Математична деревоподібна модель хмарних обчислень для білінгових систем

Abstract

The work synthesizes a mathematical apparatus for modeling hierarchical relationships in cloud billing architectures. A method for transforming dynamic graphs into static relational algebra objects has been developed, minimizing computational entropy and eliminating performance degradation typical of recursive queries. The mathematical justification for replacing iterative procedures with operations on typed vectors and composite type arrays provides a theoretical basis for constructing high-load systems with predictable response times. The proposed approach transforms tree traversal complexity into a logarithmic search within a denormalized rule space, making open-source RDBMS competitive with proprietary solutions in the financial sector.