Fog Radio Access Network (F-RAN) architectures can leverage both cloud processing and edge caching for content delivery to the users. To this end, F-RAN utilizes caches at the edge nodes (ENs) and fronthaul links connecting a cloud processor to ENs. Assuming time-invariant content popularity, existing information-theoretic analyses of content delivery in F-RANs rely on offline caching with separate content placement and delivery phases. In contrast, this work focuses on the scenario in which the set of popular content is time-varying, hence necessitating the online replenishment of the ENs caches along with the delivery of the requested files. The analysis is centered on the characterization of the long-term Normalized Delivery Time (NDT), which captures the temporal dependence of the coding latencies accrued across multiple time slots in the high signal-to-noise ratio regime. Online edge caching and delivery schemes are investigated for both serial and pipelined transmission modes across fronthaul and edge segments. Analytical results demonstrate that, in the presence of a time-varying content popularity, the rate of fronthaul links sets a fundamental limit to the long-term NDT of F- RAN system. Analytical results are further verified by numerical simulation, yielding important design insights.
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