A Generic Framework for Monitoring Timing Constraints over Uncertain Events

This paper provides a comprehensive approach to the problem of monitoring timing constraints over event streams for which the timestamp values are inherently uncertain. We first propose a generic framework for capturing the early detection of the violation of timing constraints, based on the notion of probabilistic violation time. In doing so, we provide a systemic approach for deriving a set of necessary constraints at compilation time. Our work is innovative in that the framework is formulated to be "modular" with respect to the probability distributions on timestamp values. We demonstrate the applicability of the framework for two different timestamp models, Gaussian and histogram. The Gaussian model is appropriate for representing event timing from a wide variety of sensors with well-modelled physical noise characteristics; we show how we can efficiently derive the probabilistic violation time of timing constraints by exploiting the relation between the Gaussian distribution parameters. The histogram model can be used where the timestamps of events are available from measurements only as arbitrary probability distributions: we show how to derive an efficient timing constraint monitoring method for the histogram model