Delay Controllability: Multi-Agent Coordination under Communication Delay

Simple Temporal Networks with Uncertainty provide a useful framework for modeling temporal constraints and, importantly, for modeling actions with uncertain durations. To determine whether we can construct a schedule for a given network, we typically consider one of two types of controllability: dynamic or strong. These controllability checks have strict conditions on how uncertainty is resolved; uncertain outcomes are either recognized immediately or not at all. In this paper, we introduce delay controllability, a novel generalization of both strong and dynamic controllability that additionally exposes a large range of controllability classes in between. To do so, we use a delay function γ to parameterize our controllability checking. This delay function represents the difference between when an event happens and the time that it is observed. We also provide a single unified algorithm for checking delay controllability that runs in O(n) time, matching the best known runtime for dynamic controllability, which we use to motivate the decision to generalize dynamic and strong controllability. We conclude by providing an empirical evaluation of delay controllability, demonstrating its superior accuracy and practical efficiency as compared to other existing approximations.