A simplified theory of multiple vehicle-type macroscopic kinematic waves based on the cumulative flow

A multi-class dynamic traffic network flow model with heterogeneous vehicles is presented. Single type kinematics wave method is extended to multiple type kinematics wave method. There assume only two flow conditions on link, one is queue condition, various vehicles can not overtake, and the speeds of various type vehicles are same. The other is free flow condition; each type of vehicles can run according to the each type of free-flow velocity. This problem is partly solved in using and extending the cumulative flow model by presented by Newell (1993). The simulation results show the model can demonstrate the multiple vehicle type dynamic traffic flow on a link.