Generalized Singular Value Decomposition Approach for Consistent On-Line Dynamic Traffic Assignment

Abstract

A framework for ensuring operational consistency of on-line dynamic traffic assignment in networks with advanced traffic management and information systems is proposed and investigated. Formulated within a stage-based rolling horizon framework, the model first solves a deterministic dynamic traffic assignment problem to predict the traffic network state for the near future while optimizing certain controller and user objectives and later seeks consistency between the predicted system state and the actual conditions unfolding on line. This approach ensures that future state predictions and path assignments are consistent with the current actual system state rather than the previously predicted (presumed) system state. The consistency problem is formulated as a constrained least-squares model. It is underdetermined, rank deficient, and potentially ill conditioned for general networks. In addition, it lacks well-behaved properties and has a fixed-point element, characteristics inherited from the dynamic traffic assignment problem. It is solved using orthogonal transformations based on generalized singular value decomposition (GSVD). Simulation experiments are conducted to analyze the effectiveness of the GSVD-based solution algorithm vis-à-vis ensuring consistency. The experiments emphasize the reliability and stability of GSVD in addressing the on-line consistency problem.