Block arrivals in the Bitcoin blockchain

Bitcoin is a electronic payment system where payment transactions are verified and stored in a data structure called the blockchain. Bitcoin miners work individually to solve a computationally intensive problem, and with each solution a Bitcoin block is generated, resulting in a new arrival to the blockchain. The difficulty of the computational problem is updated every 2,016 blocks in order to control the rate at which blocks are generated. In the original Bitcoin paper, it was suggested that the blockchain arrivals occur according to a homogeneous Poisson process. Based on blockchain block arrival data and stochastic analysis of the block arrival process, we demonstrate that this is not the case. We present a refined mathematical model for block arrivals, focusing on both the block arrivals during a period of constant difficulty and how the difficulty level evolves over time.