Optimal Scheduling on Parallel Processors under Precedence Constraints and General Costs
نویسندگان
چکیده
We consider preemptive and nonpreemptive scheduling of partially ordered tasks on parallel processors, where the precedence relations have an interval order, an in-forest, or a uniform out-forest structure. Processing times of tasks are random variables with an ILR (increasing in likelihood ratio) distribution in the nonpreemptive case and an exponential distribution in the preemptive case. We consider a general cost that is a function of time and of the uncompleted tasks and show that the Most Successors policy (MS) stochastically minimizes the cost function when it satisses certain agreeability conditions. A consequence is that MS stochastically minimizes makespan, weighted owtime, and weighted number of late jobs.
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