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

TL;DR

This paper presents an approximation algorithm for stochastic non-preemptive co-flow scheduling in distributed systems, utilizing a time-indexed relaxation to achieve competitive ratios based on system parameters.

Contribution

It introduces a novel approximation algorithm using time-indexed linear relaxation for stochastic non-preemptive co-flow scheduling.

Findings

Achieves a competitive ratio of $(2\log{m}+1)(1+\sqrt{m}\Delta)(1+m\\Delta)\frac{3+\\Delta}{2}$ for zero-release times.

Achieves a competitive ratio of $(2\\log{m}+1)(1+\\sqrt{m}\Delta)(1+m\\Delta)(2+\\Delta)$ for general release times.

Provides a feasible scheduling approach with theoretical performance guarantees.

Abstract

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.