On nonlocal hydrodynamic model explaining synchronized traffic flow

Abstract Similar to the treatment of self-propelled particles, a generalized car following model with multiple look-ahead was utilized for the study of vehicular traffic. With the assumption of no skewness in velocity distribution and through iterative procedure, it is possible to construct a second order nonlocal hydrodynamic model. In contrast with two-phase fluid-dynamic models with a fundamental diagram, the model has the advantage of microscopically determined relaxation time parameters. Although the rigor is reduced a little compared with the Navier–Stokes like traffic flow model previously studied, the phase transition from free flow to synchronized flow, then from synchronized flow to wide moving jam is reproduced. The catch effect of synchronized flow is also revealed. The simulations suggest that the nonlocality in relaxation time and steady velocity, even though without nonlocality in viscocity, i.e., velocity variance, gives another explanation of synchronized flow.