Fractional time-varying grey traffic flow model based on viscoelastic fluid and its application

Abstract

Existing traffic flow models are insufficient to excavated the characteristics of fluids and are usually a constant coefficient differential model. They cannot reflect the characteristics of a traffic flow system changing with time, resulting in their poor adaptability. Firstly, the viscoelastic traffic flow model is simplified. The fractional viscoelastic traffic flow model is established in combination with modelling principle of the Bass model and successful application of fractional calculus in viscoelastic fluid. Conformable fractional derivative and the fractional grey model are then introduced to establish a fractional grey viscoelastic traffic flow model that can reflect time-varying characteristics. Finally, the new model is compared with traditional statistical models in terms of model efficiency and stability and is applied to the modelling of traffic flow and traffic congestion level in multiple scenarios. The modelling results are compared with six other models. Results show that the new model has better stability and modelling effect.