Throughput Scaling in Random Wireless Networks: A Non-Hierarchical Multipath Routing Strategy

Franceschetti et al. have recently shown that per-node throughput in an extended, ad hoc wireless network with $\Theta(n)$ randomly distributed nodes and multihop routing can be increased from the $\Omega({1 \over \sqrt{n} \log n})$ scaling demonstrated in the seminal paper of Gupta and Kumar to $\Omega({1 \over \sqrt{n}})$. The goal of the present paper is to understand the dependence of this interesting result on the principal new features it introduced relative to Gupta-Kumar: (1) a capacity-based formula for link transmission bit-rates in terms of received signal-to-interference-and-noise ratio (SINR); (2) hierarchical routing from sources to destinations through a system of communal highways; and (3) cell-based routes constructed by percolation. The conclusion of the present paper is that the improved throughput scaling is principally due to the percolation-based routing, which enables shorter hops and, consequently, less interference. This is established by showing that throughput $\Omega({1 \over \sqrt{n}})$ can be attained by a system that does not employ highways, but instead uses percolation to establish, for each source-destination pair, a set of $\Theta(\log n)$ routes within a narrow routing corridor running from source to destination. As a result, highways are not essential. In addition, it is shown that throughput $\Omega({1 \over \sqrt{n}})$ can be attained with the original threshold transmission bit-rate model, provided that node transmission powers are permitted to grow with $n$. Thus, the benefit of the capacity bit-rate model is simply to permit the power to remain bounded, even as the network expands.