  Large-scale blockages like buildings affect the performance of urban cellular
networks, especially at higher frequencies. Unfortunately, such blockage
effects are either neglected or characterized by oversimplified models in the
analysis of cellular networks. Leveraging concepts from random shape theory,
this paper proposes a mathematical framework to model random blockages and
analyze their impact on cellular network performance. Random buildings are
modeled as a process of rectangles with random sizes and orientations whose
centers form a Poisson point process on the plane. The distribution of the
number of blockages in a link is proven to be Poisson random variable with
parameter dependent on the length of the link. A path loss model that
incorporates the blockage effects is proposed, which matches experimental
trends observed in prior work. The model is applied to analyze the performance
of cellular networks in urban areas with the presence of buildings, in terms of
connectivity, coverage probability, and average rate. Analytic results show
while buildings may block the desired signal, they may still have a positive
impact on network performance since they can block significantly more
interference.
