Effective task scheduling is crucial for achieving good performance in high performance computing. Many scheduling algorithms have been devised for heterogeneous computing and CPOP is one of the scheduling algorithms. In this paper we present new scheduling algorithms, CPOC and CPOC_E by modifying the CPOP. We use a cluster of processors for critical-path tasks while a single processor is used in the CPOP. This heuristic is useful for realistic Grid computing environments in which communication costs are not arbitrarily heterogeneous. In an additional heuristic the critical-path tasks are considered to finish (or start) as early as possible when non critical-path tasks are scheduled. For performance study we developed a task graph generator and a tool which would support more realistic network configuration. The experimental results show our scheduling algorithm outperforms the CPOP as well as the HEFT.
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