BSTL: Bayesian Signal Temporal Logic for Predictive Edge Service Monitoring

Edge service monitoring is crucial for ensuring the robustness and reliability of service executions. Predictive monitoring, in particular, enables proactive detection of potential service violations. Existing predictive monitoring approaches, often leveraging Signal Temporal Logic (STL) for requirement specification, primarily focus on deterministic signals, and thus, lack probabilistic guarantees for uncertainty interpretation. To address these challenges, this paper introduces Bayesian STL (BSTL), an extension of STL that enables probabilistic reasoning over stochastic signals. Specifically, Bayesian Neural Networks (BNNs) are utilized to transform deterministic sequential predictions into sequences of posterior probability distributions. 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, wherein service constraints are formally specified by BSTL formulae and interpreted with both qualitative and quantitative semantics. Besides, confidence levels and constraint thresholds ensuring robust satisfaction of BSTL formulae are rigorously estimated. Extensive experiments on publicly available datasets demonstrate that BSTL outperforms baseline techniques in expressiveness, robustness, and applicability.