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Actual task execution models over the networked processors, e.g., cluster, grid and utility computing have been studied and developed for maximizing the system throughput by utilizing computational resources. One of major trends in task execution types is to divide the required data into several pieces and then distribute them to workers like "master-worker model". In contrast to such a data intensive job, how to divide a computational intensive job into several execution units for parallel execution is under discussion from theoretical points of view. If we take task parallelization into account in a grid environment such as a computational grid environment, an effective task scheduling strategy should be established. In the light of combining task scheduling concepts and grid computing methodologies, heterogeneity with respect to processing power, communication bandwidth and so on should be incorporated into a task scheduling strategy. If we assume the situationwheremultiple jobs are being submitted in the unknown number of computational resources over the Internet, objective functions can be considered as follows: (i) Minimization of the schedule length (the time duration from per each job, (ii) Minimization of the completion time of the last job, (iii) Maxmization of the degree of contribution to the total speed up ratio for each computational resources. As one solution for those three objective functions, in the literature(Kanemitsu, 2010) we proposed a method for minimizing the schedule length per one job with a small number of computational resources (processors) for a set of identical processors. The objective of the method is “utilization of computational resources”. The method is based on “task clustering” (A. Gerasoulis, 1992), in which tasks are merged into one “cluster” as an execution unit for one processor. As a result, several clusters are generated and then each of which becomes one assignment unit. The method proposes to impose the lower bound for every cluster size to limit the number of processors. Then the literature theoretically showed the near-optimal lower bound to minimize the schedule length.

On the Effect of Applying the Task Clustering for Identical Processor Utilization to Heterogeneous Systems