Interval-Based Timing Constraints Their Satisfactions and Applications

In real-time distributed systems, it is often difficult to timestamp an event with a point value. Hence, constraints based on intervals are more realistic. However, when a constraint is extended from point-based to interval-based, its satisfaction is not a simple Boolean value; instead, a satisfaction probability is associated with the constraint. We study the satisfaction probability of interval- based timing constraints when event occurrence times are nonuniformly distributed in given time intervals. An algorithm is developed to derive implicit constraints from a set of given interval-based constraints. Our study shows that there are bounds for certain constraint configurations. These analytical results are further applied in two application domains in which constraints are based on single and composite event models, respectively.