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.
Bibliographical noteFunding Information:
The work of both Rowel Gundlach and David Koops is supported by the Netherlands Organisation for Scientific Research (NWO) through Gravitation-grant NETWORKS-024.002.003.
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- confirmation times
- corrected diffusion approximation
- cramer-lundberg model