Asymptotic Laws for Joint Content Replication and Delivery in Wireless Networks

Abstract

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 √ N down to O(1).

The Throughput-Outage Tradeoff of Wireless One-Hop Caching Networks

“…This allows to focus on the essential aspect of caching at the nodes, and avoid the analytical complication of randomly placed nodes. The same approach is taken in [24], where multi-hop D2D communication is considered under the protocol model for a network of nodes placed deterministically on a squared grid. If the aggregate distributed 2 Scaling law order notation: given two functions f and g, we say that: 1) f (n) = O (g(n)) if there exists a constant c and integer N such that f (n) ≤ cg(n) for n > N .…”

“…Under the same assumption made here of the user requests distribution, [24] finds a deterministic replication caching scheme and a multi-hop routing scheme that achieves order-optimal average throughput. Besides the consideration of multihop and single hop, there are several other key differences between our work and [24]. First, [24] considers a deterministic caching placement approach, which depends on the files popularity distribution.…”

“…Besides the consideration of multihop and single hop, there are several other key differences between our work and [24]. First, [24] considers a deterministic caching placement approach, which depends on the files popularity distribution. This approach is not robust when users move between cells.…”

“…In contrast, mobility is easily handled by our scheme which is based on independent random caching. Next, in [24], the transmission range is fixed, where each node can only reach its four neighbors. Besides the deterministic caching placement, the key aspect of the problem is the design of the routing protocol and analyze the traffic through the bottleneck link of the network.…”

“…This, in turn, determines the point of the throughput-outage tradeoff at which the system operates. Finally, [24] only gives the order of the throughput as the number of users n goes to infinity, but does not characterizes the multiplicative constant of the throughput leading term in the scaling law. Therefore, it is difficult to understand in which regime of (large but finite n) the scaling laws become relevant.…”