903 research outputs found
A survey of offline algorithms for energy minimization under deadline constraints
Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given
Energy-Efficient Scheduling for Homogeneous Multiprocessor Systems
We present a number of novel algorithms, based on mathematical optimization
formulations, in order to solve a homogeneous multiprocessor scheduling
problem, while minimizing the total energy consumption. In particular, for a
system with a discrete speed set, we propose solving a tractable linear
program. Our formulations are based on a fluid model and a global scheduling
scheme, i.e. tasks are allowed to migrate between processors. The new methods
are compared with three global energy/feasibility optimal workload allocation
formulations. Simulation results illustrate that our methods achieve both
feasibility and energy optimality and outperform existing methods for
constrained deadline tasksets. Specifically, the results provided by our
algorithm can achieve up to an 80% saving compared to an algorithm without a
frequency scaling scheme and up to 70% saving compared to a constant frequency
scaling scheme for some simulated tasksets. Another benefit is that our
algorithms can solve the scheduling problem in one step instead of using a
recursive scheme. Moreover, our formulations can solve a more general class of
scheduling problems, i.e. any periodic real-time taskset with arbitrary
deadline. Lastly, our algorithms can be applied to both online and offline
scheduling schemes.Comment: Corrected typos: definition of J_i in Section 2.1; (3b)-(3c);
definition of \Phi_A and \Phi_D in paragraph after (6b). Previous equations
were correct only for special case of p_i=d_
Reclaiming the energy of a schedule: models and algorithms
We consider a task graph to be executed on a set of processors. We assume
that the mapping is given, say by an ordered list of tasks to execute on each
processor, and we aim at optimizing the energy consumption while enforcing a
prescribed bound on the execution time. While it is not possible to change the
allocation of a task, it is possible to change its speed. Rather than using a
local approach such as backfilling, we consider the problem as a whole and
study the impact of several speed variation models on its complexity. For
continuous speeds, we give a closed-form formula for trees and series-parallel
graphs, and we cast the problem into a geometric programming problem for
general directed acyclic graphs. We show that the classical dynamic voltage and
frequency scaling (DVFS) model with discrete modes leads to a NP-complete
problem, even if the modes are regularly distributed (an important particular
case in practice, which we analyze as the incremental model). On the contrary,
the VDD-hopping model leads to a polynomial solution. Finally, we provide an
approximation algorithm for the incremental model, which we extend for the
general DVFS model.Comment: A two-page extended abstract of this work appeared as a short
presentation in SPAA'2011, while the long version has been accepted for
publication in "Concurrency and Computation: Practice and Experience
Speed-scaling with no Preemptions
We revisit the non-preemptive speed-scaling problem, in which a set of jobs
have to be executed on a single or a set of parallel speed-scalable
processor(s) between their release dates and deadlines so that the energy
consumption to be minimized. We adopt the speed-scaling mechanism first
introduced in [Yao et al., FOCS 1995] according to which the power dissipated
is a convex function of the processor's speed. Intuitively, the higher is the
speed of a processor, the higher is the energy consumption. For the
single-processor case, we improve the best known approximation algorithm by
providing a -approximation algorithm,
where is a generalization of the Bell number. For the
multiprocessor case, we present an approximation algorithm of ratio
improving the best known result by a factor of
. Notice that our
result holds for the fully heterogeneous environment while the previous known
result holds only in the more restricted case of parallel processors with
identical power functions
Energy Efficient Scheduling and Routing via Randomized Rounding
We propose a unifying framework based on configuration linear programs and
randomized rounding, for different energy optimization problems in the dynamic
speed-scaling setting. We apply our framework to various scheduling and routing
problems in heterogeneous computing and networking environments. We first
consider the energy minimization problem of scheduling a set of jobs on a set
of parallel speed scalable processors in a fully heterogeneous setting. For
both the preemptive-non-migratory and the preemptive-migratory variants, our
approach allows us to obtain solutions of almost the same quality as for the
homogeneous environment. By exploiting the result for the
preemptive-non-migratory variant, we are able to improve the best known
approximation ratio for the single processor non-preemptive problem.
Furthermore, we show that our approach allows to obtain a constant-factor
approximation algorithm for the power-aware preemptive job shop scheduling
problem. Finally, we consider the min-power routing problem where we are given
a network modeled by an undirected graph and a set of uniform demands that have
to be routed on integral routes from their sources to their destinations so
that the energy consumption is minimized. We improve the best known
approximation ratio for this problem.Comment: 27 page
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