The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model Original Research Article

In this paper a direct simulation Monte Carlo (DSMC) method is applied to a spatial homogeneous mesoscopic vehicular traffic flow model, based on a Boltzmann-like master equation. In contrast to gas kinetics, where in a collision a velocity jump change occurs, the interaction now changes the acceleration value of the following car in a leading car pair. There are no conservation laws in a single interaction. Therefore the Bird simulation scheme seems not to be the right choice for the approximation of the interaction integral. It is shown that a Nanbu like scheme is natural for this process. To avoid the typical double loop computational effort of the Nanbu scheme, a sampling algorithm developed by Babovsky is applied. Several car interaction profiles are examined and their resulting stochastic equilibrium solutions are discussed. First, simple interaction profiles are used to compare the simulation results with analytic calculated velocity distributions showing excellent agreement. Second, a realistic distance threshold interaction profile is applied to the simulation and the results are shown to be in qualitative agreement with measured traffic flow data. The simulation procedure seems to be applicable to study the influence of different interaction profiles to the macroscopic vehicular traffic flow quantities in stochastic equilibrium.