The dynamic system of the traffic assignment problem: Part II. Computation

In the preceding paper, we demonstrated the existence of the dynamic system of the traffic assignment problem (TAP), called J-system, whose steady states are J-equilibria (JE) and only stable steady states are user-equilibria (UE). Based on this new definition of UE, in this paper, we develop algorithms for computing both JE and UE of general transportation networks. To find JE, we can use Newton’s method or the finite difference method; to find UE, we propose a perturbation-based method and a hybrid method incorporating Frank-Wolfe’s method. With an example, we show that both Newton’s and finite difference methods converge exponentially measured by J-index of convergence, and the perturbation-based method yields UE solutions. We also present methods for solving TAP with variable demand. The finite difference method and the perturbation-based method are intrinsic to J-system and readily applicable for solving TAP of any general networks. The implementation and efficiency of these methods for solving TAP of large-scale transportation networks will be investigated in the future.