Modeling of Nonlinear Stochastic Dynamic Traffic Flow

Most dynamic flow models are developed under deterministic assumptions or simple linear models. Although these models can describe dynamic phenomena, they cannot adapt a variance of the real world. However, in the developing trend of intelligent transportation systems, operators have to understand and accurately predict traffic flow to predict, evaluate, and manage the performance of present and future systems. Thus, a model capable of describing variant traffic phenomena, which encompasses both nonlinearity and stochasticity, is necessary. This study formulates nonlinear stochastic dynamic traffic flow models based on conventional macroscopic models; the nonlinear terms are decomposed by polynomials to reduce the complexity of the models. Then, the Itô equation is introduced to convert the deterministic model to a stochastic one. Also considered here is the traffic flow model with a diffusion effect.