Tolerating faults while maximizing reward

The imprecise computation (IC) model is a general scheduling framework that is capable of expressing the precision vs. timeliness tradeoff involved in many current real-time applications. In that model, each task comprises mandatory and optional parts. While allowing greater scheduling flexibility, the mandatory parts in the IC model still have hard deadlines, and hence they must be completed before the task's deadline, even in the presence of faults. In this paper, we address fault-tolerant (FT) scheduling issues for IC tasks. First, we propose two recovery schemes, namely immediate recovery and delayed recovery. These schemes can be readily applied to provide fault tolerance to the mandatory parts by scheduling the optional parts appropriately for recovery operations. After deriving the necessary and sufficient conditions for both schemes, we consider the FT-optimality problem, i.e. generating a schedule which is FT and whose reward is maximum among all possible FT schedules. For immediate recovery, we present and prove the correctness of an efficient FT-optimal scheduling algorithm. For delayed recovery, we show that the FT-optimality problem is NP-hard, and thus is intractable.