9,957 research outputs found
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
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
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
Speed Scaling for Energy Aware Processor Scheduling: Algorithms and Analysis
We present theoretical algorithmic research of processor scheduling in an energy aware environment using the mechanism of speed scaling. We have two main goals in mind. The first is the development of algorithms that allow more energy efficient utilization of resources. The second goal is to further our ability to reason abstractly about energy in computing devices by developing and understanding algorithmic models of energy management. In order to achieve these goals, we investigate three classic process scheduling problems in the setting of a speed scalable processor.
Integer stretch is one of the most obvious classical scheduling objectives that has yet to be considered in the speed scaling setting. For the objective of integer stretch plus energy, we give an online scheduling algorithm that, for any input, produces a schedule with integer stretch plus energy that is competitive with the integer stretch plus energy of any schedule that finishes all jobs.
Second, we consider the problem of finding the schedule, S, that minimizes some quality of service objective Q plus B times the energy used by the processor. This schedule, S, is the optimal energy trade-off schedule in the sense that: no schedule can have better quality of service given the current investment of energy used by S, and, an additional investment of one unit of energy is insufficient to improve the quality of service by more than B. When Q is fractional weighted flow, we show that the optimal energy trade-off schedule is unique and has a simple structure, thus making it easy to check the optimality of a schedule. We further show that the optimal energy trade-off schedule can be computed with a natural homotopic optimization algorithm.
Lastly, we consider the speed scaling problem where the quality of service objective is deadline feasibility and the power objective is temperature. In the case of batched jobs, we give a simple algorithm to compute the optimal schedule. For general instances, we give a new online algorithm and show that it has a competitive ratio that is an order of magnitude better than the best previously known for this problem
Models and algorithms for energy-efficient scheduling with immediate start of jobs
We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlogn) time in the single-machine case and in O(n²m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution
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