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<p>The problem of obtaining optimal processing time in a distributed computing systemconsisting 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 ahierarchy 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 computationalresults. In addition, it also extends these results to a more general framework. The aboveanalysis is carried out for the cases in which the root processor may or may not beequipped with a front-end processor. Illustrative examples are given for all casesconsidered.</p>
Index Termsresource allocation; distributed processing; optimisation; trees (mathematics); optimalsequencing; distributed single-level tree networks; communication delays; optimalprocessing time; distributed computing system; communication links; single-level treearchitecture; distributed processing; optimal load distribution; load sequencing;processor-link arrangement; closed-form expressions; general case; computationalresults; root processor; front-end processor; optimal arrangement

V. Bharadwaj, V. Mani and D. Ghose, "Optimal Sequencing and Arrangement in Distributed Single-Level Tree Networks with Communication Delays," in IEEE Transactions on Parallel & Distributed Systems, vol. 5, no. , pp. 968-976, 1994.
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