Capacity Costs of Probability Ambiguity and Support Rectangularization in Edge–Cloud Scheduling
- 1School of Computer Science and Engineering, Yeungnam University, Gyeongsan 38541, Republic of Korea
- 2Department of Information and Communication Engineering, Yeungnam University, Gyeongsan 38541, Republic of Korea
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.
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BibTeX
@article{salim2026capacity,
title = {{Capacity Costs of Probability Ambiguity and Support Rectangularization in Edge–Cloud Scheduling}},
author = {Mikail Mohammed Salim and Farheen Naaz},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203821},
url = {https://www.mdpi.com/2227-7390/14/20/3821},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Capacity Costs of Probability Ambiguity and Support Rectangularization in Edge–Cloud Scheduling
AU - Mikail Mohammed Salim
AU - Farheen Naaz
PY - 2026
DA - 2026/10/20
JO - Mathematics
DO - 10.3390/math14203821
UR - https://www.mdpi.com/2227-7390/14/20/3821
AB - 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.
SN - 2227-7390
ER -