Transaction-Confirmation Time for Bitcoin: A Queueing Analytical Approach to Blockchain Mechanism

Bitcoin is a virtual currency based on a transaction-ledger database called blockchain. The blockchain is maintained and updated by mining process in which a number of nodes called miners compete for finding answers of very difficult puzzle-like problem. Transactions issued by users are grouped into a block, and the block is added to the blockchain when an algorithmic puzzle specialized for the block is solved. A recent study reveals that newly arriving transactions are not included in the block being under mining. In this paper, we model the mining process with a queueing system with batch service, analyzing the transaction-confirmation time. We consider an $$M/\text{ G }^B/1$$ with batch service, in which a newly arriving transaction cannot enter the service facility even when the number of transactions in the service facility does not reach the maximum batch size, i.e., the block-size limit. In this model, the sojourn time of a transaction corresponds to its confirmation time. We consider the joint distribution of the number of transactions in system and the elapsed service time, deriving the mean transaction-confirmation time. In numerical examples, we show how the block-size limit affects the transaction-confirmation time.