Stochastic Non-preemptive Co-flow Scheduling with Time-Indexed Relaxation

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 $(2\log{m}+1)(1+\sqrt{m}\Delta)(1+m{\Delta}){(3+\Delta)}/{2}$ for zero-release times, and $(2\log{m}+1)(1+\sqrt{m}\Delta)(1+m\Delta)(2+\Delta)$ for general release times, where $\Delta$ represents the upper bound of squared coefficient of variation of processing times, and $m$ is the number of servers.