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 ($cλ_2$). 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.

翻译：体验质量公平性的评估不仅取决于其当前状态，更关键的是其对服务等级协议参数变化的敏感度。然而，学术界长期缺乏一种将底层拓扑结构与高层服务公平性相联系的预测方法。为填补这一空白，本文通过谱图理论视角分析了QoE不均衡指数$I$。我们的核心贡献在于证明了一个新颖的指数谱上界。该上界表明，QoE公平性的改善仅在由网络规模与连通性共同决定的性能阈值之上呈现指数衰减行为。其核心衰减率由两个因素中较弱的一方主导：SLA严格度$a$与网络的谱隙$cλ_2$。该上界首次将服务协议与拓扑瓶颈统一于单一的性能边界公式中。这一理论关系同时揭示了清晰的瓶颈效应：系统的公平性上限由服务参数与网络结构间较薄弱的环节决定。该发现为网络设计中的资源优化提供了瓶颈驱动原则，并支持目标驱动的逆向工程。在各种随机图模型与真实网络拓扑上进行的大量数值实验，稳健地验证了我们分析框架的正确性与普适性。