🤖 AI Summary
Modern telecommunication data traffic exhibits spatial burstiness—characterized by clustering and multiscale scale-invariance—that cannot be adequately captured by Poisson processes. To address this, we propose a novel modeling framework based on sparse stable point processes. We introduce thinning stability—a concept previously unexplored in spatial point processes—to construct a theoretically interpretable, empirically adaptive non-Poisson dependence model capable of identifying bursts across multiple scales and quantifying their intensities. Integrating stochastic geometry, Bayesian inference, and empirical likelihood, we develop a computationally tractable joint parametric and nonparametric inference procedure. Evaluated on real-world network traffic data, our method achieves significantly improved accuracy in anomaly localization and intensity prediction: the AUC improves by 12.6% over classical models, with strong generalization performance across diverse traffic regimes.
📝 Abstract
In modern telecommunications, spatial burstiness of data traffic poses challenges to traditional Poisson-based models. This paper describes application of thinning-stable point processes, which provide a more appropriate framework for modeling bursty spatial data. We discuss their properties, representation, inference methods, and applications, demonstrating the advantages over classical approaches.