Speed Scaling On Parallel Servers with MapReduce Type Precedence Constraints

TL;DR

This paper studies speed scaling in parallel servers with precedence constraints, proposing algorithms that balance energy costs and flow times, with competitive ratios independent of the number of jobs or servers.

Contribution

It introduces simple speed scaling algorithms for precedence-constrained jobs on multiple servers, achieving competitive ratios independent of system size.

Findings

Algorithms have competitive ratios depending on power function and task size ratios.

Proposed methods effectively balance energy consumption and job flow times.

Results are applicable to systems with large task volumes and precedence constraints.

Abstract

A multiple server setting is considered, where each server has tunable speed, and increasing the speed incurs an energy cost. Jobs arrive to a single queue, and each job has two types of sub-tasks, map and reduce, and a {\bf precedence} constraint among them: any reduce task of a job can only be processed once all the map tasks of the job have been completed. In addition to the scheduling problem, i.e., which task to execute on which server, with tunable speed, an additional decision variable is the choice of speed for each server, so as to minimize a linear combination of the sum of the flow times of jobs/tasks and the total energy cost. The precedence constraints present new challenges for the speed scaling problem with multiple servers, namely that the number of tasks that can be executed at any time may be small but the total number of outstanding tasks might be quite large. We present simple speed scaling algorithms that are shown to have competitive ratios, that depend on the power cost function, and/or the ratio of the size of the largest task and the shortest reduce task, but not on the number of jobs, or the number of servers.