Capacity Costs of Probability Ambiguity and Support Rectangularization in Edge–Cloud Scheduling
Year: 2026
Type: article
Abstract: Edge–cloud task scheduling reserves uplink capacity before the wireless service state is known. The reserve depends on both the probability law over a prescribed service-state library and the geometry representing that library. This study separates and quantifies these two effects in a fixed-workload finite-state model. We eliminate post-state bandwidth–CPU recourse exactly, derive a quadratic capacity representation in inverse-square-root spectral efficiencies, and compare empirical (EMP), Wasserstein, hard-support (HARD), and rectangular (BOX) uncertainty models under schedule reoptimization. The analysis yields an exact support-rectangularization premium, a resource-weighted joint-extreme deficit with a relative-cost factor below two, a sandwich bound on the optimized premium, and a finite hardening radius for chance-constrained capacity. Across 60 instances, mean savings from retaining joint support are 6.45–9.32% relative to rectangular protection. Across 20 instances, mean relative increases are 7.39–10.82% for EMP-to-HARD, 8.80–9.26% for support rectangularization, and 16.98–20.89% for EMP-to-BOX; all are deterministic optimization bounds. Positive lower bounds persist for both changed-target workloads, all nine nested-support cases, and both probability-side variations, while intermediate Wasserstein capacity changes under the alternative transport metric. Probability protection and support geometry impose distinct, quantifiable capacity costs.
Source: Mathematics
DOI: 10.3390/math14203821
Authors: Mikail Mohammed Salim, Farheen Naaz
Institution: Yeungnam University
Language: English
Topic: IoT and Edge/Fog Computing
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7223056876