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

2026-02-08

AI Summary

This work addresses the challenge of quantifying how network topology influences fairness in Quality of Experience (QoE), particularly in the absence of theoretical tools linking Service Level Agreement (SLA) parameters to QoE fairness. Leveraging spectral graph theory, the paper establishes—for the first time—an analytical relationship between a QoE imbalance index and network topology, proposing a unified exponential spectral upper bound that jointly characterizes SLA constraints and topological bottlenecks. This bound reveals a bottleneck effect wherein QoE fairness is governed by the weaker of two factors: SLA strictness and the network’s spectral gap. Moreover, it exhibits an exponential decay with increasing network size and connectivity. Extensive simulations on both random graph models and real-world topologies confirm the universality of the proposed bound, offering a theoretical foundation and optimization pathway for QoE-fairness-oriented inverse network design.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Evaluation and Analysis
• Game Theory and Economic Paradigms: Fair Division

Application Category

• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• QoE fairness
• spectral graph theory
• wireless communication networks
• SLA sensitivity
• network topology

Innovation

• spectral graph theory
• QoE fairness
• exponential spectral bound
• bottleneck effect
• network topology