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 nonpreemptive 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 logm+1)(1+ √ m∆)(1+m∆)(3 + ∆)/2 for zero-release times, and (2 logm+1)(1+ √ m∆)(1+m∆)(2+ ∆) for general release times, where∆ represents the upper bound of squared coefficient of variation of processing times, and m is the number of servers.