6. Lateral Dimension Modeling and Application

The movements of vehicles predominantly occur in a two-dimensional space. Conventional microscopic traffic flow approaches typically employ car-following models to depict longitudinal movement and lane changing models to describe lateral movement. However, even during car-following processes where longitudinal movement is dominant, there are still significant lateral movements that occur. This chapter focuses on capturing the lateral dimensional movement in both car-following and lane changing processes. To effectively capture the stochastic nature of lateral movement, we utilize stochastic differential equations. The lateral dynamics are decomposed into two components: the actual lateral movement and noise disturbance. The lateral movement is characterized by a parameterized function derived from trajectory observations during lane changes, while the lateral noise is modeled using classical Brownian motion. We derive the Fokker–Planck equation to capture the marginal distribution. By applying the proposed model to various scenarios, we demonstrate its ability to describe the lateral dynamics of vehicular movement. Our findings highlight the importance of considering lateral movement in addition to longitudinal movement in microscopic traffic flow modeling.