  The synchronization process inherent to the Bitcoin network gives rise to an
infinite-server model with the unusual feature that customers interact. Among
the closed-form characteristics that we derive for this model is the busy
period distribution which, counterintuitively, does not depend on the arrival
rate. We explain this by exploiting the equivalence between two specific
service disciplines, which is also used to derive the model's stationary
distribution. Next to these closed-form results, the second major contribution
concerns an asymptotic result: a fluid limit in the presence of service delays.
Since fluid limits arise under scalings of the law-of-large-numbers type, they
are usually deterministic, but in the setting of the model discussed in this
paper the fluid limit is random (more specifically, of growth-collapse type).
