**7. Conclusion and future works**

In this chapter, we presented a policy for deciding the assignment unit size to a processor and a task clustering for processor utilization in heterogeneous distributed systems. We defined the indicative value for the schedule length for heterogeneous distributed systems. Then we theoretically proved that minimizing the indicative value leads to minimization of the schedule length. Furthermore, we defined the lower bound of the cluster size by assuming the initial mapping state. From the experimental results, it is concluded that minimizing the indicative value has good effect on the schedule length. However, we found that the lower bound of the cluster size should be adjusted with taking an assigned processor's ability into account.

As a future work, we will study on how to adjust the lower bound of the cluster size for obtaining the better schedule length and more effective processor utilization.

### **8. References**

A. Gerasoulis and T. Yang., A Comparison of Clustering Heuristics for Scheduling Directed Acyclic Graphs on Multiprocessors, *Journal of Parallel and Distributed Computing*, Vol. 16, pp. 276-291, 1992.

**Section 2** 

**Advances in Grid Computing -** 

**Resources Management** 

