A discrete traffic kinetic model – integrating the lagged cell transmission and continuous traffic kinetic models

Continuous traffic kinetic models are difficult to solve because of the occurrence of integro-differential equations in the models. In this paper, we formulate a discrete traffic kinetic model by extending the cell transmission mechanism, which can capture not only the number of vehicles, but also the velocity probability distribution. The variation in the velocity probability distribution is modeled on the basis of vehicle conservation and cell transmission to avoid integro-differential terms. An example with a discontinuous initial density is analyzed to demonstrate the validity of the proposed discrete traffic kinetic model. From the evolution curve of the velocity probability distribution, we can see that the proposed model can be used to describe the diffusion process of vehicles from a high density to a low density section.