10,066 research outputs found
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
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
Order Acceptance and Scheduling: A Taxonomy and Review
Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area
Project portfolio management: capacity allocation, downsizing decisions and sequencing rules.
This paper aims to gain insight into capacity allocation, downsizing decisions and sequencing rules when managing a portfolio of projects. By downsizing, we mean reducing the scale or size of a project and thereby changing the project's content. In previous work, we have determined the amount of critical capacity that is optimally allocated to concurrently executed projects with deterministic or stochastic workloads when the impact of downsizing is known. In this paper, we extend this view with the possibility of sequential processing, which implies that a complete order is imposed on the projects. When projects are sequenced instead of executed in parallel, two effects come into play: firstly, unused capacity can be shifted to later projects in the same period; and secondly, reinvestment revenues gain importance because of the differences in realization time of the sequenced projects. When project workloads are known, only the second effect counts; when project workloads are stochastic, however, the project's capacity usage is uncertain so that unused capacity can be shifted to later projects in the same period. In this case, both effects need to be taken into account. In this paper, we determine optimal sequencing rules when the selection and capacity-allocation decisions for a set of projects have already been made. We also consider a combination of parallel and sequential planning and we perform simulation experiments that confirm the appropriateness of our capacity-allocation methods.Project portfolio management; Downsizing; Sequencing;
Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model
We consider the online scheduling problem to minimize the weighted ell_p-norm of flow-time of jobs. We study this problem under the rejection model introduced by Choudhury et al. (SODA 2015) - here the online algorithm is allowed to not serve an eps-fraction of the requests. We consider the restricted assignments setting where each job can go to a specified subset of machines. Our main result is an immediate dispatch non-migratory 1/eps^{O(1)}-competitive algorithm for this problem when one is allowed to reject at most eps-fraction of the total weight of jobs arriving. This is in contrast with the speed augmentation model under which no online algorithm for this problem can achieve a competitive ratio independent of p
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