Non-Clairvoyant Batch Sets Scheduling: Fairness is Fair enough

TL;DR

This paper analyzes non-clairvoyant scheduling strategies for job sets with unknown characteristics, providing near-optimal competitive ratios for minimizing set flowtime and makespan in an online setting.

Contribution

It introduces the EQUIoEQUI strategy for set flowtime and proves its asymptotic optimality, along with the EQUI strategy for makespan, in non-clairvoyant scheduling.

Findings

EQUIoEQUI achieves a competitive ratio of (2+√3+o(1)) * (ln n / ln ln n).

EQUI achieves a competitive ratio of (1+o(1)) * (ln n / ln ln n).

Both strategies are asymptotically optimal for their respective metrics.

Abstract

Scheduling questions arise naturally in many different areas among which operating system design, compiling,... In real life systems, the characteristics of the jobs (such as release time and processing time) are usually unknown and unpredictable beforehand. The system is typically unaware of the remaining work in each job or of the ability of the job to take advantage of more resources. Following these observations, we adopt the job model by Edmonds et al (2000, 2003) in which the jobs go through a sequence of different phases. Each phase consists of a certain quantity of work and a speed-up function that models how it takes advantage of the number of processors it receives. We consider the non-clairvoyant online setting where a collection of jobs arrives at time 0. We consider the metrics setflowtime introduced by Robert et al (2007). The goal is to minimize the sum of the completion time of the sets, where a set is completed when all of its jobs are done. If the input consists of a single set of jobs, this is simply the makespan of the jobs; and if the input consists of a collection of singleton sets, it is simply the flowtime of the jobs. We show that the non-clairvoyant strategy EQUIoEQUI that evenly splits the available processors among the still unserved sets and then evenly splits these processors among the still uncompleted jobs of each unserved set, achieves a competitive ratio (2+\sqrt3+o(1))\frac{ln n}{lnln n} for the setflowtime minimization and that this is asymptotically optimal (up to a constant factor), where n is the size of the largest set. For makespan minimization, we show that the non-clairvoyant strategy EQUI achieves a competitive ratio of (1+o(1))\frac{ln n}{lnln n}, which is again asymptotically optimal.