Design and analysis of load distribution strategies with start-up costs in scheduling divisible loads on distributed networks

Optimal distribution of divisible loads in bus and linear networks is considered in this paper. The problem of minimizing the processing time is investigated by including all the overhead components that could penalize the performance of the system, in addition to the inherent communication and computation delays. In the case of bus networks, closed-form solutions for the processing time are derived and the influence of overheads on the optimal processing time is analyzed. For the first time in this domain of research, the concept of sequencing is realized for the case of bus networks. Through rigorous analysis, an optimal sequence to distribute the load among the processors is identified, whenever it exists. In the case when such an optimal sequence fails to exist, we present an O(m) greedy algorithm to obtain a suboptimal sequence based on some important properties of the overhead factors. In the case of linear networks, we consider two different scenarios, namely, when the processors are equipped with front-end and when they are not equipped with front-end. As in the case of bus networks, here too, necessary and sufficient conditions for the existence of optimal processing time are derived and performance study is carried out. Numerical examples are presented to illustrate the concepts.