Probabilistic Temporal Networks with Ordinary Distributions: Theory, Robustness and Expected Utility

Abstract

Most existing works in Probabilistic Simple Temporal Networks (PSTNs) base their frameworks on well-defined, parametric probability distributions. Under the operational contexts of both strong and dynamic control, this paper addresses robustness measure of PSTNs, i.e. the execution success probability, where the probability distributions of the contingent durations are ordinary, not necessarily parametric, nor symmetric (e.g. histograms, PERT), as long as these can be discretized. In practice, one would obtain ordinary distributions by considering empirical observations (compiled as histograms), or even hand-drawn by field experts. In this new realm of PSTNs, we study and formally define concepts such as degree of weak/strong/dynamic controllability, robustness under a predefined dispatching protocol, and introduce the concept of PSTN expected execution utility. We also discuss the limitation of existing controllability levels, and propose new levels within dynamic controllability, to better characterize dynamic controllable PSTNs based on based practical complexity considerations. We propose a novel fixed-parameter pseudo-polynomial time computation method to obtain both the success probability and expected utility measures. We apply our computation method to various PSTN datasets, including realistic planetary exploration scenarios in the context of the Mars 2020 rover. Moreover, we propose additional original applications of the method.