  As distributed ledgers, blockchains run consensus protocols which trade
capacity for consistency, especially in non-ideal networks with incomplete
connectivity and erroneous links. Existing studies on the tradeoff between
capacity and consistency are only qualitative or rely on specific assumptions.
This paper presents discrete-time Markov chain models to quantify the capacity
of Proof-of-Work based public blockchains in non-ideal networks. The
comprehensive model is collapsed to be ergodic under the eventual consistency
of blockchains, achieving tractability and efficient evaluations of blockchain
capacity. A closed-form expression for the capacity is derived in the case of
two miners. Another important aspect is that we extend the ergodic model to
analyze the capacity under strong consistency, evaluating the robustness of
blockchains against double-spending attacks. Validated by simulations, the
proposed models are accurate and reveal the effect of link quality and the
distribution of mining rates on blockchain capacity and the ratio of stale
blocks.
