Stochastic Non-preemptive Co-flow Scheduling with Time-Indexed Relaxation
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Co-flows model a modern scheduling setting that is commonly found in a variety of applications in distributed and cloud computing. A stochastic co-flow task contains a set of parallel flows with randomly distributed sizes. Further, many applications require non-preemptive scheduling of co-flow tasks. This paper gives an approximation algorithm for stochastic non-preemptive co-flow scheduling. The proposed approach uses a time-indexed linear relaxation, and uses its solution to come up with a feasible schedule. This algorithm is shown to achieve a competitive ratio of (2m+1)(1+√(mΔ))(1+m√(Δ))(3+Δ)/2 for zero-release times, and (2m+1)(1+√(mΔ))(1+m√(Δ))(2+Δ) for general release times, where Δ represents the upper bound of squared coefficient of variation of processing times, and m is the number of servers.
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