An abstraction-refinement theory for the analysis and design of concurrent real-time systems

Abstract

Concurrent real-time systems with shared resources belong to the class of safety-critical systems for which it is required to determine both temporally and functionally conservative guarantees. However, the growing complexity of real-time systems makes it more and more challenging to apply standard techniques for their analysis. Especially the presence of both cyclic data dependencies and cyclic resource dependencies makes many related analysis approaches inapplicable. The usage of Static Priority Preemptive (SPP) scheduling further impedes the employment of many classical analysis techniques. To address this growing complexity and to be able to give guarantees nevertheless we present an abstraction-refinement theory for real-time systems. We introduce a timed component model that is defined in such a generic way that both real-time system implementations and any kinds of analysis models for such applications can be expressed therein. Thereafter, we devise three different abstraction-refinement theories for the timed component model, exclusion, inclusion and bounding. Exclusion can be used to remove unconsidered corner cases, inclusion allows for the substitution of uncertainty with non-determinism, while bounding permits to replace non-determinism with determinism. The latter enables the creation of efficiently analyzable models that can be used to give temporal or functional guarantees on non-deterministic and non-monotone implementations. We use such abstractions to construct analysis models from concurrent real-time systems with shared resources and SPP scheduling. On these models we apply various analysis techniques, with the goal to increase analysis accuracy. Our first accuracy improvement is achieved by combining the rather coarse state-of-the-art period-and-jitter interference characterization with an explicit consideration of cyclic data dependencies. The interference-limiting effect of such cycles can be exploited even more with an iterative buffer sizing. Next we replace period-and-jitter with execution intervals, resulting in an even higher accuracy. In our last approach we increase both accuracy and applicability by enabling the support of real-time systems with tasks consisting of multiple phases and operating at different rates. With a modification of this approach we further enable the analysis of applications with multiple shared resources. Finally, we also present the so-called HAPI simulator that is capable of simulating any kinds of concurrent real-time systems with shared resources.