Virtual Screening in a Desktop Grid: Replication and the Optimal Quorum

We propose a mathematical model of a desktop grid computing system that solves tasks with two possible answers. Replication is used in order to reduce the error risk: wrong answers are returned with some known probabilities and penalty is added to the calculation cost in case of an error. We solve the optimization problems to determine the optimal quorum for tasks of varying duration. Beside the general case, we consider reliable answers of one kind. We apply the model to the problem of virtual screening and show how replication reduces the average cost. Also we demonstrate that when penalties are close to but lower than the critical values, taking different duration of tasks into account significantly reduces the penalty threat at very low additional cost.