A new traffic kinetic model for heterogeneous condition

•The paper derives a general formula of homogeneous discrete kinetic model with an adaptive grid.•The paper introduces local density and the law of gravity to model vehicle interaction.•The paper develops a heterogeneous model which integrates CTM with homogeneous D–T model.•The proposed model overcomes solution of partial differential equations.

The paper aims to integrate Cell Transmission Model (CTM) and the Delitala–Tosin model of a homogeneous condition based on the so-called Kinetic Theory of Active Particles (KTAP) to model the heterogeneous condition. The integrations overcome solution of partial differential equations, and transforms to solution of ordinary differential equations. The deficiency of solving partial differential equations is that an improper difference scheme can cause instability and non-convergence. In order to consider the difference in local densities, space variable is also discrete in the paper. In order to take the effect of distance on interaction into account, the paper introduces law of gravity to model interaction. Finally, we give some numerical result of four heterogeneous traffic cases and compare them with those treated in the paper by Delitala–Tosin where the fixed grid is used and by Coscia–Delitala–Frasca where the adaptive grid is used.