Scheduling multiple divisible loads on a linear processor network

Min, Veeravalli, and Barlas have recently proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments [18, 19]. We show on a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal scheduling for any instance, once the number of installments per load is given. Then, we formally prove that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in [18, 19]. Such a cost model cannot be used to design practical multi-installment strategies. Finally, through extensive simulations we confirmed that the best solution is always produced by the linear programming approach.