Queueing Analysis of Fault-Tolerant Computer Systems
IEEE Transactions on Software Engineering
Single machine flow-time scheduling with a single breakdown
Acta Informatica
Production batching with machine breakdowns and safety stocks
Operations Research
Dynamic scheduling with incomplete information
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
A single server queue with service interruptions
Queueing Systems: Theory and Applications
The Completion Time of Programs on Processors Subject to Failure and Repair
IEEE Transactions on Computers
Analysis of link failures in an IP backbone
Proceedings of the 2nd ACM SIGCOMM Workshop on Internet measurment
Probability in the Engineering and Informational Sciences
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Sensor scheduling in mobile robots using incomplete information via Min-Conflict with Happiness
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
General stochastic single-machine scheduling with regular cost functions
Mathematical and Computer Modelling: An International Journal
Single machine scheduling under potential disruption
Operations Research Letters
Minimizing makespan on a single machine subject to random breakdowns
Operations Research Letters
Scheduling deteriorating jobs on a single machine subject to breakdowns
Journal of Scheduling
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This paper considers the problem of scheduling a set of jobs on a single machine subject to stochastic breakdowns with incomplete information on the probability distributions involved in the decision process. We focus on the preemptive-repeat discipline, under which a machine breakdown leads to the loss of the work done on the job being processed. The breakdown process of the machine is allowed to depend on the job it is processing. The processing times required to complete the jobs, and the machine uptimes and downtimes, are random variables with incomplete information on their probability distributions characterized by unknown parameters. We establish the preemptive-repeat model with incomplete information and investigate its probabilistic characteristics. We show that optimal static policies can be obtained for a wide range of performance measures, which are determined by the prior distributions of the unknown parameters. We derive optimal dynamic policies via Gittins indices represented by the posterior distributions, which are updated adaptively based on processing histories. Under appropriate conditions, the optimal dynamic policies can be calculated by one-step reward rates in a closed form. As a by-product, we also show that our incomplete information model subsumes the traditional preemptive-repeat models with complete information as extreme cases.