Stochastic Performance Modeling for Practical Byzantine Fault Tolerance Consensus in Blockchain

07/01/2021
by   Fan-Qi Ma, et al.
0

The practical Byzantine fault tolerant (PBFT) consensus mechanism is one of the most basic consensus algorithms (or protocols) in blockchain technologies, thus its performance evaluation is an interesting and challenging topic due to a higher complexity of its consensus work in the peer-to-peer network. This paper describes a simple stochastic performance model of the PBFT consensus mechanism, which is refined as not only a queueing system with complicated service times but also a level-independent quasi-birth-and-death (QBD) process. From the level-independent QBD process, we apply the matrix-geometric solution to obtain a necessary and sufficient condition under which the PBFT consensus system is stable, and to be able to numerically compute the stationary probability vector of the QBD process. Thus we provide four useful performance measures of the PBFT consensus mechanism, and can numerically calculate the four performance measures. Finally, we use some numerical examples to verify the validity of our theoretical results, and show how the four performance measures are influenced by some key parameters of the PBFT consensus. By means of the theory of multi-dimensional Markov processes, we are optimistic that the methodology and results given in this paper are applicable in a wide range research of PBFT consensus mechanism and even other types of consensus mechanisms.

READ FULL TEXT
research
10/25/2022

Dynamic Practical Byzantine Fault Tolerance and Its Blockchain System: A Large-Scale Markov Modeling

In a practical Byzantine fault tolerance (PBFT) blockchain network, the ...
research
12/25/2021

On the Byzantine-Fault-Tolerant Consensus for Blockchain among Connected Vehicles

It is a critical matter for a blockchain system whether a Byzantine faul...
research
07/27/2020

AlphaBlock: An Evaluation Framework for Blockchain Consensus Protocols

Consensus protocols play a pivotal role to balance security and efficien...
research
07/27/2021

Two Basic Queueing Models of Service Platforms in Digital Sharing Economy

This paper describes two basic queueing models of service platforms in d...
research
09/03/2022

A Markov Process Theory for Network Growth Processes of DAG-based Blockchain Systems

Note that the serial structure of blockchain has many essential pitfalls...
research
07/14/2021

A Byzantine Fault-Tolerant Consensus Library for Hyperledger Fabric

Hyperledger Fabric is an enterprise grade permissioned distributed ledge...
research
06/11/2021

Stochastic modelling of blockchain consensus

Blockchain and general purpose distributed ledgers are foundational tech...

Please sign up or login with your details

Forgot password? Click here to reset