中文摘要：

基于可分任务理论，研究大规模计算中的应用调度问题。利用线性规划得到了周期性的多趟调度算法的数学模型。针对同构计算平台进行参数优化，得到如下解析结果：（1）在处理机选定的情况下得到优化的调度趟数；（2）在趟数给定的情况下得到优化的处理机选择方法；（3）对于给定的任务，得到优化的处理机选择方法和相应的趟数。仿真结果表明所得结果的正确性。

英文摘要：

To study large-scale application scheduling problem based on divisible load theory. We built an optimal model for periodic multi-installment algorithm by linear programming. For homogeneous systems, we derive closed-form expressions of optimal parameters. Analytical solutions are presented as follows： （1） for a given number of processors, optimal number of installments is derived; （2） for a given number of installments, the optimal number of processors is obtained; （3） for a given workload, the optimal number of involved processors and the according number of installments are achieved. The results are verified by simulations.