Abstract 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.

The temporal correctness of safety-critical systems is typically guaranteed via a response-time analysis (RTA). However, as systems become complex (e.g., parallel tasks running on a multicore platform), most existing RTAs either become pessimistic or do not scale well. 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.One fundamental limitation of the SAG analysis is that it suffers from state-space explosion when there are large uncertainties in the timing parameters of the input jobs, which may impede its applicability to some industrial use cases. In this paper, we improve the scalability of the SAG analysis by introducing partial-order reduction (POR) rules that avoid combinatorial exploration of all possible scheduling decisions. An empirical evaluation shows that our solution is able to reduce the runtime by five orders of magnitude and the number of explored states by 98%, at a negligible cost of an over-estimation of 0.1% on the tasks’ worst-case response-time (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.

The temporal correctness of safety-critical systems is typically guaranteed via a response-time analysis (RTA). However, as the systems become complex (e.g., parallel tasks running on a multicore platform), most existing RTAs either become pessimistic or do not scale with respect to e.g., the number of tasks or period values. To make a trade-off between accuracy and scalability, recently, a new reachability-based RTA called schedule-abstraction graph (SAG) has been introduced by Nasri et al. It explores the space of possible decisions that a scheduling policy can take while dispatching a set of tasks or jobs on processing resources. The analysis is at least three orders of magnitude faster than other exact RTAs and is able to identify many more schedulable task sets than the existing fixed-point iteration-based analyses. One fundamental limitation of the SAG analysis is that in its reachability graph, each edge can only account for a single scheduling decision. Therefore, the graph grows exponentially when there are large uncertainties in the release time or execution time of the jobs. In this paper, we improve the scalability of the SAG analysis by introducing partial-order reduction (POR) rules that allow combining multiple scheduling decisions on one edge and hence avoiding combinatorial exploration of all possible scheduling decisions. An empirical evaluation shows that our solution is able to reduce the runtime by five orders of magnitude and the number of explored states by 98%.