Analysis of the confirmation time in proof-of-work blockchains

In blockchain networks driven by Proof of Work, clients spend a certain amount of cryptocurrency (called fees) to control the speed of confirmation of the transactions that they generate. In fact, transactions are confirmed according to a strong priority policy that favors those offering the highest fees. The problem of determining the optimal fee to offer to satisfy certain delay requirements is still widely open and, at the state of the art, mainly reactive methods based on historical data are available. In this work, we propose a queueing model based on the exact transient analysis of a M/MB/1 system to address this problem. The model takes into account (i) the state of the Mempool (the backlog of pending work) when the transaction is generated, (ii) the current transaction arrival intensity and (iii) the distribution of the fees offered by other transactions to the miners. We apply the model to study the performance of the Bitcoin blockchain. Its parameterization is based on an extensive statistical analysis of the transaction characteristics. To this aim, we collected data from over 1.5 million of pending transactions observed in the Mempool of our Bitcoin node. The outcome of our analysis allows us to provide an algorithm to quickly compute the expected transaction confirmation time given the blockchain state, and to highlight new insights on the relations between the transaction fees and confirmation time in BTC blockchain.