On the Worst Case of Scheduling with Task Replication on Computational Grids

We study the problem of scheduling tasks in a computational grid. We give analytical results for Workqueue with Replication (WQR) based algorithms. There are several works presenting simulation results for scheduling algorithms for computational grid, but few provide analytical evidence of the quality of the solution of these algorithms. In this paper we show that under the TPCC metric there is an optimal algorithm if the machines speed are predictable and tasks have the same length. If machines speed are not predictable we show an approximation result for the WQRxx algorithm and show that the result is tight. When tasks have different lengths the problem of minimizing the makespan does not admit an approximation algorithm, even when machines speed are predictable. On the other hand, we show that the WQR based algorithm is a m-approximation when minimizing the TPCC in the unpredictable case, and this result is tight. To finish we show how to add replication to any scheduling algorithm using a simple interface and present computational simulations comparing the quality of the solutions of some well know algorithms with the addition of replication.