A Day-To-Day Dynamical Model for the Path-Shift Behavior of Drivers under Disequilibrium of Traffic Networks with Fixed Demand

摘要

Transportation networks are often subjected to perturbed conditions leading to trafficdisequilibrium. Under such conditions, the traffic evolution is typically modeled as a dynamicalsystem that captures the aggregated effect of paths-shifts by drivers over time. This paperproposes a day-to-day (DTD) dynamical model that bridges two important gaps in the literature.First, existing DTD models generally consider current path flows and path costs and neglect thesensitivity of path costs with respect to flow. The proposed DTD model simultaneously capturesthe three factors mentioned above in modeling the flow shift by drivers. As a driver canpotentially perceive the sensitivity of path costs with the congestion level based on pastexperience, incorporating this factor enhances consistency with the real-world. In addition, itsmoothens the time trajectory of path flows, a desirable property for practice where the iterativesolution procedure is typically terminated at an arbitrary point due to computational timeconstraints. Second, this study provides a criterion to classify the set of paths for an O-D pairinto two subsets under traffic disequilibrium: the set of expensive paths and the set of attractivepaths. This facilitates the flow shifts from the set of expensive paths to the set of attractive paths,enabling a higher degree of freedom in modeling flow shift compared to that of focusing on justthe shortest path. In addition, it also helps to preclude flow shifts among the expensive paths,which is more consistent with the real-world. The results of computational experiments validatethese modeling properties and illustrate the benefits of using the proposed model in comparisonto existing DTD dynamic models.