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In this paper, we study an NP-hard problem of a single machine schedulingminimizing the makespan, where the mixed-critical tasks with an uncertainprocessing time are scheduled. We show the derivation of F-shaped tasks fromthe probability distribution function of the processing time, then we study thestructure of problems with two and three criticality levels for which wepropose efficient exact algorithms and we present computational experiments forinstances with up to 200 tasks. Moreover, we show that the considered problemis approximable within a constant multiplicative factor.

On Solving Non-preemptive Mixed-criticality Match-up Scheduling Problem with Two and Three Criticality Levels