit of the convergence process when decreasing the vehicle and time step size in the simulation coherently. The experiments presented in this study indicate this strong connection which provides a justification for the analytical model and a theoretical foundation for the simulation.

Authors 6

1. Theresa Ziemke corresponding

   Technische Universität Berlin

   Affiliation as printed

   Technische Universität Berlin, Combinatorial Optimization and Graph Algorithms, Straβe des 17. Juni 136, 10623 Berlin, Germany

   Technische Universität Berlin, Transport Systems Planning and Transport Telematics, Salzufer 17-19, 10587 Berlin, Germany

2. Leon Sering

   Technische Universität Berlin

   Affiliation as printed

   Technische Universität Berlin, Combinatorial Optimization and Graph Algorithms, Straβe des 17. Juni 136, 10623 Berlin, Germany

3. Laura Vargas Koch Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Management Science, Kackertstraβe 7, 52072 Aachen, Germany

4. Max Zimmer

   Technische Universität Berlin

   Affiliation as printed

   Technische Universität Berlin, Combinatorial Optimization and Graph Algorithms, Straβe des 17. Juni 136, 10623 Berlin, Germany

5. Kai Nagel

   Technische Universität Berlin

   Affiliation as printed

   Technische Universität Berlin, Transport Systems Planning and Transport Telematics, Salzufer 17-19, 10587 Berlin, Germany

6. Martin Skutella

   Technische Universität Berlin

   Affiliation as printed

   Technische Universität Berlin, Combinatorial Optimization and Graph Algorithms, Straβe des 17. Juni 136, 10623 Berlin, Germany