Fault tolerant scheduling of tasks of two sizes under resource augmentation

• Published in: Journal of scheduling Vol. 20; no. 6; pp. 695 - 711
• Main Authors: Kowalski, Dariusz R., Wong, Prudence W. H., Zavou, Elli
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-12-2017; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Augmentation; Business and Management; Calculus of Variations and Optimal Control; Optimization; Computation; Crashes; Fault tolerance; Microprocessors; Operations Research/Decision Theory; Optimization; Production scheduling; Scheduling algorithms; Supply Chain Management; Task scheduling; Resource augmentation; Online algorithms; Adversarial failures; Scheduling; Competitive analysis; Task sizes
• ISSN: 1094-6136; 1099-1425
• DOI: 10.1007/s10951-017-0541-1

Guaranteeing the eventual execution of tasks in machines that are prone to unpredictable crashes and restarts may be challenging, but is also of high importance. Things become even more complicated when tasks arrive dynamically and have different computational demands, i.e., processing time (or sizes). In this paper, we focus on the online task scheduling in such systems, considering one machine and at least two different task sizes. More specifically, algorithms are designed for two different task sizes while the complementary bounds hold for any number of task sizes bigger than one. We look at the
latency
and 1-
completed load
competitiveness properties of deterministic scheduling algorithms under worst-case scenarios. For this, we assume an
adversary
, that controls the machine crashes and restarts as well as the task arrivals of the system, including their computational demands. More precisely, we investigate the effect of
resource augmentation
—in the form of processor speedup—in the machine’s performance, by looking at the two efficiency measures for different speedups. We first identify the threshold of the speedup under which competitiveness cannot be achieved by any deterministic algorithm, and above which there exists some deterministic algorithm that is competitive. We then propose an online algorithm, named
γ
-Burst
, that achieves both latency and 1-completed-load competitiveness when the speedup is over the threshold. This also proves that the threshold identified is also sufficient for competitiveness.