Stochastic modelling of blockchain consensus

TL;DR

This paper introduces a stochastic model based on random-walk theory to analyze blockchain consensus dynamics, identifying regimes of optimal and congested states and exploring phase transitions in decentralized networks.

Contribution

It presents a minimalistic stochastic framework for understanding blockchain consensus, classifies system performance regimes, and investigates phase transitions during consensus emergence.

Findings

Identifies functional and non-functional regimes in blockchain systems.

Discovers a phase transition during consensus formation.

Provides insights into sub-optimal states in decentralized networks.

Abstract

Blockchain and general purpose distributed ledgers are foundational technologies which bring significant innovation in the infrastructures and other underpinnings of our socio-economic systems. These P2P technologies are able to securely diffuse information within and across networks, without need for trustees or central authorities to enforce consensus. In this contribution, we propose a minimalistic stochastic model to understand the dynamics of blockchain-based consensus. By leveraging on random-walk theory, we model block propagation delay on different network topologies and provide a classification of blockchain systems in terms of two emergent properties. Firstly, we identify two performing regimes: a functional regime corresponding to an optimal system function; and a non-functional regime characterised by a congested or branched state of sub-optimal blockchains. Secondly, we discover a phase transition during the emergence of consensus and numerically investigate the corresponding critical point. Our results provide important insights into the consensus mechanism and sub-optimal states in decentralised systems.