In this work we consider the problem of an optimal geographic placement of content in wireless cellular networks modelled by Poisson point processes. Specifically, for the typical user requesting some particular content and whose popularity follows a given law (e.g. Zipf), we calculate the probability of finding the content cached in one of the base stations. Wireless coverage follows the usual signal-to-interference-and noise ratio (SINR) model, or some variants of it. We formulate and solve the problem of an optimal randomized content placement policy, to maximize the user's hit probability. The result dictates that it is not always optimal to follow the standard policy "cache the most popular content, everywhere". In fact, our numerical results regarding three different coverage scenarios, show that the optimal policy significantly increases the chances of hit under high-coverage regime, i.e., when the probabilities of coverage by more than just one station are high enough.

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This article introduces a novel family of decentralised caching policies, applicable to wireless networks with finite storage at the edge-nodes (stations). These policies are based on the Least-Recently-Used replacement principle, and are, here, referred to as spatial multi-LRU. Based on these, cache inventories are updated in a way that provides content diversity to users who are covered by, and thus have access to, more than one station. Two variations are proposed, namely the multi-LRU-One and -All, which differ in the number of replicas inserted in the involved caches. By introducing spatial approximations, we propose a Che-like method to predict the hit probability, which gives very accurate results under the Independent Reference Model (IRM). It is shown that the performance of multi-LRU increases the more the multicoverage areas increase, and it approaches the performance of other proposed centralised policies, when multi-coverage is sufficient. For IRM traffic multi-LRU-One outperforms multi-LRU-All, whereas when the traffic exhibits temporal locality the -All variation can perform better.

A device-to-device (D2D) wireless network is considered, where user devices also have the ability to cache content. In such networks, users are mobile and communication links can be spontaneously activated and dropped depending on the users' relative position. Receivers request files from transmitters, these files having a certain popularity and file-size distribution. In this work a new performance metric is introduced, namely the Service Success Probability, which captures the specificities of D2D networks. For the Poisson Point Process case for node distribution and the SNR coverage model, explicit expressions are derived. Simulations support the analytical results and explain the influence of mobility and file-size distribution on the system performance, while providing intuition on how to appropriately cache content on mobile storage space. Of particular interest is the investigation on how different file-size distributions (Exponential, Uniform, or Heavy-Tailed) influence the performance.