Quasi-variational inequality formulations and solution approaches for dynamic user equilibria

摘要: Dynamic User Equilibrium (DUE) is one of the most challenging problems Traffic Assignment (DTA), aiming to predict optimal dynamic traffic flow pattern in a given transportation network by assuming that each motorist trying minimize his/her individual travel cost. Existing methodologies for DUE study can not capture rigorously nature problem and produce results with reasonable accuracy. This research motivated such need particular, we apply Quasi-Variational Inequality (QVI) technique formulate derive solution algorithms based on certain merit functions. This uses two major approaches modeling solving DUE. Firstly, path-based model presented. Three reformulations this are developed. One reformulation VI from which establish existence condition problem. The other QVI formulations be used algorithm mode. It turns out temporarily fixing path pattern, formulation reduced well-defined Nonlinear Complementarity Problem (NCP). NCP sub-problem further studied, including its properties. To solve sub-problem, use GAMS (General Algebraic Modeling Systems) language PATH solver high accuracy (e.g., 1.0e-6). The inherent path-numeration requirement prohibits possibility applying practical networks. Therefore, propose link-node destinations. Two formulations, defined disaggregated aggregated link inflows respectively, Furthermore, uniqueness conditions discussed. We then design an iterative scheme models, formulated solved iteration. facilitate convergence process, devise approximate function monitor help construct step sizes algorithm. Numerical show generate or