Asymptotic laws for content replication and delivery in wireless networks

A key consideration in novel communication paradigms in multihop wireless networks regards the scalability of the network. We investigate the case of nodes making random requests on content stored in multiple replicas over the wireless network. We show that, in contrast to the conventional paradigm of random communicating pairs, multihop communication is a sustainable scheme for certain values of file popularity, cache and network size. In particular, we formulate the joint problem of replication and routing and compute an order optimal solution. Assuming a Zipf file popularity distribution, we vary the number of files M in the system as a function of the nodes N, let both go to infinity and identify the scaling regimes of the required link capacity, from O(√N) down to O(1).