EXTENSION OF A VARIATIONAL METHOD TO TRAFFIC NETWORK

This paper discusses and implements a variational method of solving a kinetic traffic flow model, which turns out to be equivalent to the well-known LWR model under a flow-density relationship or the fundamental diagram. Assuming that the fundamental diagram is piece-wise linear and that there exists a positive constant which is the integral multiples of all the involved slopes of the fundamental diagram, the solution can be shown to be "exact" in a cell network that takes the aforementioned constant as the cell speed. The variational method is then extended to solve traffic network problems through the design of a simple computational scheme, based on the Riemann solver at a junction. The extended variational method is also shown to be more efficient than the standard Godunov scheme when fewer multipliers are included in the fundamental diagram.