Knowledge is Power: Online Performance of Non-uniform Tasks in Fault-prone Environments

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 work we explore the impact of parallelism and faults on the competitiveness of such a system. If the system had complete knowledge of future events and unbounded computation capability, it could make the best possible decisions and achieve optimal performance. Unfortunately, we show that no parallel deterministic algorithm can be competitive against the optimal solution provided in the idealistic scenario, even with tasks of only two different execution times. On the positive side, we show that providing additional energy to the system, in the form of processor speed-scaling, it is possible to develop deterministic algorithms that compare in favour to the optimal solution with complete knowledge. We identify thresholds on the speedup under which such competitiveness cannot be achieved by any deterministic algorithm and above which there exist competitive algorithms with small competitive ratio.