Scheduling multiple divisible loads on a linear processor network

TL;DR

This paper critically evaluates existing strategies for scheduling divisible loads on linear networks, demonstrating their limitations and proposing an optimal solution approach that outperforms previous methods in efficiency and accuracy.

Contribution

It provides a formal analysis showing the inadequacy of previous models and introduces an optimal scheduling method based on linear programming for divisible loads.

Findings

Previous strategies can be suboptimal or infeasible.

Optimal schedules involve infinite installments under the linear cost model.

Linear programming yields the best solutions in simulations.

Abstract

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. 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 schedule for any instance, once the number of installments per load is given. Then, we formally state that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in the original papers. Therefore, 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, while solutions of the original papers can be far away from the optimal.