Industrial Fog computing deploys various industrial services, such as automatic monitoring/control and imminent failure detection, at the Fog Nodes (FNs) to improve the performance of industrial systems. Much effort has been made in the literature on the design of fog network architecture and computation offloading. This paper studies an equally important but much less investigated problem of service hosting where FNs are adaptively configured to host services for Sensor Nodes (SNs), thereby enabling corresponding tasks to be executed by the FNs. The problem of service hosting emerges because of the limited computational and storage resources at FNs, which limit the number of different types of services that can be hosted by an FN at the same time. Considering the variability of service demand in both temporal and spatial dimensions, when, where, and which services to host have to be judiciously decided to maximize the utility of the Fog computing network. Our proposed Fog configuration strategies are tailored to battery-powered FNs. The limited battery capacity of FNs creates a long-term energy budget constraint that significantly complicates the Fog configuration problem as it introduces temporal coupling of decision making across the timeline. To address all these challenges, we propose an online distributed algorithm, called Adaptive Fog Configuration (AFC), based on Lyapunov optimization and parallel Gibbs sampling. AFC jointly optimizes service hosting and task admission decisions, requiring only currently available system information while guaranteeing close-to-optimal performance compared to an oracle algorithm with full future information.
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