Mechanism design for aggregating energy consumption and quality of service in speed scaling scheduling

TL;DR

This paper explores game-theoretic mechanisms for scheduling jobs with deadlines on speed-scaled machines, focusing on energy costs and strategic behavior, and analyzes equilibrium existence under different charging schemes.

Contribution

It introduces and compares two charging schemes for energy-aware scheduling games, highlighting conditions for the existence of pure Nash equilibria.

Findings

Proportional cost share may lack pure Nash equilibria.

Marginal cost share always admits pure Nash equilibria.

Marginal cost overcharges by a constant factor.

Abstract

We consider a strategic game, where players submit jobs to a machine that executes all jobs in a way that minimizes energy while respecting the given deadlines. The energy consumption is then charged to the players in some way. Each player wants to minimize the sum of that charge and of their job's deadline multiplied by a priority weight. Two charging schemes are studied, the proportional cost share which does not always admit pure Nash equilibria, and the marginal cost share, which does always admit pure Nash equilibria, at the price of overcharging by a constant factor.