Fault-Tolerant Parallel Execution of Workflows with Deadlines

Workflows of dependent tasks are a widespread model for parallel applications, often statically scheduled prior to application. Static schedules can tolerate processor failures due to permanent faults by placing duplicate tasks during the scheduling process. Schedules for workflows with deadlines can be extended to include frequency scaling information to optimize energy consumption. Frequency scaling can also be used in case of a fault to minimize its effects on the schedule makespan, however for the price of additional energy consumption. We investigate the interplay between these two parameters and quantify the energy increase to be expected in case of a fault and a given makespan increase. This knowledge enables the user to inform the scheduler about the makespan increase that is tolerable in case of a fault, where tolerable includes both the related performance aspects and the expected increase in energy. To achieve this, we model small taskgraphs from a benchmark suite as integer linear programs and determine with the help of a solver energy-optimal schedules for the fault-free case and for all possible fault positions with several levels of makespan increase. We present averages and distribution depending on makespan increase for a processor with hypothetical power profile. Additionally, we present two heuristics to modify task frequency settings in case of a fault, to restrict the makespan increase to a given value. Comparison with optimal frequency settings from the benchmark suite indicate that the heuristics only incur a small energy overhead.