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Register a new userFreshness-Optimal Caching for Information Updating Systems with Limited Cache Storage Capacity
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Added by
Minquan Cheng
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper, we investigate a cache updating system with a server containing $N$ files, $K$ relays and $M$ users. The server keeps the freshes
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We consider a cache updating system with a source, a cache with limited storage capacity and a user. There are $n$ files. The source keeps the freshes
We consider a cache updating system with a source, a cache and a user. There are $n$ files. The source keeps the freshest version of the files which are updated with known rates $lambda_i$. The cache downloads and keeps the freshest version of the files from the source with rates $c_i$. The user gets updates from the cache with rates $u_i$. When the user gets an update, it either gets a fresh update from the cache or the file at the cache becomes outdated by a file update at the source in which case the user gets an outdated update. We find an analytical expression for the average freshness of the files at the user. Next, we generalize our setting to the case where there are multiple caches in between the source and the user, and find the average freshness at the user. We provide an alternating maximization based method to find the update rates for the cache(s), $c_i$, and for the user, $u_i$, to maximize the freshness of the files at the user. We observe that for a given set of update rates for the user (resp. for the cache), the optimal rate allocation policy for the cache (resp. for the user) is a $threshold$ $policy$, where the optimal update rates for rapidly changing files at the source may be equal to zero. Finally, we consider a system where multiple users are connected to a single cache and find update rates for the cache and the users to maximize the total freshness over all users.
We consider a system consisting of a server, which receives updates for $N$ files according to independent Poisson processes. The goal of the server is to deliver the latest version of the files to the user through a parallel network of $K$ caches. We consider an update received by the user successful, if the user receives the same file version that is currently prevailing at the server. We derive an analytical expression for information freshness at the user. We observe that freshness for a file increases with increase in consolidation of rates across caches. To solve the multi-cache problem, we first solve the auxiliary problem of a single-cache system. We then rework this auxiliary solution to our parallel-cache network by consolidating rates to single routes as much as possible. This yields an approximate (sub-optimal) solution for the original problem. We provide an upper bound on the gap between the sub-optimal solution and the optimal solution. Numerical results show that the sub-optimal policy closely approximates the optimal policy.
We address a centralized caching problem with unequal cache sizes. We consider a system with a server of files connected through a shared error-free link to a group of cache-enabled users where one subgroup has a larger cache size than the other. We propose an explicit caching scheme for the considered system aimed at minimizing the load of worst-case demands over the shared link. As suggested by numerical evaluations, our scheme improves upon the best existing explicit scheme by having a lower worst-case load; also, our scheme performs within a multiplicative factor of 1.11 from the scheme that can be obtained by solving an optimisation problem in which the number of parameters grows exponentially with the number of users.
We consider updating strategies for a local cache which downloads time-sensitive files from a remote server through a bandwidth-constrained link. The files are requested randomly from the cache by local users according to a popularity distribution which varies over time according to a Markov chain structure. We measure the freshness of the requested time-sensitive files through their Age of Information (AoI). The goal is then to minimize the average AoI of all requested files by appropriately designing the local caches downloading strategy. To achieve this goal, the original problem is relaxed and cast into a Constrained Markov Decision Problem (CMDP), which we solve using a Lagrangian approach and Linear Programming. Inspired by this solution for the relaxed problem, we propose a practical cache updating strategy that meets all the constraints of the original problem. Under certain assumptions, the practical updating strategy is shown to be optimal for the original problem in the asymptotic regime of a large number of files. For a finite number of files, we show the gain of our practical updating strategy over the traditional square-root-law strategy (which is optimal for fixed non time-varying file popularities) through numerical simulations.
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