A Quantitative Study on Performance of Proof of Stake (PoS)-based Blockchain Network

Abstract

A new quantitative model to estimate the performance of a PoS (Proof of Stake) consensus protocol-based blockchain (e.g., Ethereum) is proposed in this paper. The proposed new PoS-based chain model has the number of validators (m) in the network as a central variable in the model such that m = 1 in PoW and m ≫ 1 in PoS. A unified binomial distribution is assumed with respect to the number of validators and then a multinomial distribution is assumed with respect to the number of transaction slots pending on the current block to be posted [14], thereby establishing a quantitative model to express the steady-state probability to have 0 ≤ i ≤ n number of trasactions slots with 1 ≤ j ≤ number of validators across the blockchain network given transaction slots arrival rate (λ) and block posting rate $\left( {\frac{\mu }{j}} \right)$ by number of validators. Extensive numerical simulations will be conducted to evaluate a few base performance metrics such as average transaction waiting time, average size of block and throughput, to mention a few. The simulation results will reveal a quantitative insight into the PoS in comparison to PoW. Ultimately, the proposed quantitative model will establish a theoretical foundation to guide the PoS-based chain developers with specific respect to performance.