F2VD: Fluid Rates to Virtual Deadlines for Precise Mixed-Criticality Scheduling on a Varying-Speed Processor

Increasingly complex and integrated systems design has led to more timing uncertainty, which may result in pessimism in time-sensitive system design and analysis. To mitigate such pessimism, mixed-criticality (MC) design for real-time systems has been proposed, where highly critical tasks, often with extremely pessimistic execution time estimates, can share the processor with less critical ones in a manner that the latter is sacrificed, completely or partially, to guarantee temporal correctness to the former, when the extremely pessimistic scenario does happen. In contrast to such sacrifice of tasks, the precise MC scheduling model has recently been investigated, where all tasks, including less critical ones, must fully complete their execution in all circumstances. Meanwhile, the processor may operate at a degraded speed when the tasks' runtime behaviors are far from the extreme pessimistic estimates and would recover to the full processing speed once the extremely pessimistic scenario does happen. This paper presents a generalized fluid-scheduling-based solution to this problem, where feasible fluid-scheduling rates for each task are derived from an optimization problem. Furthermore, this paper proposes a novel algorithm F2VD for setting virtual deadlines from any feasible fluid rates, such that any fluid-scheduling-based solution can be converted to a deadline-based scheduling approach with no schedulability loss, where the latter is generally considered much more practical and easier to implement. Experimental studies based on randomly generated task sets are conducted to verify the theoretical results as well as the effectiveness of the proposed algorithms.