Queuing Theory of Improved Practical Byzantine Fault Tolerant Consensus

Abstract

In recent years, the use of consensus mechanism to maintain the security of blockchain system has become a considerable concern of the community. Delegated proof of stake (DPoS) and practical Byzantine fault tolerant (PBFT) consensus mechanisms are key technologies in maintaining the security of blockchain system. First, this study proposes a consensus mechanism combining DPoS and PBFT, which can rapidly deal with malicious witness nodes and shorten the time of block verification. Second, the M/PH/1 queuing model is used to analyze the performance of the proposed consensus mechanism, and the performance of the improved practical Byzantine fault tolerant consensus mechanism is evaluated from steady-state conditions and key performance measure of the system. Third, the current study uses the theoretical method of open (Jackson) queuing network, combined with the blockchain consensus process, and provides theoretical analysis with special cases. Lastly, this research utilizes numerical examples to verify the computability of the theoretical results. The analytic method is expected to open a series of potentially promising research in queueing theory of blockchain systems.

Keywords

• blockchain
• practical Byzantine fault tolerant
• delegated proof of stake
• phase-type distribution
• queueing theory