Modeling Microscopic Freeway Traffic Using Cusp Catastrophe Theory

This paper proposes a framework based on stochastic cusp catastrophe theory to model microscopic freeway traffic flow. The approach considers that each driver-regardless of being aggressive or timid-may shift his/her behavior and behave aggressively or timidly during driving. Based on the proposed modeling approach, the spacing of a driver is a function of his speed and acceleration. Moreover, the driver's behavior comprises of two equilibrium states-being aggressive or timid-and a shift between these states is considered to occur as a catastrophe phenomenon. Different models are developed with varying sampling intervals, while some of them possess memory properties. Results show that the cusp catastrophe model may accurately describe microscopic traffic, especially when compared to linear or logistic models. Results for models with memory are even more promising. Based on the proposed method, preliminary results on the critical regions of breakdown conditions or attitude shifting are described and discussed.