5. A Stochastic Two-Dimensional IDM with Vehicular Dynamics

The movement of vehicles exhibits inherent stochasticity and occurs in a two-dimensional space. Traditional approaches to modeling vehicular movement primarily rely on microscopic traffic flow models that adopt a stimulus-reaction framework. However, with the advent of autonomous vehicles, these conventional models have become increasingly inadequate. Firstly, most of these models are deterministic and fail to capture the time-varying stochastic nature of vehicle behavior. Secondly, these models do not incorporate detailed vehicle kinetic information, resulting in limited output. In this chapter, we address these limitations by proposing a novel microscopic traffic flow model based on stochastic differential equations. Our model considers both steering and acceleration/deceleration as control inputs and incorporates a noise source characterized by the Ornstein–Uhlenbeck process. The formulation of control inputs is inspired by the intelligent driver model. The experimental results demonstrate that our model effectively captures the stochastic nature of two-dimensional vehicle movements, providing richer and more informative outputs.