Monitoring of timing constraints with confidence threshold requirements

We propose an algorithm for monitoring timing constraints to satisfy confidence threshold requirements when there is uncertainty in the exact timing of event occurrences. In our model, a timed event trace is examined for possible satisfaction/violation with respect to a given set of timing constraints. Every event occurrence has a timestamp given by a time interval. Assuming that the time of occurrence is uniformly distributed over the time interval, our algorithm determines whether the probability that a timing constraint has been satisfied exceeds a specified threshold value. Timing constraints are composed of deadline and delay constraints for which satisfaction probabilities are defined. A confidence threshold is a minimum satisfaction probability of the timing constraint. A timing constraint is violated if the confidence threshold is not reached by the timed event trace. We present a ptime monitoring algorithm for detecting timing violation by finding the earliest expiration time (EET) of the deadline timer for each of the cases P = 100%, 50% /spl les/ P < 100%, and 0% < P < 50%, where P is the confidence threshold of the timing constraint. We give a derivation of the implicit constraints needed for computing the EET, and we show how to use an all-pairs shortest path algorithm to compute the implicit constraints.