  The blockchain paradigm provides a mechanism for content dissemination and
distributed consensus on Peer-to-Peer (P2P) networks. While this paradigm has
been widely adopted in industry, it has not been carefully analyzed in terms of
its network scaling with respect to the number of peers. Applications for
blockchain systems, such as cryptocurrencies and IoT, require this form of
network scaling.
  In this paper, we propose a new stochastic network model for a blockchain
system. We identify a structural property called \emph{one-endedness}, which we
show to be desirable in any blockchain system as it is directly related to
distributed consensus among the peers. We show that the stochastic stability of
the network is sufficient for the one-endedness of a blockchain. We further
establish that our model belongs to a class of network models, called monotone
separable models. This allows us to establish upper and lower bounds on the
stability region. The bounds on stability depend on the connectivity of the P2P
network through its conductance and allow us to analyze the scalability of
blockchain systems on large P2P networks. We verify our theoretical insights
using both synthetic data and real data from the Bitcoin network.
