The inhomogeneous kinematic wave traffic flow model as a resonant nonlinear system

The kinematic wave traffic flow model for an inhomogeneous road is studied as a resonant nonlinear system, where an additional conservation law is introduced to model time-variant road inhomogeneities such as changes in grades or number of lanes. This resonant system has two families of waves, one of which is a standing wave originated at the inhomogeneity. The nature of these waves is examined and their time–space structures are studied under Riemann initial conditions and proper entropy conditions. Moreover, the system is solved numerically with Godunov's method, and the solutions are found to be consistent with those of Daganzo and Lebacque for the same initial conditions. Finally, the numerical approximation is applied to model traffic flow on a ring road with a bottleneck and the results conform to expectations.