A semi-discrete model of traffic flow in correspondence with a continuum model under Lagrange coordinate system

Abstract

We propose a semi-discrete model by dividing traffic flow into moving particles, and establish its corresponding relation with a conserved high-order (CHO) continuum model under the Lagrange coordinate system. This suggests that they should share the same or similar properties and we prove the boundedness of solutions and analytically derive a traveling wave or wide moving jam in the CHO model. Indeed, the numerical simulation based on the semi-discrete model verifies these properties and especially indicates that the simulated wide moving jams converge to the analytical solution for sufficiently refined division of traffic flow.