Optimal Time-Critical Scheduling via Resource Augmentation

Abstract

We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worst-case analysis, no good on-line algorithms exist for these problems, and for some variants no good off-line algorithms exist unless P = "P.We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the on-line algorithm is allowed more resources than the optimal off-line algorithm to which it is compared.Using this approach, we establish that several well-known on-line algorithms, that have poor performance from an absolute worst-case perspective, are optimal for the problems in question when allowed moderately more resources. For the optimization of average flow time, these are the first results of any sort, for any MP-hard version of the problem, that indicate that it might be possible to design good approximation algorithms.* caphillQcs.sandia.gov. DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any wamntyY express or implied, or assumes any legal tiability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disdased, or represents that its use wouid not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necesSarily state or reflect those of the United States Government or any agency thereof.

Meeting Deadlines: How Much Speed Suffices?

“…This is the first significant improvement since the seminal results in [8]. Our algorithm is best possible in the class of deadline ordered algorithms with respect to speed resource augmentation.…”

“…In fact, for m ≥ 2, there does not exist any optimal online algorithm [3]. To overcome this hardness, Phillips, Stein, Torng, and Wein [8] proposed the use of resource augmentation [5]: Given an online algorithm A we determine the speed s ≥ 1 such that A is optimal on m speed-s processors for any instance that is feasible for m processors of unit speed. We are interested in the smallest s for which…”

“…EDF is optimal on a single machine [2]. On m machines, speed s = 2 − 1/m is necessary and sufficient to guarantee its optimality [8]. Since its introduction more than a decade ago, this upper bound on the speed requirement for online algorithms has been improved only marginally.…”

“…The algorithm Least Laxity First (LLF) schedules at any point in time m jobs with minimum laxity among the available jobs. LLF is also optimal on a single machine [3], and more generally, it is optimal on m machines when running at speed 2 − 1/m [8]. In this paper we provide a lower bound on the speed required (Section 4) by demonstrating a feasible instance for which LLF requires a speed…”

A Constant-Approximate Feasibility Test for Multiprocessor Real-Time Scheduling

“…Regarding the analysis of EDF, it is known [12] that any feasible task system on m machines of unit capacity is EDF-schedulable on m machines of speed 2 − 1/m. This result holds for EDF and other policies and has not been improved since then.…”