A BITCOIN-INSPIRED INFINITE-SERVER MODEL WITH A RANDOM FLUID LIMIT MARIA FROLKOVA & MICHEL MANDJES Abstract. 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 character- istics 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). Key words. Stochastic-process limit ◦ fluid limit ◦ growth-collapse process ◦ Bitcoin. Affiliations. M. Frolkova and M. Mandjes are with Korteweg-de Vries Institute for Mathemat- ics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, the Netherlands. M. Frolkova is corresponding author (email:
[email protected]). 1. Introduction The Bitcoin network is a payment system where all transactions between participants are carried out in the digital Bitcoin currency. These transactions are stored in a database called blockchain. In fact, every Bitcoin user maintains a blockchain version, thus keeping track of the global Bitcoin transaction history. This ensures transparency | one of the advertized Bitcoin features. Informa- tion spreads across the network via peer-to-peer communication.