43 research outputs found
Power-Aware Speed Scaling in Processor Sharing Systems
Energy use of computer communication systems has quickly become a vital design consideration. One effective method for reducing energy consumption is dynamic speed scaling, which adapts the processing speed to the current load. This paper studies how to optimally scale speed to balance mean response time and mean energy consumption under processor sharing scheduling. Both bounds and asymptotics for the optimal speed scaling scheme are provided. These results show that a simple scheme that halts when the system is idle and uses a static rate while the system is busy provides nearly the same performance as the optimal dynamic speed scaling. However, the results also highlight that dynamic speed scaling provides at least one key benefit - significantly improved robustness to bursty traffic and mis-estimation of workload parameters
A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State
We study classical deadline-based preemptive scheduling of tasks in a
computing environment equipped with both dynamic speed scaling and sleep state
capabilities: Each task is specified by a release time, a deadline and a
processing volume, and has to be scheduled on a single, speed-scalable
processor that is supplied with a sleep state. In the sleep state, the
processor consumes no energy, but a constant wake-up cost is required to
transition back to the active state. In contrast to speed scaling alone, the
addition of a sleep state makes it sometimes beneficial to accelerate the
processing of tasks in order to transition the processor to the sleep state for
longer amounts of time and incur further energy savings. The goal is to output
a feasible schedule that minimizes the energy consumption. Since the
introduction of the problem by Irani et al. [16], its exact computational
complexity has been repeatedly posed as an open question (see e.g. [2,8,15]).
The currently best known upper and lower bounds are a 4/3-approximation
algorithm and NP-hardness due to [2] and [2,17], respectively. We close the
aforementioned gap between the upper and lower bound on the computational
complexity of speed scaling with sleep state by presenting a fully
polynomial-time approximation scheme for the problem. The scheme is based on a
transformation to a non-preemptive variant of the problem, and a discretization
that exploits a carefully defined lexicographical ordering among schedules
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 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
Speed scaling for weighted flow time
Intel's SpeedStep and AMD's PowerNOW technologies allow the Windows XP operating system to dynamically change the speed of the processor to prolong battery life. In this setting, the operating system must not only have a job selection policy to determine which job to run, but also a speed scaling policy to determine the speed at which the job will be run. We give an online speed scaling algorithm that is O(1)-competitive for the objective of weighted flow time plus energy. This algorithm also allows us to efficiently construct an O(1)-approximate schedule for minimizing weighted flow time subject to an energy constraint
Online Primal-Dual For Non-linear Optimization with Applications to Speed Scaling
We reinterpret some online greedy algorithms for a class of nonlinear
"load-balancing" problems as solving a mathematical program online. For
example, we consider the problem of assigning jobs to (unrelated) machines to
minimize the sum of the alpha^{th}-powers of the loads plus assignment costs
(the online Generalized Assignment Problem); or choosing paths to connect
terminal pairs to minimize the alpha^{th}-powers of the edge loads (online
routing with speed-scalable routers). We give analyses of these online
algorithms using the dual of the primal program as a lower bound for the
optimal algorithm, much in the spirit of online primal-dual results for linear
problems.
We then observe that a wide class of uni-processor speed scaling problems
(with essentially arbitrary scheduling objectives) can be viewed as such load
balancing problems with linear assignment costs. This connection gives new
algorithms for problems that had resisted solutions using the dominant
potential function approaches used in the speed scaling literature, as well as
alternate, cleaner proofs for other known results