Spectral Graph Analysis for Predicting QoE Fairness Sensitivity in Wireless Communication Networks

TL;DR

This paper introduces a spectral graph theory-based method to predict how network topology influences QoE fairness sensitivity, revealing an exponential decay behavior and bottleneck effects that guide resource optimization.

Contribution

It proves a novel exponential spectral upper bound linking network topology and QoE fairness sensitivity, unifying service parameters and network structure in a single analytical framework.

Findings

Exponential decay of QoE fairness improvement above a performance threshold.

Fairness ceiling is determined by the weaker link between SLA stringency and spectral gap.

The spectral bound is validated across various network topologies.

Abstract

The evaluation of Quality of Experience (QoE) fairness depends not only on its current state but, more critically, on its sensitivity to changes in Service Level Agreement (SLA) parameters. However, the academic community has long lacked a predictive method connecting underlying topology to high-level service fairness. To bridge this gap, this paper analyzes a QoE imbalance index ($I$) through the lens of spectral graph theory.Our core contribution is the proof of a novel exponential spectral upper bound. This bound reveals that the improvement of QoE fairness exhibits an exponential decay behavior only above a performance threshold determined jointly by network size and connectivity. Its core decay rate is dominated by the weaker of two factors: the SLA stringency ($a$) and the network's spectral gap ($c\lambda_2$). The upper bound unifies the service protocol and the topological bottleneck within a single performance bound formula for the first time.This theoretical relationship also reveals a clear bottleneck effect, where the system's fairness ceiling is determined by the weaker link between service parameters and network structure. This finding provides a bottleneck-driven principle for resource optimization in network design and enables goal-driven reverse engineering. Extensive numerical experiments on various random graph models and real-world network topologies robustly validate the correctness and universality of our analytical framework.