Theoretical Considerations on Bitcoin Scalability Problem and Block Size Distribution

Abstract

In Bitcoin Core (BTC), there exists an upper limit of the block size around 1MB, which causes the Bitcoin scalability problem that severely limits transaction processing capacity.On the other hand, Bitcoin SV (BSV) forked from BTC is known to eliminate this limit.In BSV, the size of mined blocks is generally not uniform, but a mixture of various different sizes.Block miners in BSV can get more transaction fees as a reward, while there is a risk that the success rate of block mining decreases because it has to take a longer time to verify all the transactions in the block.For this reason, the selection of block size depends on mining strategy of each miner.To the best of our knowledge, there has been no detailed report on how each miner selects a block size.In this paper, we firstly formulated the Bitcoin scalability problem using a mathematical model of transaction processing capacity.Then, we investigated the probability distributions of block size in both Scaling Test Network (STN) and Mainnet of BSV.As a result, we found that the aggregate block size distribution in STN follows an exponential distribution, while that in the Mainnet follows a power-law distribution whose exponent is around one.We demonstrated a theoretical explanation of the difference between two distributions in the STN and Mainnet with a unified manner based on an underlying incentive mechanism.