The Application of Cusp Catastrophe Theory to Analyze Road Traffic Potential Characteristics, Considering Headway, with Urban Data

Local data are essential for the analysis of abrupt conditions in traffic flow. In this research, we address the shortcomings of real-time traffic flow detection data, which inadequately represent the density characteristics of vehicular traffic. To mitigate this issue, we establish mathematical relationships among traffic flow density, time headway, and vehicle speed, based on the fundamental characteristics of traffic flow dynamics. This framework allows for the estimation of density across various road segments. Recognizing the nonlinear dynamics that characterize traffic flow, we introduce a microscopic traffic flow cusp catastrophe potential function that incorporates headway, utilizing cusp catastrophe theory alongside microscopic traffic flow parameters to analyze real-time variations in traffic flow potential characteristics. In the experimental section, we developed fitting regression functions for traffic flow parameters using road detection data from the cities of Nanjing and Yueyang in China. We also compared outcomes derived from the theoretical model with the parameter estimation results obtained from the data, which facilitated the calculation of traffic flow characteristics, such as cusp density and volume over a one-month period. The results derived from the proposed potential function exhibit the functions’ greater capacity to capture the complex fluctuations in traffic flow compared to traditional traffic potential functions, thereby providing a valuable instrument with which to evaluate traffic flow characteristics in conjunction with real-time monitoring data.