A Multidimensional Traffic Split and Assignment Model for Travel Reservation Strategy Under Recurrent Urban Congestion

Travel Reservation Strategy (TRS) provides a capacity-constrained approach for managing recurrent congestion by regulating access to selected urban road links. This study develops a Multidimensional Traffic Split and Assignment (MDTSA) model to evaluate TRS within a heterogeneous multimodal transportation system. The model integrates traveler heterogeneity in value of time, five travel alternatives, non-separable car–bus road impedance, reservation-access constraints, and joint mode–route choice under stochastic user equilibrium. A variational inequality formulation is solved using the Method of Successive Weighted Averages. Numerical experiments on the Sioux Falls network show that TRS increases average network speed by 8.1%, reduces average road saturation by 12.5%, decreases total generalized travel cost by 2.3%, and lowers vehicle-hours traveled by 6.5%. The strategy also shifts travel demand away from private cars, whose modal share decreases by 2.48 percentage points, while bus and metro shares increase by 1.91 percentage points in total. Model-comparison results indicate that neglecting traveler heterogeneity or combined travel modes weakens the estimated effects of TRS, while sensitivity analysis shows that the main performance improvements remain stable across the tested reservation-capacity ratios and demand levels. These findings demonstrate the value of multidimensional equilibrium modeling for evaluating reservation-based urban traffic management.