Replicated Data Placement for Uncertain Scheduling

Scheduling theory is a common tool to analyze the performance of parallel and distributed computing systems, such as their load balance. How to distribute the input data to be able to execute a set of tasks in a minimum amount of time can be modeled as a scheduling problem. Often these models assume that the computation time required for each task is known accurately. However in many practical case, only approximate values are available at the time of scheduling. In this paper, we investigate how replicating the data required by the tasks can help coping with the inaccuracies of the processing times. In particular, we investigate the problem of scheduling independent tasks to optimize the make span on a parallel system where the processing times of the tasks are only known up to a multiplicative factor. The problem is decomposed in two phases: a first offline phase where the data of the tasks are placed and a second online phase where the tasks are actually scheduled. For this problem we investigate three different strategies, each allowing a different degree of replication of tasks: a) No Replication b) Replication everywhere and c) Replication in groups. We propose approximation algorithms and theoretical lower bound on achievable approximation ratios. This allows us to study the trade off between the number of replication and the guarantee on the makespan.