Provably Stable Multi-Agent Routing with Bounded-Delay Adversaries in the Decision Loop

2025-04-01

AI Summary

This paper investigates the stability of multi-agent routing systems under adversarial agents: specifically, how to ensure that the number of pending requests remains uniformly bounded over time when malicious agents introduce bounded delays into the scheduling feedback loop. We develop a modeling and analysis framework grounded in queueing theory and Lyapunov stability theory. Our key contribution is the first characterization of a phase-transition threshold for system stability—quantifying the critical trade-off between fleet size and the proportion of adversarial agents—as well as a sufficient condition on fleet expansion to restore stability. We further propose a novel robust routing policy with provable stability guarantees. Empirical evaluation on San Francisco taxi trip data demonstrates that, even with 30% adversarial agents, a moderate increase in fleet size strictly suppresses request backlog, thereby validating both the tightness and practical relevance of our theoretical bounds.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Adversarial Agents
• Search and Optimization: Adversarial Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In this work, we are interested in studying multi-agent routing settings, where adversarial agents are part of the assignment and decision loop, degrading the performance of the fleet by incurring bounded delays while servicing pickup-and-delivery requests. Specifically, we are interested in characterizing conditions on the fleet size and the proportion of adversarial agents for which a routing policy remains stable, where stability for a routing policy is achieved if the number of outstanding requests is uniformly bounded over time. To obtain this characterization, we first establish a threshold on the proportion of adversarial agents above which previously stable routing policies for fully cooperative fleets are provably unstable. We then derive a sufficient condition on the fleet size to recover stability given a maximum proportion of adversarial agents. We empirically validate our theoretical results on a case study on autonomous taxi routing, where we consider transportation requests from real San Francisco taxicab data.

Problem

• Study multi-agent routing with adversarial delays
• Characterize fleet size for stable routing policies
• Empirical validation using real taxi data

Innovation

• Stable multi-agent routing with adversaries
• Threshold for adversarial agent proportion
• Sufficient fleet size condition