Eduard Malokhvii, Heorhii Kuchuk, Andrii Korobko, Nataliia Zhovnir, Serhii Oryshchenko
The paper develops an integrated theoretical and mathematical framework for information processing on resource-limited Industrial Internet of Things (IIoT) end devices operating within cloud–fog–edge architectures. The study is motivated by heterogeneous, nonstationary event streams whose direct transmission to upper tiers is often infeasible due to bandwidth scarcity, strict latency targets, and the energy and computational limitations of end devices. Consequently, the end device must execute sensing-driven preprocessing, manage finite-buffer queues, and regulate outgoing traffic while preserving the informativeness required for monitoring, control, and analytics. The proposed formalization treats the end device as an active decision node that shapes system dynamics by controlling local transformations and offloading decisions under time-varying resource conditions. A class- and priority-aware stream model captures heterogeneity in criticality and service requirements, while finite-buffer queueing dynamics represent delay and loss under bursty arrivals and constrained service capacity. The device state is described by a resource vector reflecting available CPU capacity, memory and buffer occupancy, channel quality and transmission rate, and energy-related limitations, enabling state-dependent admissibility conditions for local computation and communication. An operator-level processing chain systematizes the end-device reduction pipeline, including preprocessing, informativeness assessment, adaptive filtering, temporal and semantic aggregation, controlled compression, and compact feature formation. The chain produces structured, semantically annotated packets supporting lightweight local decision-making and selective offloading to fog or cloud tiers. A multi-criteria efficiency structure is specified to jointly account for latency, packet loss, energy expenditure, communication load, and informativeness preservation, thereby enabling Pareto-oriented synthesis of admissible adaptive policies. The research objective is to establish unified decision variables, constraints, and stability and feasibility conditions coupling queue behavior with resource limitations, providing an analytically traceable basis for subsequent method construction, parameter tuning, and scenario-driven validation in realistic industrial environments. Unlike purely empirical benchmarking, the contribution is intentionally analytical: it consolidates fragmented models of local reduction and offloading, and exposes explicit operator definitions for reproducible analysis.