Fixed-point fast sweeping weighted essentially non-oscillatory method for multi-commodity continuum traffic equilibrium assignment problem

This work presents a fixed-point fast sweeping weighted essentially non-oscillatory method for the multi-commodity continuum traffic equilibrium assignment problem with elastic travel demand. The commuters' origins (i.e. home locations) are continuously dispersed over the whole city with several highly compact central business districts. The traffic flows from origins to the same central business district are considered as one commodity. The continuum traffic equilibrium assignment model is formulated as a static conservation law equation coupled with an Eikonal equation for each commodity. To solve the model, a pseudo-time-marching approach and a third order finite volume weighted essentially non-oscillatory scheme with Lax-Friedrichs flux splitting are adopted to solve the conservation law equation, coupled with a third order fast sweeping numerical method for the Eikonal equation on rectangular grids. A fixed-point fast sweeping method that utilizes Gauss-Seidel iterations and alternating sweeping strategy is designed to improve the convergence for steady state computations of the problem. A numerical example is given to show the feasibility of the model and the effectiveness of the solution algorithm.