Grey prediction model based on Euler equations and its application in highway short-term traffic flow

As the urbanization rate in China has continued to increase, the highway congestion problem has become more severe, significantly reducing the efficiency of traffic operations. To accurately predict highway short-term traffic flow and effectively solve congestion issues, in this paper, the basic equations of fluid mechanics are described, variable coefficient differential Euler equations are introduced into a grey model and a high-order variable coefficient grey prediction model is constructed based on the principle of grey differential information. The model is solved using mathematical methods such as recursive sequences and mathematical transformations, and the time response function of the model is obtained. The order of derivatives can be used to effectively simulate fluctuations in traffic flow data; therefore, to improve the accuracy of the new model, the particle swarm optimization algorithm is used to optimize the order of the new model, leading to refined modelling steps. Finally, the new model is applied to a case study of traffic flow on highways in Canada, and its efficacy is assessed from three distinct viewpoints. The findings demonstrate that the new model can stably predict traffic flow under different prediction methods, and the performance of the new model under different traffic flow conditions is verified using four different periods of traffic flow data. The findings indicate that the simulation and prediction results of the new model are superior to those of six other grey models. The new model can be used to effectively determine the fluctuation patterns of highway traffic flow data and yields good stability and prediction accuracy.