To quantify the travel time and cost characteristics of mixed traffic involving electric vehicles (EVs) and fuel-powered vehicles on roads, in this paper, we comprehensively consider three factors affecting road impedance: queue length, waiting time, and service rate. Initially, a time characteristic function and a cost characteristic function for mixed traffic impedance are constructed. From the perspective of travel time, we consider the impact of EV penetration on the actual road capacity and introduce a capacity coefficient to modify the BPR (Bureau of Public Roads) road impedance function. Given that different types of vehicles might need to wait at charging stations, we employ queuing theory to calculate the queuing time at these stations and construct an impedance model that considers travel time. From the perspective of travel costs, we account for the energy consumption costs and road usage fees for different types of vehicles. The energy consumption cost for travel mileage is obtained by multiplying the unit mileage energy consumption cost of mixed traffic by the travel mileage. For road usage fees, we adopt the conventional method of multiplying the per-kilometer rate for each vehicle type by the travel mileage, thus constructing an impedance model that incorporates travel costs. Finally, in the numerical analysis section, based on the vehicle travel mileage, we categorize travel into short-, medium-, and long-distance trips for analysis. With the constructed mixed traffic impedance model, we conduct a detailed analysis of the travel time and cost characteristics of mixed traffic over different travel distances. We explore the specific impacts of the electric vehicle penetration rate, traffic flow volume, and travel mileage on road impedance. The results indicate that as the penetration rate of electric vehicles increases, the total energy consumption of the transportation system significantly decreases. Moreover, at high electric vehicle penetration rates, although an increase in traffic flow leads to higher traffic impedance and longer travel times, the overall travel costs are reduced. This demonstrates that increasing the penetration rate of electric vehicles positively contributes to reducing the energy consumption and costs of transportation systems.

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.