Macroscopic Modeling Framework Unifying Kinematic Wave Modeling and Three-Phase Traffic Theory

probabilities (4–7 ), commonly using (stochastic) queuing analysis and nucleation models. These modeling approaches are thoroughly discussed elsewhere (7 ). Here, use is proposed of a coupled set of partial differential equations describing both the traffic dynamics [using the first-order model of Lighthill and Witham (2) and Richards (3)] and the dynamics of the phase-transition probabilities. The proposed modeling framework can be considered as a relatively straightforward generalization of the kinematic wave theory to three-phase theory. The focus is on dynamic modeling of the phase-transition probabilities and the implications this has for the properties of the first-order model. Other issues discussed by Kerner (such as the two-dimensional area depicting stable states in synchronized flow) are not considered in this paper.