#Stability and Scalibility of Blockchain Systems

      



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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 is desirable in any blockchain system. We prove that whenever the blockchain network model is stochastically stable, then a blockchain is one-ended. We further establish that our model is monotone separable and use this result to establish upper and lower bounds on the stability region. The bounds on stability depend on the conductance of the P2P network 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.