Energy Efficient Scheduling via Partial Shutdown

TL;DR

This paper introduces new machine activation problems focused on energy-efficient scheduling in data centers, providing approximation algorithms and schemes to minimize energy costs while maintaining scheduling efficiency.

Contribution

It formulates the machine activation problem with activation costs and develops approximation algorithms, including a PTAS for related parallel machines, advancing energy-efficient scheduling methods.

Findings

Approximation algorithms achieve constant-factor makespan and cost bounds.

A greedy algorithm yields a 2-approximate makespan with logarithmic cost increase.

A polynomial-time approximation scheme (PTAS) for related parallel machines achieves near-optimal makespan with bounded activation cost.

Abstract

Motivated by issues of saving energy in data centers we define a collection of new problems referred to as "machine activation" problems. The central framework we introduce considers a collection of $m$ machines (unrelated or related) with each machine $i$ having an {\em activation cost} of $a_i$. There is also a collection of $n$ jobs that need to be performed, and $p_{i,j}$ is the processing time of job $j$ on machine $i$. We assume that there is an activation cost budget of $A$ -- we would like to {\em select} a subset $S$ of the machines to activate with total cost $a(S) \le A$ and {\em find} a schedule for the $n$ jobs on the machines in $S$ minimizing the makespan (or any other metric). For the general unrelated machine activation problem, our main results are that if there is a schedule with makespan $T$ and activation cost $A$ then we can obtain a schedule with makespan $\makespanconstant T$ and activation cost $\costconstant A$, for any $\epsilon >0$. We also consider assignment costs for jobs as in the generalized assignment problem, and using our framework, provide algorithms that minimize the machine activation and the assignment cost simultaneously. In addition, we present a greedy algorithm which only works for the basic version and yields a makespan of $2T$ and an activation cost $A (1+\ln n)$. For the uniformly related parallel machine scheduling problem, we develop a polynomial time approximation scheme that outputs a schedule with the property that the activation cost of the subset of machines is at most $A$ and the makespan is at most $(1+\epsilon) T$ for any $\epsilon >0$.