Quantifying controllability in temporal networks with uncertainty

Abstract

Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We provide new insights inspired by a geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability — continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods for predicting the degrees of strong and dynamic controllability for uncontrollable networks. We further generalize these metrics by defining likelihood of controllability, a controllability measure that applies to Probabilistic Simple Temporal Networks (PSTNs). Finally, we empirically demonstrate that these metrics are good predictors of actual dispatch success rate for STNUs and PSTNs.