Block arrivals in the Bitcoin blockchain

TL;DR

This paper analyzes Bitcoin blockchain block arrivals, showing they do not follow a Poisson process as previously assumed, and introduces a refined stochastic model accounting for difficulty adjustments over time.

Contribution

It provides a new mathematical model for Bitcoin block arrivals that accounts for variable difficulty levels and challenges the Poisson process assumption.

Findings

Block arrivals do not follow a homogeneous Poisson process.

A refined stochastic model better describes block arrival patterns.

Difficulty adjustments significantly influence block arrival dynamics.

Abstract

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.