Throughput Maximization in Multiprocessor Speed-Scaling

Abstract

In the classical energy minimization problem, introduced in [Yao et al., FOCS’95], we are given a set of $n$ jobs each one characterized by its release date, its deadline, its processing volume and we aim to find a feasible schedule of the jobs on a single speed-scalable machine so that the total energy consumption is minimized. Here, we study the throughput maximization version of the problem where we are given a budget of energy $E$ and where every job has also a value. Our goal is to determine a feasible schedule maximizing the (weighted) throughput of the jobs that are executed between their respective release dates and deadlines. We first consider the preemptive non-migratory multiprocessor case in a fully heterogeneous environment in which every job has a machine-dependent release date, deadline and processing volume and every machine obeys to a different speed-to-power function. We present a polynomial time greedy algorithm based on the primal-dual scheme that approximates the optimum solution within a factor depending on the energy functions (the factor is constant for typical energy functions of form $P(z) = z^{\alpha }$). Then, we focus on the non-preemptive case for which we consider a fixed number of identical parallel machines and two important families of instances: (1) equal processing volume jobs; and (2) agreeable jobs. For both cases we present optimal pseudo-polynomial-time algorithms.

Research supported by FMJH program Gaspard Monge in Optimization and Operations Research and by EDF, by the project PHC CAI YUANPEI (27927VE) and by the project ALGONOW, co-financed by the European Union (European Social Fund - ESF).