Scheduling for Multi-Phase Parallelizable Jobs

TL;DR

This paper studies online scheduling of multi-phase jobs on identical servers, proposing an LCFS-based algorithm with constant competitive ratio for minimizing total flow time, considering limited parallelizability and sequential phases.

Contribution

It introduces a novel LCFS-based scheduling algorithm for multi-phase jobs with limited parallelizability, achieving constant competitive ratio in an online setting.

Findings

The proposed algorithm has a constant competitive ratio depending only on .

Improved competitive ratio for the case with all jobs known beforehand.

Effective scheduling strategy for minimizing flow time in multi-phase parallelizable jobs.

Abstract

With multiple identical unit speed servers, the online problem of scheduling jobs that migrate between two phases, limitedly parallelizable or completely sequential, and choosing their respective speeds to minimize the total flow time is considered. In the limited parallelizable regime, allocating $k$ servers to a job, the speed extracted is $k^{1/\alpha}, \alpha>1$, a sub-linear, concave speedup function, while in the sequential phase, a job can be processed by at most one server with a maximum speed of unity. A LCFS based algorithm is proposed for scheduling jobs which always assigns equal speed to the jobs that are in the same phase (limitedly parallelizable/sequential), and is shown to have a constant (dependent only on $\alpha > 1$) competitive ratio. For the special case when all jobs are available beforehand, improved competitive ratio is obtained.