Predicting confirmation times of Bitcoin transactions

We study the distribution of confirmation times of Bitcoin transactions, conditional on the size of the current memory pool. We argue that the time until a Bitcoin transaction is confirmed resembles the time to ruin in a corresponding Cramer-Lundberg process. This well-studied model gives mathematical insights in the mempool behaviour over time. Specifically, for situations where one chooses a fee, such that the total size of incoming transactions with higher fee is close to the total size of transactions leaving the mempool (heavy traffic), a diffusion approximation leads to an inverse Gaussian distribution for the confirmation times. The results of this paper are particularly interesting for users that want to make a Bitcoin transaction during heavy-traffic situations, as evaluation of the well-known inverse Gaussian distribution is computationally straightforward.