MATHEMATICAL MODELLING OF CONTINUOUS OPTIMAL MULTILEVEL PARALLELING

摘要

A method of description and optimization of the continuous structure of hierarchical processing system is presented. The structure of the system is defined as a finite sequence of density functions of distributions. Each distribution will correspond to the connections between this and previous level and shows how the size of previous level is distributed between the sizes of this level. Corresponding optimization problem is a calculus of variations problem. Some reduced variants of this problem have good mathematical properties and is solved analytically. The approach is given in terms of convex analysis, integer programming and calculus of variations.