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

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.