A novel car-following inertia gray model and its application in forecasting short-term traffic flow - Xiao, Xinping; Duan, Huiming; Wen, Jianghui (Applied Mathematical Modelling, 2020)
•A novel inertia gray model is proposed based on classic car-following models.•The models reveal the problem of the transformation of the micro model and macro model.•The models use the problem of the mechanical characteristics and inertia process traffic flow data.•The models can predict the flow of a specific period of time evaluating to the state of traffic flow. Real-time and accurate short-term traffic flow prediction results can provide real-time and effective information for traffic information systems. Based on classic car-following models, this paper establishes differential equations according to the traffic state and proposes a car-following inertial gray model based on the information difference of the differential and gray system, in combination with the mechanical characteristics of traffic flow data and the characteristics of an inertial model. Furthermore, analytical methods are used to study the parameter estimation and model solution of the new model, and the important properties, such as the original data, inertia coefficient and simulation accuracy, are studied. The effectiveness of the model is verified in two cases. The performance of the model is better than that of six other prediction models, and the structural design of the new model is more reasonable than that of the existing gray models. Moreover, the new model is applied to short-term traffic flow prediction for three urban roads. The results show that the simulation and prediction effects of the model are better than those of other gray models. In terms of the traffic flow state, an optimal match between short-term traffic flow prediction and the new model is achieved.