Asymptotic Laws for Joint Content Replication and Delivery in Wireless Networks

TL;DR

This paper analyzes how content replication and delivery scale in large wireless networks, revealing regimes where network capacity requirements vary significantly based on content popularity and network size.

Contribution

It introduces a simplified model for joint content replication and delivery, deriving asymptotic capacity laws for large networks under Zipf popularity.

Findings

Capacity scales from O(√N) to O(1) depending on regimes.

Replication density approach approximates the original problem.

Identifies regimes based on content popularity and network size.

Abstract

We investigate on the scalability of multihop wireless communications, a major concern in networking, for the case that users access content replicated across the nodes. In contrast to the standard paradigm of randomly selected communicating pairs, content replication is efficient for certain regimes of file popularity, cache and network size. Our study begins with the detailed joint content replication and delivery problem on a 2D square grid, a hard combinatorial optimization. This is reduced to a simpler problem based on replication density, whose performance is of the same order as the original. Assuming a Zipf popularity law, and letting the size of content and network both go to infinity, we identify the scaling laws and regimes of the required link capacity, ranging from O(\sqrt{N}) down to O(1).