Average Unfairness in Routing Games

2026-01-22

AI Summary

This study addresses the long-standing challenge of precisely quantifying the trade-off between fairness and efficiency in routing games. The authors propose a novel metric, termed “average unfairness,” defined as the ratio of the average user latency to the minimum possible latency, and establish its theoretical relationships with three existing notions of unfairness for the first time. Building on this foundation, they investigate the system-optimal routing problem under a constraint on average unfairness. Theoretical analysis reveals that this metric is always no greater than load-based unfairness and can significantly reduce total system latency in parallel-link networks. By integrating game theory, network flow optimization, and latency function analysis, this work provides an improved theoretical framework and practical guidance for balancing fairness and efficiency in network routing.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Mechanism Design

Application Category

• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We propose average unfairness as a new measure of fairness in routing games, defined as the ratio between the average latency and the minimum latency experienced by users. This measure is a natural complement to two existing unfairness notions: loaded unfairness, which compares maximum and minimum latencies of routes with positive flow, and user equilibrium (UE) unfairness, which compares maximum latency with the latency of a Nash equilibrium. We show that the worst-case values of all three unfairness measures coincide and are characterized by a steepness parameter intrinsic to the latency function class. We show that average unfairness is always no greater than loaded unfairness, and the two measures are equal only when the flow is fully fair. Besides that, we offer a complete comparison of the three unfairness measures, which, to the best of our knowledge, is the first theoretical analysis in this direction. Finally, we study the constrained system optimum (CSO) problem, where one seeks to minimize total latency subject to an upper bound on unfairness. We prove that, for the same tolerance level, the optimal flow under an average unfairness constraint achieves lower total latency than any flow satisfying a loaded unfairness constraint. We show that such improvement is always strict in parallel-link networks and establish sufficient conditions for general networks. We further illustrate the latter with numerical examples. Our results provide theoretical guarantees and valuable insights for evaluating fairness-efficiency tradeoffs in network routing.

Problem

• routing games
• fairness
• latency
• unfairness measures
• constrained system optimum

Innovation

• average unfairness
• routing games
• fairness-efficiency tradeoff
• constrained system optimum
• latency functions