Formalization and quantitative metrics for functional stability of edge computing systems

Edge computing systems operate in conditions where component failures, intermittent backhaul connectivity, resource exhaustion and adversarial disturbances are part of the normal operating envelope rather than rare events. Classical reliability and fault-tolerance models, oriented toward monolithic systems and binary working/failed states, do not capture the differentiated quality requirements of services co-located on a resource-constrained edge node. This article proposes a formal framework of functional stability that shifts the unit of analysis from the system to the individual function. Strong and weak forms of stability are defined through a continuous quality function and per-function quality thresholds. A system of base parameters (disturbance tolerance, recovery time, degradation depth, admissible degradation) and aggregate metrics (cumulative quality, functional availability, integral stability) is introduced and connected to the formal definitions by nine theorems. The framework is instantiated for edge computing scenarios and illustrated through two analytical case studies: a UAV swarm and an edge AI inference service with cloud fallback. The proposed metrics distinguish architectural alternatives that classical availability cannot separate and expose the dependence of architectural ranking on the explicitly selected disturbance-class set.