A unified framework for traffic assignment: deriving static and quasi dynamic models consistent with general first order dynamic traffic assignment models

This paper presents a theoretical framework to derive static, quasi-dynamic, and semi-dynamic traffic assignment models from a general first order dynamic traffic assignment model. By explicit derivation from a dynamic model, the resulting models maintain maximum consistency with dynamic models. Further, the derivations can be done with any fundamental diagram, any turn flow restrictions, and deterministic or stochastic route choice. We demonstrate the framework by deriving static (quasidynamic) models that explicitly take queuing and spillback into account. These models are generalisations of models previously proposed in the literature. We further discuss all assumptions usually implicitly made in the traditional static traffic assignment model.