In this paper, we propose a novel analytical method, called scheduling time bound analysis, to find a tight upper bound of the worst-case response time in a distributed real-time embedded system, considering execution time variations of tasks, jitter of input arrivals, and scheduling anomaly behavior in a multi-tasking system all together. By analyzing the graph topology and worstcase scheduling scenarios, we measure the conservative scheduling time bound of each task. The proposed method supports an arbitrary mixture of preemptive and non-preemptive processing elements. Its speed is comparable to compositional approaches while it gives a much tighter bound. The advantages of the proposed approach compared with related work were verified by experimental results with randomly generated task graphs and a real-life automotive application.

Abstract-Finding a tight upper bound of the worst-case response time in a distributed real-time embedded system is a very challenging problem since we have to consider execution time variations of tasks, jitter of input arrivals, scheduling anomaly behavior in a multi-tasking system, all together. In this paper, we translate the problem as an optimization problem and propose a novel solution based on ILP (Integer Linear Programming). In the proposed technique, we formulate a set of ILP formulas in a compositional way for modeling flexibility, but solve the problem holistically to achieve tighter upper bounds. To mitigate the time complexity of the ILP method, we perform static analysis based on a scheduling heuristic to reduce the number of variables and confine the variable ranges. Preliminary experiments with the benchmarks used in the related work and a real-life example show promising results that give tight bounds in an affordable solution time.