NOVÁK, A. and Z. HANZÁLEK. Computing the execution probability of jobs with replication in mixed-criticality schedules. Annals of Operations Research. 2022, 309(1), 209-232. ISSN 0254-5330. DOI 10.1007/s10479-021-04445-x.
Mixed-criticality scheduling addresses the problem of sharing common resources among jobs of different degrees of criticality and uncertain processing times. The processing time of jobs is observed during the online execution of the schedule with the prolongations of critical jobs being compensated by the rejection of less critical ones. One of the central questions in the field of mixed-criticality scheduling is ensuring the high reliability of the system with as few resources as possible. In this paper, we study the computation of the execution probability of jobs with uncertain processing times in a static mixed-criticality schedule. The aim is to compute the execution probability of jobs (i.e., the objective function of a schedule), which is a problem solvable by a closed-form formula when the jobs are not replicated. We introduce the job replication, i.e., scheduling a single job multiple times, as a new mechanism for increasing the execution probability of jobs. We show that the general problem with job replication becomes #P-hard, which is proven by the reduction from the counting variant of 3-SAT problem. To compute the execution probability, we propose an algorithm utilizing the framework of Bayesian networks. Furthermore, we show that cases of practical interest admit a polynomial-time algorithm and are efficiently solvable. The proposed methodology demonstrates an interesting connection between schedules with uncertain execution and probabilistic graphical models and opens a new approach to the analysis of mixed-criticality schedules.
eng
dc.format.mimetype
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.relation.ispartof
Annals of Operations Research
dc.subject
Mixed-criticality
eng
dc.subject
Job replication
eng
dc.subject
Scheduling
eng
dc.subject
Bayesian networks
eng
dc.subject
Computational complexity
eng
dc.subject
Uncertain processing time
eng
dc.title
Computing the execution probability of jobs with replication in mixed-criticality schedules