  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.
