On Ledger Inconsistency Time in Bitcoin's Blockchain Delivery Network

In this work we analyze the blockchain forking events, blockchain partitioning, and duration of inconsistent state of the ledger in a Bitcoin delivery network. Using a comprehensive probabilistic model, we obtain the probability distribution of two- and three-way forks, the forked partition sizes, and the duration of ledger inconsistency until the resolution. We show that the three-way forking probability is substantially lower than that of a two-way forking and that the partition sizes in the case of two-way forking tend to equalize when the number of nodes increases. Finally, we show that the duration of ledger inconsistency state exhibits long tail probability distribution which means that successive forking events can force the ledger to remain inconsistent for long time.