Stochastic Modeling and Simulation of Multi-Lane/Class Traffic

Alexandros Sopasakis
Lund Institute of Technology

We present a novel stochastic model describing vehicle behavior and interactions at the microscopic level. We built an Asymmetric Simple Exclusion process on a lattice-based domain. The model allows vehicles to ascertain their situation locally and enables them to act as independent entities in order to improve their outlook based on physically relevant Arrhenius look-ahead dynamics.

Hierarchical closures and mean field approximations are implemented to derive a class of corresponding traffic flow PDEs for this microscopic process. As a result microscopic parameters have direct functional representations with their corresponding macroscopic equivalents. Our approach relies heavily on ?rst deriving approximate differential mesoscopic equations. These approximations become exact in the long range (Kac interaction potentials case) and are used to give a ?rst indication, via linearized stability analysis, of the interesting regimes for the stochastic model. Real-time kinetic Monte Carlo simulations of the microscopic model are implemented in order to understand but also predict traffic behavior. An interesting and mainly unknown phenomenon between lattice-based and lattice-free modeling approaches is also highlighted.

Back to Mathematics of Traffic Flow Modeling, Estimation and Control