Numerical modelling of macroscopic traffic flow based on driver physiological response using a modified wave propagation algorithm

In this paper, a novel numerical method, using the Godunov-type finite volume technique, the flux wave version of Modified Wave Propagation Algorithm (MWPA) with high-resolution is presented to solve one-dimensional second-order macroscopic model of traffic flow.

To demonstrate the effectiveness of the proposed approach, the commonly employed Payne–Whitham model and PW based on driver physiological response have been used. The hyperbolic nonlinear Partial Derivatives Equations (PDEs) of traffic flow which do not have analytical solution are solved considering a new Riemann wave speeds, based on an augmented Riemann solver. In this method, nonlinear equations are first transformed into a diagonal quasi-linear problem with linear characteristic curves, the corresponding source terms are involved in the flux difference of finite volume computational cells. The second-order wave solutions and their initial jump conditions are considered and the obtained numerical results are compared with Roe Decomposition Technique (RDT) as a common method in macroscopic traffic flow models discretization for the PW model before and after considering driver physiological response.

The problem of queue propagation in uniform traffic flow condition with two discontinuities including shock waves and subsequent rarefaction waves with periodic boundary conditions was selected as a numerical example. Velocity and density profiles at different times, the spatio-temporal changes of the two mentioned variables and traffic flow rates were presented.

The numerical results indicate that the proposed method provides a more realistic behavior for the two mentioned models regarding the basic variables of traffic flow.