  Throughput scaling laws of an ad hoc network equipping directional antennas
at each node are analyzed. More specifically, this paper considers a general
framework in which the beam width of each node can scale at an arbitrary rate
relative to the number of nodes. We introduce an elastic routing protocol,
which enables to increase per-hop distance elastically according to the beam
width, while maintaining an average signal-to-interference-and-noise ratio at
each receiver as a constant. We then identify fundamental operating regimes
characterized according to the beam width scaling and analyze throughput
scaling laws for each of the regimes. The elastic routing is shown to achieve a
much better throughput scaling law than that of the conventional
nearest-neighbor multihop for all operating regimes. The gain comes from the
fact that more source--destination pairs can be simultaneously activated as the
beam width becomes narrower, which eventually leads to a linear throughput
scaling law. In addition, our framework is applied to a hybrid network
consisting of both wireless ad hoc nodes and infrastructure nodes. As a result,
in the hybrid network, we analyze a further improved throughput scaling law and
identify the operating regime where the use of directional antennas is
beneficial.
