Mixed-criticality systems often need to fulfill safety standards that dictate different requirements for each criticality level, for example given in the ‘probability of failure per hour’ format. A recent trend suggests designing this kind of systems by jointly scheduling tasks of different criticality levels on a shared platform. When this is done, the usual assumption is that tasks of lower criticality are degraded when a higher criticality task needs more resources, for example when it overruns a bound on its execution time. However, a way to quantify the impact this degradation has on the overall system is not well understood. Meanwhile, to improve schedulability and to avoid over-provisioning of resources due to overly pessimistic worst-case execution time estimates of higher criticality tasks, a new paradigm emerged where task’s execution times are modeled with random variables. In this paper, we analyze a system with probabilistic execution times, and propose metrics that are inspired by safety standards. Among these metrics are the probability of deadline miss per hour, the expected time before degradation happens, and the duration of the degradation. We argue that these quantities provide a holistic view of the system’s operation and schedulability.

混合关键性系统通常需要满足针对每个关键性级别规定不同要求的安全标准，例如“每小时故障概率”格式。最近的趋势表明，通过在共享平台上联合调度不同关键级别的任务来设计这种系统。完成此操作后，通常的假设是，当较高关键性任务需要更多资源时（例如，当其执行时间超出限制时），较低关键性的任务就会降级。但是，对这种降级对整个系统的影响进行量化的方法尚不清楚。同时，为了提高可调度性并避免由于对高关键性任务的最悲观的最坏情况执行时间估计过于悲观而导致的资源超额配置，一个新的范例出现了，其中任务的执行时间用随机变量建模。在本文中，我们分析了具有概率执行时间的系统，并提出了受安全标准启发的指标。这些指标包括每小时错过最后期限的概率，降级发生之前的预期时间以及降级的持续时间。我们认为这些数量提供了系统运行和可调度性的整体视图。