We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the non-clairvoyant setting where the size of a job is only known when the job finishes. We show an online algorithm WLAPS that is 8α-competiti...

We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a O(logP )-competitive algorithm, where P is the maximum-to-minimum processing time ratio, improving upon theO(log P )-competitive algorithm of Chekuri, Khanna and Zhu (STOC 2001). We also design a O(logD)-competitive al...

In this paper we study some aspects of weighted flow time. We first show that the online algorithm Highest Density First is an O(1)-speed O(1)-approximation algorithm for P |ri ,pmtn| ∑ wiFi . We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any c-competitive online algori...

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 algorit...

Appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. One type of scheduling problems is just-in-time (JIT) scheduling and in this area, motivated by JIT manufacturing, this study investigates a mathematical model for...