[ToC]

 

J. P. Lebacque, J. B. Lesort, and F. Giorgi, "Introducing Buses into First-Order Macroscopic Traffic Flow Models," Transportation Research Record, 1998

INFLUENCE OF THE BUS ON THE SURROUNDING TRAFFIC

This result generalizes to the moving frame the classic method of construction of the entropy solutions of the LWR model. Applying Expression 19, which is valid even in the case of discontinuities, it is straightforward to construct an analytical solution of the LWR model in the moving frame and particularly the solutions to the Riemann problem (which are scale invariant). The rules for calculation of solutions across a discontinuity in the moving frame are basically the same as those that would apply in a fixed frame [as described by Lebacque (13) using Expressions 17, 18, and 19. Figure 4 indicates such solutions in the moving frame.... Neglecting bus size leads to welcome simplifications