Online Parallel Scheduling of Non-uniform Tasks: Trading Failures for Energy

TL;DR

This paper investigates how parallelism and failures affect online scheduling of tasks with different execution times, showing that increased energy via speedup enables competitive algorithms in fault-prone systems.

Contribution

It models the impact of failures and parallelism on online scheduling, identifying thresholds where competitiveness is achievable with speedup and proposing algorithms that attain bounded competitiveness.

Findings

Fault-free environment allows optimal scheduling with redundancy avoidance.

Failures prevent deterministic algorithms from being competitive without speedup.

Speedup thresholds determine when competitive algorithms are possible.

Abstract

Consider a system in which tasks of different execution times arrive continuously and have to be executed by a set of processors that are prone to crashes and restarts. In this paper we model and study the impact of parallelism and failures on the competitiveness of such an online system. In a fault-free environment, a simple Longest-in-System scheduling policy, enhanced by a redundancy-avoidance mechanism, guarantees optimality in a long-term execution. In the presence of failures though, scheduling becomes a much more challenging task. In particular, no parallel deterministic algorithm can be competitive against an offline optimal solution, even with one single processor and tasks of only two different execution times. We find that when additional energy is provided to the system in the form of processor speedup, the situation changes. Specifically, we identify thresholds on the speedup under which such competitiveness cannot be achieved by any deterministic algorithm, and above which competitive algorithms exist. Finally, we propose algorithms that achieve small bounded competitive ratios when the speedup is over the threshold.