Stochastic two dimensional car following model by stochastic differential equation

Two dimensional microscopic traffic flow model is already proposed based on current car following (CF) or lane changing (LC) theory. Its stochastic counterpart, especially that considers the stochastic lateral movement is still lacking. To fill this gap, we proposed a stochastic two dimensional car following model. The lateral movement component is described by a stochastic differential equation, which is developed from Brownian motion, while the longitudinal movement component is developed by embedding stochastic term in the intelligent driver model. All the parameters in the two dimensional car following model have clear physical meanings and is calibrated using real-world data by employing the PSO optimization method. The model is then discretized based on Euler scheme. The state space is also discretized into spatial-temporal-speed grid. The discretization of the model and the state space lead to a Markov chain of the system. The validation results show that the model is able to describe the marginal distribution of the spatial-temporal evolution. The lane changing duration distribution can also be well produced.