A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway

As a new attempt to solve hyperbolic conservation laws with spatially varying fluxes, the weighted essentially non-oscillatory (WENO) method is applied to solve a multi-class traffic flow model for an inhomogeneous highway. The numerical scheme as well as an analytical study is based upon a modified equivalent system that is written in a “standard” hyperbolic conservation form. Numerical examples, which include the difficult traffic signal control problem, are used to demonstrate the effectiveness of the WENO scheme in which the results are in good agreement with the analytical counterparts.