Optimal deployment of caches in the plane

We consider wireless caches placed in the plane according to a homogeneous Poisson process. A data file is stored at the caches, which have limited storage capabilities. Clients can contact the caches to retrieve the data. The caches store the data according to one of the two data allocation strategies: partitioning & coding. We consider the Pareto front of the expected deployment cost of the caches and the expected cost of a client retrieving the data from the caches. We show that there is a strong trade-off between the expected retrieval and the expected deployment cost under the partitioning and the coding strategies. We also show that under coding, it is optimal to deploy a high number of caches, each with low storage capacity.