Development and comparative evaluation of high-order traffic flow models

Five high-order continuum traffic flow models are compared: Payne's original model, Papageorgiou's improved model, the semiviscous model and the viscous model, a proposed high-order model, and the simple continuum model based on the pipeline cases. The stability of the high-order models is analyzed and the shock structure investigated in all models. In addition, the importance of the proper choice of finite-difference method is addressed. For this reason, three explicit finite-difference methods for numerical implementation - the Lax method, the explicit Euler method, and the upwind scheme with flux vector splitting - are discussed. The test with hypothetical data and the comparison of numerical results with field data suggest that high-order models implemented through the upwind method are more accurate than the simple continuum model. For congested cases, the proposed high-order model appears to be more accurate than the other high-order models for all cases tested.