Model and algorithm for the quantity adjustment user equilibrium traffic assignment problem with link capacity constraints

This research investigates the model and solution techniques of the quantity adjustment user equilibrium link capacitated traffic assignment problem (QUE-CTAP) to provide more realistic traffic assignment results. Given that the existing quantity adjustment user equilibrium traffic assignment problem (QUE-TAP) model is limited to small experimental networks with low saturation levels, this paper defines path quantity signal intensity, eliminates the assumption of non-negative residual capacity on the path, reformulates the QUE-TAP model, and develops a QUE-TAP solution algorithm appropriate for real congested networks. The QUE-CTAP model extends the QUE-TAP by introducing explicit capacity side constraints. While it deviates from strict adherence to the QUE principle, QUE-CTAP follows a modified version by employing explicitly defined generalized quantity signal intensity instead of quantity signal intensity. Solving QUE-CTAP presents significant challenges compared to QUE-TAP. This paper introduces a QUE-CTAP solving algorithm designed for real-world networks. In the main loop, the algorithm updates the Lagrange multipliers for capacity side constraints and performs column generation simultaneously. Within the inner loop, the Lagrange multipliers serve as fixed costs for links, facilitating the sequential resolution of origin-destination (OD) pairs. Numerical results demonstrate that the models and algorithms developed in this paper effectively manage networks of practical scale. Compared to QUE-TAP, QUE-CTAP enhances capacity resource utilization by redirecting excess traffic to non-saturated paths, thereby reshaping traffic distribution patterns.