Scaling Analysis of LLM Hardware Infrastructure through Uniform Estimates

Sharma, VA

doi:https://doi.org/10.55041/ijcope.v2i8.175

Volume 02, Issue 8

Published on: August 2026

SCALING ANALYSIS OF LLM HARDWARE INFRASTRUCTURE THROUGH UNIFORM ESTIMATES

VA Sharma

Dept. of mathematics ,Arts, commerce and science college, Amravati

DOI:https://doi.org/10.55041/ijcope.v2i8.175

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Abstract

As a methodological illustration we indicate how the same asymptotic and summation techniques supply analytic tools for the derivation of rigorous scaling laws that appear in performance models of GPU clusters, data-centre resource allocation, and the hardware infrastructure supply chains that underpin the training of large language models (LLMs). In this expanded version we develop these links further: the uniform bounds on the Macdonald kernel furnish a priori capacity and latency estimates for large GPU fleets; the Watson-type asymptotic describe the continuous-to-discrete transition that occurs when the number of accelerators tends to infinity; and the Poisson-type identities convert continuous resource integrals into discrete sums over GPU ranks, data-centre racks, or nodes of a global semiconductor supply chain. These analytic devices are shown to be formally analogous to the resilience and digital-twin frameworks that appear in the contemporary literature on infrastructure supply chains.

Keywords

Kontorovich–Lebedev transform; Watson lemma; asymptotic expansions; index transforms; scaling analysis; GPU clusters; data-centre infrastructure; LLM training systems: infrastructure supply chain; digital twins; supply-chain resilience.

How to Cite this Paper

Sharma, V. (2026). Scaling Analysis of LLM Hardware Infrastructure through Uniform Estimates. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.175

Sharma, VA. "Scaling Analysis of LLM Hardware Infrastructure through Uniform Estimates." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.175.

Sharma, VA. "Scaling Analysis of LLM Hardware Infrastructure through Uniform Estimates." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.175.

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•Published on: Aug 21 2026

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