Open Problems on Non-preemptive Scheduling of Mixed-Criticality Real-Time Systems

In many industrial systems, design complexity is partly reduced by the use of non-preemptive message passing or execution. Doing so, context switch overheads are diminished and resource sharing mechanisms are simplified. However, in a mixedcriticality system, long blocking time caused by non-preemptive execution of a task which has lower priority than some other high criticality (HC) tasks might threaten schedulability of the HC tasks in their HC mode. In single criticality systems, it has been proven that non-preemptive scheduling is an NP-Hard problem for periodic [1] or harmonic tasks [2], where each period is an integer multiple of shorter periods. In this work, we want to extend the existing solutions for single criticality systems to two criticality systems to solve the scheduling problem of the Vestal task model for mixed criticality systems [3]. Recently, an online non-preemptive non-work-conserving scheduling algorithm called Precautious-RM has been introduced in [4]. This algorithm prioritizes the jobs according to rate monotonic, however, it schedules a job only if its execution will not cause a deadline miss for the next instance of the task with the smallest period. Otherwise, it schedules an idle interval until the next release of the highest priority task. It has O(n) computational complexity and it guarantees the schedulability of harmonic tasks in three cases: a) period ratio is 2, b) period ratio is greater than 2, and c) tasks have arbitrary period ratio, yet there are enough vacant intervals. A vacant interval is defined as the slack of two consecutive instances of the task with the smallest period. Period ratio is defined as the ratio of two consecutive periods, i.e., Ti/Ti−1 if the periods are sorted in ascending order. In the third case, suggested conditions are only sufficient since the general problem is NP-Hard, i.e., system is schedulable by Precautious-RM if each task has its guaranteed slot before its deadline.