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We consider updating strategies for a local cache which downloadstime-sensitive files from a remote server through a bandwidth-constrained link.The files are requested randomly from the cache by local users according to apopularity distribution which varies over time according to a Markov chainstructure. We measure the freshness of the requested time-sensitive filesthrough their Age of Information (AoI). The goal is then to minimize theaverage AoI of all requested files by appropriately designing the local cache'sdownloading strategy. To achieve this goal, the original problem is relaxed andcast into a Constrained Markov Decision Problem (CMDP), which we solve using aLagrangian approach and Linear Programming. Inspired by this solution for therelaxed problem, we propose a practical cache updating strategy that meets allthe constraints of the original problem. Under certain assumptions, thepractical updating strategy is shown to be optimal for the original problem inthe asymptotic regime of a large number of files.  For a finite number of files, we show the gain of our practical updatingstrategy over the traditional square-root-law strategy (which is optimal forfixed non time-varying file popularities) through numerical simulations.

Cache Updating Strategy Minimizing the Age of Information with Time-Varying Files' Popularities