Policy Stability for Measuring Operational Performance in Task Assignment with Time-Windows Under Internal Adversarial Influence

Abstract

We study autonomous pickup-and-delivery routing problems in which internal adversarial agents spoof their locations to attract request assignments and then intentionally leave those requests unserviced. Such attacks disrupt the centralized scheduler, causing delays, cancellations, and routing instability. A routing policy is stable if its cost remains uniformly bounded over time. Existing policy-cost formulations typically characterize cost through the work required to service outstanding requests. Such a formulation requires analyzing agent-specific route execution and is therefore not well suited to adversarial settings, where non-cooperative agents may arbitrarily deviate from assigned routes or fail to service requests altogether. We introduce a new policy-cost formulation based only on observable system signals, namely the numbers of outstanding and canceled requests. Under bounded arrivals and finite request time windows, we show that stability under this formulation is equivalent to keeping the expected cumulative number of canceled requests uniformly bounded over time, an important operational metric in both cooperative and adversarial settings. We also extend cooperative fleet-sizing guarantees to finite time-window settings and highlight that request time windows are not merely a modeling detail, but are essential for ruling out \emph{degenerate stability}, a regime in which policies are certified as stable despite undesirable large request backlogs.