Load Partitioning and Trade-Off Study for Large Matrix-Vector Computations in Multicast Bus Networks with Communication Delays

In this paper we consider the problem of computing a large matrix-vector product in a network-based distributed computing environment comprising computers equipped with communication co-processors that may be used for communication off-loading. Communication delays, which are significant in such systems, are specifically taken into account. The important contribution of this study is to show that the optimal load partitioning, and the subsequent performance of the network, depends critically on many network parameters and load characteristics. In particular, it is shown that the size of the load plays an important role in determining the performance of the network. We consider only row-wise striping of the matrix in order to better allocate the computational burden among the processors. We derive closed-form solutions to the optimal load partitioning problem and show the existence of optimal load sharing conditions. An important and practically relevant trade-off study, from the architecture point of view, between the number of processors and the bus bandwidth is presented. Several practical load distribution strategies are considered and complete analyses for each of them is presented