Online Non-preemptive Scheduling on Unrelated Machines with Rejections

Abstract

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be incurred from the expensive task of saving the memory’s state or from loading data into and out of memory. Thus, it is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers for desktops, servers, and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive online schedulers are known to have strong theoretical guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst-case analysis approaches, and even resource-augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This article considers online non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this article shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the article presents algorithms for the following three objectives: minimizing the total flow-time, minimizing the total weighted flow-time plus energy where energy is a convex function, and minimizing the total energy under the deadline constraints. The algorithms for the first two problems have a small constant competitive ratio while rejecting only a constant fraction of jobs. For the last problem, we present a constant competitive ratio without rejection. Beyond specific results, the article asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive.

Two-Agent Scheduling with Resource Augmentation on Multiple Machines

“…Going further with the model, we believe it is possible to remove the speed augmentation, which is only used in the algorithm's analysis, as it was successfully done in another work on a single agent problem with on-line tasks [17]. Another interesting perspective is to extend the model to the weighted case, or with related/unrelated machines.…”

“…In the context of scheduling on a single machine, Feng et al [11] studied the common two-agent problem of Agnetis et al with the additional feature that jobs can be rejected with a given penalty to the objective value of the corresponding agent. In the on-line setting, Lucarelli et al also introduced the speed augmentation and rejection models to the total (weighted) flow-time minimization problem on unrelated [20,17,18] and related machines [19]. The authors proposed several algorithms whose competitiveness was proved using the dual fitting technique.…”