11 research outputs found
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
Multiprocessor speed scaling for jobs with arbitrary sizes and deadlines
In this paper we study energy efficient deadline scheduling on multiprocessors in which the processors consumes power at a rate of sα when running at speeds, where α ℠2. The problem is to dispatch jobs to processors and determine the speed and jobs to run for each processor so as to complete all jobs by their deadlines using the minimum energy. The problem has been well studied for the single processor case. For the multiprocessor setting, constant competitive online algorithms for special cases of unit size jobs or arbitrary size jobs with agreeable deadlines have been proposed by Albers et al. (2007). A randomized algorithm has been proposed for jobs of arbitrary sizes and arbitrary deadlines by Greiner et al. (2009). We propose a deterministic online algorithm for the general setting and show that it is O(logαP)-competitive, where P is the ratio of the maximum and minimum job size
Energy-efficient algorithms for non-preemptive speed-scaling
We improve complexity bounds for energy-efficient speed scheduling problems
for both the single processor and multi-processor cases. Energy conservation
has become a major concern, so revisiting traditional scheduling problems to
take into account the energy consumption has been part of the agenda of the
scheduling community for the past few years.
We consider the energy minimizing speed scaling problem introduced by Yao et
al. where we wish to schedule a set of jobs, each with a release date, deadline
and work volume, on a set of identical processors. The processors may change
speed as a function of time and the energy they consume is the th power
of its speed. The objective is then to find a feasible schedule which minimizes
the total energy used.
We show that in the setting with an arbitrary number of processors where all
work volumes are equal, there is a approximation algorithm, where
is the generalized Bell number. This is the first constant
factor algorithm for this problem. This algorithm extends to general unequal
processor-dependent work volumes, up to losing a factor of
in the approximation, where is the maximum
ratio between two work volumes. We then show this latter problem is APX-hard,
even in the special case when all release dates and deadlines are equal and
is 4.
In the single processor case, we introduce a new linear programming
formulation of speed scaling and prove that its integrality gap is at most
. As a corollary, we obtain a
approximation algorithm where there is a single processor, improving on the
previous best bound of
when
Throughput Maximization in Multiprocessor Speed-Scaling
We are given a set of jobs that have to be executed on a set of
speed-scalable machines that can vary their speeds dynamically using the energy
model introduced in [Yao et al., FOCS'95]. Every job is characterized by
its release date , its deadline , its processing volume if
is executed on machine and its weight . We are also given a budget
of energy and our objective is to maximize the weighted throughput, i.e.
the total weight of jobs that are completed between their respective release
dates and deadlines. We propose a polynomial-time approximation algorithm where
the preemption of the jobs is allowed but not their migration. Our algorithm
uses a primal-dual approach on a linearized version of a convex program with
linear constraints. Furthermore, we present two optimal algorithms for the
non-preemptive case where the number of machines is bounded by a fixed
constant. More specifically, we consider: {\em (a)} the case of identical
processing volumes, i.e. for every and , for which we
present a polynomial-time algorithm for the unweighted version, which becomes a
pseudopolynomial-time algorithm for the weighted throughput version, and {\em
(b)} the case of agreeable instances, i.e. for which if and only
if , for which we present a pseudopolynomial-time algorithm. Both
algorithms are based on a discretization of the problem and the use of dynamic
programming
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
Energy-Efficient Multiprocessor Scheduling for Flow Time and Makespan
We consider energy-efficient scheduling on multiprocessors, where the speed
of each processor can be individually scaled, and a processor consumes power
when running at speed , for . A scheduling algorithm
needs to decide at any time both processor allocations and processor speeds for
a set of parallel jobs with time-varying parallelism. The objective is to
minimize the sum of the total energy consumption and certain performance
metric, which in this paper includes total flow time and makespan. For both
objectives, we present instantaneous parallelism clairvoyant (IP-clairvoyant)
algorithms that are aware of the instantaneous parallelism of the jobs at any
time but not their future characteristics, such as remaining parallelism and
work. For total flow time plus energy, we present an -competitive
algorithm, which significantly improves upon the best known non-clairvoyant
algorithm and is the first constant competitive result on multiprocessor speed
scaling for parallel jobs. In the case of makespan plus energy, which is
considered for the first time in the literature, we present an
-competitive algorithm, where is the total number of
processors. We show that this algorithm is asymptotically optimal by providing
a matching lower bound. In addition, we also study non-clairvoyant scheduling
for total flow time plus energy, and present an algorithm that achieves -competitive for jobs with arbitrary release time and
-competitive for jobs with identical release time. Finally,
we prove an lower bound on the competitive ratio of
any non-clairvoyant algorithm, matching the upper bound of our algorithm for
jobs with identical release time
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 Transaction Scheduling in Data Systems
Natural short term fluctuations in the load of transactional data systems present an opportunity for power savings. For example, a system handling 1000 requests per second on average can expect more than 1000 requests in some seconds, fewer in others. By quickly adjusting processing capacity to match such fluctuations, power consumption can be reduced. Many systems do this already, using dynamic voltage and frequency scaling (DVFS) to reduce processor performance and power consumption when the load is low.
DVFS is typically controlled by frequency governors in the operating system or by the processor itself. The work presented in this dissertation shows that transactional data systems can manage DVFS more effectively than the underlying operating system. This is because data systems have more information about the workload, and more control over that workload, than is available to the operating system.
Our goal is to minimize power consumption while ensuring that transaction requests meet specified latency targets. We present energy-efficient scheduling algorithms and systems that manage CPU power consumption and performance within data systems. These algorithms are workload-aware and can accommodate concurrent workloads with different characteristics and latency budgets.
The first technique we present is called POLARIS. It directly manages processor DVFS and controls database transaction scheduling. We show that POLARIS can simultaneously reduce power consumption and reduce missed latency targets, relative to operating-system-based DVFS governors.
Second, we present PLASM, an energy-efficient scheduler that generalizes POLARIS to support multi-core, multi-processor systems. PLASM controls the distribution of requests to the processors, and it employs POLARIS to manage power consumption locally at each core. We show that PLASM can save power and reduce missed latency targets compared to generic routing techniques such as round-robin