Transaction Capacity, Security and Latency in Blockchains

We analyze how secure a block is after the block becomes $k$-deep, i.e., security-latency, for Nakamoto consensus under an exponential network delay model. We provide the fault tolerance and extensive bounds on safety violation probabilities given mining rate, delay rate and confirmation rules. Next, modeling the blockchain system as a batch service queue with exponential network delay, we connect the security-latency analysis to sustainable transaction rate of the queue system. As our model assumes exponential network delay, batch service queue models give a meaningful trade-off between transaction capacity, security and latency. Our results indicate that, by simply picking $k=7$-block confirmation rule in Bitcoin instead of the convention of $k=6$, mining rate, latency and throughput can be increased sixfold with the same safety guarantees. We further consider adversarial attacks on the queue service to hamper the service process. In an extreme scenario, we consider the selfish-mining attack for this purpose and provide the maximum adversarial block ratio in the longest chain under the exponential delay model. The ratio in turn reflects the maximum rate of decrease in the sustainable transaction rate of the queue.