EMPIRICAL ESTIMATION OF PARAMETERS OF THE GENERALIZED AMDAHL’S LAW IN WEB INTERFACES

Abstract

The article presents a reproducible methodology for empirical estimation of the parameters of a generalized Amdahl’s law for web interfaces, with a focus on percentile UX metrics. A multi-resource model of the critical path is proposed with stage shares α (network, JS/CPU, rendering, etc.), local speedups s for individual optimization techniques, and explicit non-additivity via interaction multipliers κ. Parameter identification is implemented on the basis of two-level factorial designs  and regression in the log space of percentiles log(P95) with stratum covariates (device class, network type, cache state). Operationalization of α is performed from Chrome trace/HAR via a robust time breakdown; estimation of s is carried out using on/off pairs and, where necessary, a difference-in-differences scheme on field (RUM) data. Forecast quality is assessed using MAPE and RMSE in log scale; uncertainty is quantified via bootstrap intervals; fact-to-forecast calibration checks bias and scale. On representative user journeys (a hero-image page and a list interface) it is shown that pairwise optimization interactions substantially affect  and , and that explicit modeling of κ reduces prediction error compared to additive assumptions. Typical errors of 6–9% are obtained for percentile metrics with correct scale calibration, which is sufficient to include the estimated (α, s, κ) in percentile-forecasting procedures and in planning “packages” of changes within CI cycles. The practical significance lies in the transition from heuristic tuning to quantitatively justified selection of optimizations with transparent interpretation of contributions and interactions. The scientific novelty consists in combining a multi-resource model with percentile regression and explicit non-additivity for industrial web systems.