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In this paper, we investigate a cache updating system with a servercontaining $N$ files, $K$ relays and $M$ users. The server keeps the freshestversions of the files which are updated with fixed rates. Each relay candownload the fresh files from the server in a certain period of time. Each usercan get the fresh files from any relay as long as the relay has stored thefresh versions of the requested files. Due to the limited storage capacity andupdating capacity of each relay, different cache designs will lead to differentaverage freshness of all updating files at users. In order to keep the averagefreshness as large as possible in the cache updating system, we formulate anaverage freshness-optimal cache updating problem (AFOCUP) to obtain an optimalcache scheme. However, because of the nonlinearity of the AFOCUP, it isdifficult to seek out the optimal cache scheme. As a result, an linearapproximate model is suggested by distributing the total update ratescompletely in accordance with the number of files in the relay in advance. Thenwe utilize the greedy algorithm to search the optimal cache scheme that issatisfied with the limited storage capacity of each relay. Finally, somenumerical examples are provided to illustrate the performance of theapproximate solution.

Freshness-Optimal Caching for Information Updating Systems with Limited Cache Storage Capacity