BSTL: Bayesian STL for Predictive Edge Service Monitoring with Probabilistic Guarantee

Edge service monitoring is essential for ensuring the robustness and efficiency of service executions, where predictive monitoring enables proactive detection of potential service violations. Current approaches for predictive monitoring, which mostly adopt Signal Temporal Logic (STL) specifications for requirements representation and evaluation, primarily focus on deterministic signals, and thus, may lack probabilistic guarantees for uncertainty interpretation. To address these challenges, this paper proposes Bayesian STL (BSTL), an extension of STL that enables probabilistic reasoning over stochastic signals. Specifically, Bayesian Neural Networks (BNNs) are employed to generate sequences of posterior probability distributions, offering more comprehensive predictive insights compared to traditional point- or interval-based methods with deterministic sequential predictions. Uncertainty interpretation over these distribution predictions is achieved by a novel expected robustness metric that jointly quantifies both the degree and probability of service satisfaction. Thereafter, a BSTL-based predictive monitoring framework is developed, where a service constraint is formally specified by a BSTL formula and interpreted with both qualitative and quantitative semantics. Besides, confidence levels and constraint thresholds ensuring robust satisfaction of a BSTL formula are rigorously estimated. Extensive experiments on publicly available datasets demonstrate that BSTL outperforms baseline techniques in terms of expressiveness, robustness, and applicability.