Wardropian Cycles make traffic assignment both optimal and fair by eliminating price-of-anarchy with Cyclical User Equilibrium for compliant connected autonomous vehicles

2025-07-25

AI Summary

Centralized path planning for connected and autonomous vehicles (CAVs) often yields system-optimal solutions that sacrifice fairness and user acceptance. Method: This paper proposes a Wardropian cycling mechanism—periodically executing user-equilibrium assignments—to jointly satisfy Wardrop’s first and second principles, thereby unifying system efficiency and individual fairness over the long term. We innovatively formulate a cyclic assignment matrix based on permutation sequences and design a hybrid algorithm (combining exact optimization with greedy heuristics) to solve the NP-hard cyclic structure, jointly optimizing cycle length and user disutility. Results: Large-scale simulations across cities including Barcelona demonstrate over 93% reduction in inequity within 10 days, zero price-of-anarchy, and a median convergence time of only 11 days—significantly enhancing both traffic efficiency and societal acceptability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Multiagent Systems: Mechanism Design

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness and ethical considerations in crowd work and in human-in-the-loop AI systems

Abstract

Connected and Autonomous Vehicles (CAVs) open the possibility for centralised routing with full compliance, making System Optimal traffic assignment attainable. However, as System Optimum makes some drivers better off than others, voluntary acceptance seems dubious. To overcome this issue, we propose a new concept of Wardropian cycles, which, in contrast to previous utopian visions, makes the assignment fair on top of being optimal, which amounts to satisfaction of both Wardrop's principles. Such cycles, represented as sequences of permutations to the daily assignment matrices, always exist and equalise, after a limited number of days, average travel times among travellers (like in User Equilibrium) while preserving everyday optimality of path flows (like in System Optimum). We propose exact methods to compute such cycles and reduce their length and within-cycle inconvenience to the users. As identification of optimal cycles turns out to be NP-hard in many aspects, we introduce a greedy heuristic efficiently approximating the optimal solution. Finally, we introduce and discuss a new paradigm of Cyclical User Equilibrium, which ensures stability of optimal Wardropian Cycles under unilateral deviations. We complement our theoretical study with large-scale simulations. In Barcelona, 670 vehicle-hours of Price-of-Anarchy are eliminated using cycles with a median length of 11 days-though 5% of cycles exceed 90 days. However, in Berlin, just five days of applying the greedy assignment rule significantly reduces initial inequity. In Barcelona, Anaheim, and Sioux Falls, less than 7% of the initial inequity remains after 10 days, demonstrating the effectiveness of this approach in improving traffic performance with more ubiquitous social acceptability.

Problem

• Achieving optimal and fair traffic assignment for CAVs
• Eliminating price-of-anarchy with cyclical user equilibrium
• Reducing inequity in travel times among travelers

Innovation

• Wardropian cycles ensure optimal and fair traffic assignment
• Greedy heuristic approximates NP-hard optimal cycle computation
• Cyclical User Equilibrium stabilizes optimal Wardropian Cycles