Partial-order reduction in reachability-based response-time analyses of limited-preemptive DAG tasks

Response-time analysis (RTA) has been a means to evaluate the temporal correctness of real-time systems since the 1970 s. While early analyses were successful in capturing the exact upper bound on the worst-case response-time (WCRT) of systems with relatively simple computing platforms and task activation models, nowadays we see that most existing RTAs either become pessimistic or do not scale well as systems become more complex (e.g., parallel tasks running on a multicore platform). To make a trade-off between accuracy and scalability, recently, a new reachability-based RTA, called schedule-abstraction graph (SAG), has been proposed. The analysis is at least three orders of magnitude faster than other exact RTAs based on UPPAAL. However, it still has a fundamental limitation in scalability as it suffers from state-space explosion when there are large uncertainties in the timing parameters of the input jobs (e.g., large release jitters or execution-time variations). This could impede its applicability to large industrial use cases, or to be integrated with automated tools that explore alternative design choices. In this paper, we improve the scalability of the SAG analysis by introducing partial-order reduction rules that avoid combinatorial exploration of all possible scheduling decisions. We include systems with dependent and independent task execution models (i.e., with and without precedence constraint). Our empirical evaluations show that the proposed solution is able to reduce the runtime by five orders of magnitude and the number of explored states by 98% in comparison to the original SAG analysis. These achievements come only at a negligible cost of an over-estimation of 0.1% on the actual WCRT. We applied our solution on an automotive case study showing that it is able to scale to realistic systems made of hundreds of tasks for which the original analysis fails to finish.