Blockchain and transaction processing time using M/M/1 queue model

Abstract

The blockchain is an irrefutably a clever invention, where the digital information gets distributed across multiple nodes. The concept was hosted in bitcoin cryptocurrency systems for distribution of coins in a distributed ledger system. Introduction of smart contracts in Ethereum blockchain explored various distinct applications ranging from financial services, supply chain management, healthcare amid others. However, current set of literatures focus more on development and realization of blockchain and petite work is done on mathematical models, performance analysis and optimization of blockchain systems. In this paper, mathematical model is developed using M/M/1 queue model to evaluate transaction processing time. In M/M/1, M symbolizes Markovian arrival and departure of transactions in blocks. The arriving and departure of the blocks are denoted by symbols λ, µ respectively and operates under exponential assumptions. Three different conditions of λ, µ are taken into consideration of complete evaluation of blocks acceptance and the mathematical tactic will open a sequence of possibly favorable research in queueing theory of blockchain systems. The research founds its limitation in acceptance rate is always one unit larger than the arrivals of blocks (termed as an ergodic condition) for stable working of the complete system.