Parametric Schedulability Analysis of Fixed Priority Real-Time Distributed Systems

Parametric analysis is a powerful tool for designing modern embedded systems, because it permits to explore the space of design parameters, and to check the robustness of the system with respect to variations of some uncontrollable variable. In this paper, we address the problem of parametric schedulability analysis of distributed real-time systems scheduled by fixed priority. In particular, we propose two different approaches to parametric analysis: the first one is a novel technique based on classical schedulability analysis, whereas the second approach is based on model checking of Parametric Timed Automata (PTA). The proposed analytic method extends existing sensitivity analysis for single processors to the case of a distributed system, supporting preemptive and non-preemptive scheduling, jitters and unconstrained deadlines. Parametric Timed Automata are used to model all possible behaviours of a distributed system, and therefore it is a necessary and sufficient analysis. Both techniques have been implemented in two software tools, and they have been compared with classical holistic analysis on two meaningful test cases. The results show that the analytic method provides results similar to classical holistic analysis in a very efficient way, whereas the PTA approach is slower but covers the entire space of solutions.Comment: Submitted to ECRTS 2013 (http://ecrts.eit.uni-kl.de/ecrts13

Ranking Policy Decisions

Policies trained via Reinforcement Learning (RL) are often needlessly complex, making them difficult to analyse and interpret. In a run with $n$ time steps, a policy will make $n$ decisions on actions to take; we conjecture that only a small subset of these decisions delivers value over selecting a simple default action. Given a trained policy, we propose a novel black-box method based on statistical fault localisation that ranks the states of the environment according to the importance of decisions made in those states. We argue that among other things, the ranked list of states can help explain and understand the policy. As the ranking method is statistical, a direct evaluation of its quality is hard. As a proxy for quality, we use the ranking to create new, simpler policies from the original ones by pruning decisions identified as unimportant (that is, replacing them by default actions) and measuring the impact on performance. Our experiments on a diverse set of standard benchmarks demonstrate that pruned policies can perform on a level comparable to the original policies. Conversely, we show that naive approaches for ranking policy decisions, e.g., ranking based on the frequency of visiting a state, do not result in high-performing pruned policies