  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.
