Out-of-Core Divisible Load Processing

In this paper, we analyze processing divisible loads in systems with a memory hierarchy. Divisible loads are computations that can be divided into parts of arbitrary sizes and these parts can be independently processed in a distributed system. The problem is to partition the load so that the total processing time, including communications and computations, is the shortest possible. Earlier works in the divisible load theory assumed distributed systems with a flat memory model. The dependence of the processing time on the size of the assigned load was assumed to be linear. A new mathematical model relaxing the above two assumptions is proposed in this article. We study distributed systems which have both the hierarchical memory model and a piecewise linear dependence of the processing time on the size of the assigned load. Performance of such systems is modeled and evaluated. Finally, we compare the efficiency of distributed processing divisible loads in multiinstallment and out-of-core modes. Multiinstallment processing consists in sending multiple small chunks of the load to processors instead of a single chunk which needs external memory. It turns out that multiinstallment is an advantageous strategy for reasonably selected load chunks sizes.