CTA: A Correlation-Tolerant Analysis of the Deadline-Failure Probability of Dependent Tasks

Estimating the worst-case deadline failure probability (WCDFP) of a real-time task is notoriously difficult, primarily because a task's execution time typically depends on prior activations (i.e., history dependence) and the execution of other tasks (e.g., via shared inputs). Previous analyses have either assumed that execution times are probabilistically independent (which is unrealistic and unsafe), or relied on complex upper-bounding abstractions such as probabilistic worst-case execution time (pWCET), which mask dependencies with pessimism. Exploring an analytically novel direction, this paper proposes the first closed-form upper bound on WCDFP that accounts for dependent execution times. The proposed correlation-tolerant analysis (CTA), based on Cantelli's inequality, targets fixed-priority scheduling and requires only two basic summary statistics of each task's ground- truth execution time distribution: upper bounds on the mean and standard deviation (for any possible job-arrival sequence). Notably, CTA does not use pWCET, nor does it require the full execution-time distribution to be known. Core parts of the analysis have been verified with the Coq proof assistant. Empirical comparison with state-of-the-art WCDFP analyses reveals that CTA can yield significantly improved bounds (e.g., a lower WCDFP than any pWCET-based method for 70% of the workloads tested at 90% pWCET utilization and 60% average utilization). Beyond accuracy gains, the favorable results highlight the potential of the previously unexplored analytical direction underlying CTA.