A challenge in the design of cyber-physical systems is to integrate the scheduling of tasks of different criticality, while still providing service guarantees for the higher critical tasks in the case of resource-shortages caused by faults. While standard real-time scheduling is agnostic to the criticality of tasks, the scheduling of tasks with different criticalities is called mixed-criticality scheduling. In this paper, we present the Lazy Bailout Protocol (LBP), a mixed-criticality scheduling method where low-criticality jobs overrunning their time budget cannot threaten the timeliness of high-criticality jobs while at the same time the method tries to complete as many low-criticality jobs as possible. The key principle of LBP is instead of immediately abandoning low-criticality jobs when a high-criticality job overruns its optimistic WCET estimate, to put them in a low-priority queue for later execution. To compare mixed-criticality scheduling methods, we introduce a formal quality criterion for mixed-criticality scheduling, which, above all else, compares schedulability of high-criticality jobs and only afterwards the schedulability of low-criticality jobs. Based on this criterion, we prove that LBP behaves better than the original Bailout Protocol (BP). We show that LBP can be further improved by slack time exploitation and by gain time collection at runtime, resulting in LBPSG. We also show that these improvements of LBP perform better than the analogous improvements based on BP.

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In a safety-critical system each service has a specific level of safety criticality. Safety standards use classifications like Safety Integrity Levels (SIL), to describe the design requirements for the individual services of a system. Techniques like redundancy can be used to achieve a higher overall dependability than the used individual components provide. Using the notion of SIL, this can be called SIL arithmetic.In this paper we describe the concept of SIL arithmetic and point out how different safety standards provide hints for their support of using SIL arithmetic. We highlight the principal benefits of SIL arithmetic and provide simple examples. But the use of SIL arithmetic in a concrete system design can also have its pitfalls, which we also discuss in this paper. We specifically discuss these issues in the context of scheduling techniques for mixed-criticality systems, where resource shortages are to be handled by the scheduler.

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