Optimal sequencing and arrangement in distributed single-level tree networks with communication delays

The problem of obtaining optimal processing time in a distributed computing system consisting of (N+1) processors and N communication links, arranged in a single-level tree architecture, is considered. It is shown that optimality can be achieved through a hierarchy of steps involving optimal load distribution, load sequencing, and processor-link arrangement. Closed-form expressions for optimal processing time is derived for a general case of networks with different processor speeds and different communication link speeds. Using these closed-form expressions, the paper analytically proves a number of significant results that in earlier studies were only conjectured from computational results. In addition, it also extends these results to a more general framework. The above analysis is carried out for the cases in which the root processor may or may not be equipped with a front-end processor. Illustrative examples are given for all cases considered