A Batch-Service Queueing System with General Input and Its Application to Analysis of Mining Process for Bitcoin Blockchain

Abstract

In Bitcoin, it is well known that the confirmation of a transaction issued by a user takes a longer time than the mean block-generation time of 10 minutes. In order to understand the stochastic behavior of the transaction-confirmation process, we consider a queueing model with batch service and general input. In our queueing model, we assume that the transaction interarrival times are independent and identically distributed (i.i.d.), and follow a general distribution, and that the transactions waiting in the queue are served in a batch manner. We define the number of transactions in queue just before a transaction arrival as the system state, deriving the steady-state distribution and the mean transaction-confirmation time by matrix analytic method. In numerical examples, we compare analytical results with trace-driven simulation, discussing the applicability of our queueing model to the prediction of the transaction-confirmation time. It is found that exponential-type distributions such as exponential distribution and hyper-exponential one can accurately estimate the mean transaction-confirmation time for the current maximum block-size limit of 1 Mbyte.