Physical network algorithm for a link-based dynamic traffic assignment model

To develop an operational Dynamic Traffic Assignment (DTA) model for real-time applications, the computational speed poses a major challenge. To solve this problem, this paper proposes a new algorithm for solving a single class link-based analytical DTA model. In this model, users follow the dynamic user optimal principle in determining their routing strategies. To solve this DTA model, the continuous variational inequality (VI) is first transformed into a discrete variational inequality. Then, a relaxation method is used to solve this discrete VI. During each relaxation, a nonlinear programming (NLP) problem is formulated and solved. Unlike the previous algorithm, which uses inflow, exit flow and number of vehicles as the basic variables, this algorithm uses the inflow variable as the unique independent variable to formulate the NLP. In solving this NLP by using F-W algorithm, a linear programming (LP) subproblem is formulated in each F-W iteration. One of the major contributions of this new algorithm is to solve this LP subproblem on a physical network instead of on an expanded time-space network. Thus, the new algorithm avoids the time-space network expansion and the shortest path searching on the expanded network, which is the previous method for solving the analytical DTA model. Consequently, the computation time can be shortened substantially. This new algorithm is validated by testing on a network. Computational experience on the Souix Fall network is also presented to demonstrate the efficiency of this algorithm.