Stochastic non-preemptive co-flow scheduling with time-indexed relaxation

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 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 log m + 1)(1 + √ m∆)(1 + m∆)(3 + ∆)/2 for zero-release times, and (2 log m + 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.Index Terms-Co-flow scheduling, stochastic flow size, nonpreemptive scheduling, time-indexed relaxation, input-queued switch.

Near Optimal Coflow Scheduling in Networks

“…Since preemption often incurs large overheads, some recent work [30] has tackled the problem of non-preemptive coflow scheduling. Mao, Aggarwal, and Chiang [21] consider the non-preemptive coflow scheduling problem with stochastic sizes and give an algorithm with an approximation factor of (2 log m + 1)(1 + √ m∆)(1 + m∆)(3 + ∆)/2, where ∆ is an upper bound of squared coefficient of variation of processing times. This simplifies to a (3 log m + 3 2 ) approximation for non-stochastic cases.…”

“…Since preemption often incurs large overheads, some recent work [30] has tackled the problem of non-preemptive coflow scheduling. Mao, Aggarwal, and Chiang [21] consider the non-preemptive coflow scheduling problem with stochastic sizes and give an algorithm with an approximation factor of (2 log m + 1)(1…”