Qualitative Properties of Solutions to Systems of Fokker‐Planck Equations for Multilane Traffic Flow

A review of recently introduced Fokker‐Planck‐type systems of partial differential equations as kinetic models of multilane traffic flow is given, and we present a series of analytical and numerical studies for these models. In particular, we present the convergence to equilibria, explain why equilibria of the present models may show jump discontinuities at the average speed, and explore synchronization on adjacent lanes from both an analytical and numerical point of view. Finally, we present numerical studies that explain the formation and propagation of stop‐and‐go waves.

Keywords:

• Traffic flow
• Fokker-Planck equation
• Kinetic models

Acknowledgments

This research was supported by the German Research Foundation (DFG), grant KL 1105/5, and Deutscher Akademischer Austauschdienst (DAAD), grant D/03/22853, as well as by grant 7847 of the Natural Sciences and Engineering Research Council of Canada. M. Herty and A. Klar would like to thank the Department of Mathematics and Statistics at the University of Victoria, Canada, for their hospitality.