Scheduling with uncertain processing times in mixed-criticality systems

Abstract

Many scheduling problems that can be identified inside safety-critical applications, such as in autonomous cars, tend to be mixed-critical. Such scheduling problems consider tasks to have different criticalities depending on the safety levels (activation of brakes vs. activation of air-conditioning). The biggest challenge in those scheduling problems arises from the uncertainty of processing times as it disturbs the predictability of the system and thus makes the certification of the system difficult. To overcome this uncertainty, we model the tasks to have multiple processing times concerning their criticality. This approach converts these scheduling problems into a deterministic scheduling with alternative processing times. Here, we study an NP-hard single machine scheduling problem with makespan minimization, where the non-preemptive tasks can have multiple processing times. To solve the problem, we propose an approximation algorithm, a novel mixed-integer linear programming block formulation, and an efficient exact branch-and-price decomposition for two criticality levels. Furthermore, we demonstrate that the optimal schedules are represented as trees, which enables to formulate an exact algorithm for the problem with three criticality levels. The efficiency of the proposed method is demonstrated for difficult problem instances with up to 1000 tasks. The experimental evaluation demonstrates that our algorithms have improved the results of the best-known method by nearly two orders of magnitude.