Priority queueing analysis of transaction-confirmation time for Bitcoin

Abstract

<p style='text-indent:20px;'>In Bitcoin system, a transaction is given a priority value according to its attributes such as the remittance amount and fee, and transactions with high priorities are likely to be confirmed faster than those with low priorities. In this paper, we analyze the transaction-confirmation time for Bitcoin system. We model the transaction-confirmation process as a queueing system with batch service, M/<inline-formula><tex-math id="M1">\begin{document}$ \mbox{G}^B $\end{document}</tex-math></inline-formula>/1. We consider the joint distribution of numbers of transactions in system and the elapsed service time, deriving the mean transaction-confirmation time. Using the result, we derive the recursive formulae of mean transaction-confirmation times of an M/<inline-formula><tex-math id="M2">\begin{document}$ \mbox{G}^B $\end{document}</tex-math></inline-formula>/1 queue with priority service discipline. In numerical examples, we show the effect of the maximum block size on the mean transaction-confirmation time, investigating the accuracy region of our queueing model. We also discuss how the increase in micropayments, which are likely to be given low priorities, affects the transaction-confirmation time.