Distributed storage in the plane

We consider storage devices located in the plane according to a general point process and specialize the results for the homogeneous Poisson process. A large data file is stored at the storage devices, which have limited storage capabilities. Hence, they can only store parts of the data. Clients can contact the storage devices to retrieve the data. We compare the expected cost of obtaining the complete data under uncoded as well as coded data allocation strategies. It is shown that for the general class of cost measures where the cost of retrieving data is increasing with the distance between client and storage devices, coded allocation outperforms uncoded allocation. The improvement offered by coding is quantified for two more specific classes of performance measures. Finally, our results are validated by computing the costs of the allocation strategies for the case that storage devices coincide with currently deployed mobile base stations.