Efficiently Approximating the Worst-Case Deadline Failure Probability Under EDF

Probabilistic timing guarantees enable a tradeoff between system safety and hardware costs in embedded real-time systems. A key metric for assessing whether timing requirements can be satisfied with sufficiently high probability is the worst-case deadline failure probability (WCDFP). This paper studies the WCDFP under earliest-deadline first (EDF) scheduling for tasks with several probabilistic execution modes (e.g., a low-needs "typical" mode and a resource-intensive exceptional" mode). Under EDF, no known approach can bound the WCDFP for practically sized workloads since the time complexity of prior approaches is exponential in the number of jobs. This paper examines the structure of the EDF WCDFP problem and establishes a safe, efficiently computable over-approximation by restricting the analysis to a set of specific intervals and providing a criterion to stop the derivation early without risking under-approximation. The analysis first assumes independent jobs and is then extended to handle dependencies (i.e., acyclic task chains). An evaluation shows that (i) even if 99.9999% of the jobs must meet their deadlines, a significantly higher utilization is possible than in the deterministic case, (ii) the analysis is scalable to 30 tasks with more than 10^60 jobs in the hyperperiod, and (iii) assuming independence in the presence of dependent tasks can severely under-estimate the WCDFP.