Closed form solutions for bus and tree networks of processors load sharing a divisible job

Optimal load allocation for load sharing a divisible job over processors interconnected in either a bus or a tree network is considered. The processors are either equipped with front-end processors or not so equipped. Closed form solutions for the minimum finish time and the optimal data allocation for each processor are obtained. The performance of large symmetric tree networks is examined by aggregating the component links and processors into a single equivalent processor. This allows an easy examination of large tree networks. In addition, it becomes possible to find a closed form solution for the optimal amount of data that is to be assigned to each processor in the tree network in order to achieve the minimum finish time