  This paper presents a novel stochastic geometry approach to the connectivity
of milimeter wave (mmWave) networks with multi-hop relaying. The random
positions and shapes of obstacles in the radio environment are modeled as a
Boolean model, whose germs are distributed according to a Poisson point process
and grains are random rectangles. The derived analytical results shed light on
how the connectivity of mmWave networks depends on key system parameters such
as the density and size of obstacles as well as relaying route window -- the
range of distances in which routing relays are selected. We find that multi-hop
relaying can greatly improve the connectivity versus single hop mmWave
transmission. We show that to obtain near-optimal connectivity the relaying
route window should be about the size of the obstacles.
