Modeling the residual queue and queue-dependent capacity in a static traffic assignment problem

TL;DR

This paper introduces a novel static traffic assignment model that explicitly incorporates residual queues and queue-dependent capacities, improving accuracy in congested, oversaturated scenarios.

Contribution

The study develops a new static traffic assignment model with queue-dependent capacity and residual queues, ensuring equilibrium flows stay within physical limits and aligning better with observed data.

Findings

Model ensures equilibrium flows are within physical capacity.

Proposed algorithm effectively solves the model.

Numerical examples demonstrate improved accuracy in oversaturated conditions.

Abstract

The residual queue during a given study period (e.g., peak hour) is an important feature that should be considered when solving a traffic assignment problem under equilibrium for strategic traffic planning. Although studies have focused extensively on static or quasi-dynamic traffic assignment models considering the residual queue, they have failed to capture the situation wherein the equilibrium link flow passing through the link is less than the link physical capacity under congested conditions. To address this critical issue, we introduce a novel static traffic assignment model that explicitly incorporates the residual queue and queue-dependent link capacity. The proposed model ensures that equilibrium link flows remain within the physical capacity bounds, yielding estimations more aligned with data observed by traffic detectors, especially in oversaturated scenarios. A generalized link cost function considering queue-dependent capacity, with an additional queuing delay term is proposed. The queuing delay term represents the added travel cost under congestion, offering a framework wherein conventional static models, both with and without physical capacity constraints, become special cases of our model. Our study rigorously analyzes the mathematical properties of the new model, establishing the theoretical uniqueness of solutions for link flow and residual queue under certain conditions. We also introduce a gradient projection-based alternating minimization algorithm tailored for the proposed model. Numerical examples are conducted to demonstrate the superiority and merit of the proposed model and solution algorithm.