Fault-tolerant real-time scheduling

Abstract

We use competitive analysis to study how to best use redundancy to achieve fault-tolerance in online real-time scheduling. We show that the optimal way to make use of spatial redundancy depends on a complex interaction of the benefits, execution times, release times, and latest start times of the jobs. We give a randomized online algorithm whose competitive ratio is $O(\log \Phi log\Delta \tfrac{{log^2 n\log m}}{{\log \log m}})$ for transient faults. Here n is the number of jobs present in the system at any one time, m is the number of processors, Φ is the ratio of maximum value density of a job to the minimum value density of a job, and Δ the ratio of the longest possible execution time to the shortest possible execution time. We show that this bound is close to optimal by giving an $\Omega (log\Delta \Phi (\tfrac{{logm}}{{loglogmloglog(m\Delta \Phi )}})^2 )$ lower bound on the competitive ratio of any randomized algorithm. In the case of permanent faults, there is a randomized online algorithm that has a competitive ratio of $O(\log \Phi log\Delta \tfrac{{\log m}}{{\log \log m}})$. We also show a lower bound of $\Omega (log\Delta \Phi \tfrac{{logm}}{{loglog(m\Delta \Phi )}})$ on the competitive ratio for interval scheduling with permanent faults.