Numerical Study on Traffic Flow with Single Parameter State Equation

Abstract

Traffic flow has been studied numerically by solving the kinematic wave equation with the second-order Monotone Upwind Scheme of Conservation Law (MUSCL), together with the boundary and initial conditions, which are examined by a computer based random generator derived from the Erlang process of order 250. With regard to traffic mixing, a fundamental flow-density diagram of road traffic is presented, where the ratio between the optimal and jam densities is used as a single parameter; its value is predicted by assuming that fast moving vehicles have a relatively large free speed but slow moving vehicles have a smaller free speed. Simple analysis for the state equation indicates that the parameter should be in a proper range from 0.333 to 0.618 to ensure a free speed beyond the optimal traffic speed. The effects of the single parameter on the spread of traffic shock wave have been discussed. It is found that, for congested traffic flow, in the case of a given flow density at the place of inlet and exit, the effects of the parameter on the propagation speed is apparent, while in the case of assigned flow rate on the inlet and the exit boundaries, the propagation speed is slightly dependent on the parameter. The propagation of density and flow rate fluctuation can be observed clearly from the corresponding 3D presentations.