Monitoring of Timing Constraints with Confidence Threshold Requirements

In many emerging time-critical applications, the exact time of event occurrences may not be known. In such cases, events can be represented as a probabilistic occurrence within a time interval. Thus, monitoring of timing constraints, generally used in time- critical systems, needs to incorporate the uncertainty of event occurrences. In this paper, we propose mechanisms to monitor the satisfaction/violation of timing constraints that can be assessed probabilistically. We assume a uniform distribution of event occurrence within a time interval. Our proposed algorithm determines whether the probability that a timing constraint has been satisfied exceeds a specified threshold value. A confidence threshold is a minimum satisfaction probability of the timing constraint. A timing constraint is violated if the confidence threshold is not reached. We design an efficient monitoring algorithm for detecting timing violations of a set of timing constraints by finding the earliest expiration time (EET) for each timing constraint. Since it is critical to derive implicit constraints for early detection of violation of timing constraints, we present the derivation of the implicit constraints under uncertainty using an all-pairs shortest path algorithm. Further, we propose pruning techniques to discard unnecessary implicit constraints. We present the properties and proofs of our approach.