Scheduling malleable tasks with interdependent processing rates: Comments and observations
Discrete Applied Mathematics
Fuzzy scheduling with swarm intelligence-based knowledge acquisition for grid computing
Engineering Applications of Artificial Intelligence
International Journal of Grid and Utility Computing
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This paper presents a generalization to classical scheduling theory by removing the restriction that only one processor can work on a given task at a particular time. Instead, it is assumed that each task can be allocated any number of identical processors from one to the maximum number available, with each task's completion time being a function of the number of processors allocated. Tasks may be started any time, but once started, a task must not have its processor allocation altered or be preempted. Two objective functions are considered: minimizing the overall completion time for the tasks (make-span) and minimizing a weighted sum of the task completion times (weighted response). Both are considered subject to a constraint on the total number of processors available. Suboptimal algorithms are developed for both of these NP-hard problems using Lagrangian relaxation, and their performances are analyzed through extensive simulations. Duality gaps for all problems tested ranged from under 1% to 92%, depending more on the problem size than the specific problem.