A Bitcoin-inspired infinite-server model with a random fluid limit. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Frolkova, Maria; Mandjes, Michel
• Is Part Of: Stochastic models. Volume 35:Issue 1(2019)
• Page Start: 1
• Page End: 32
• Publication Date: 2019-01-02
• Subjects: Fluid limit -- stochastic-process limit -- growth-collapse process; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2018.1559739
• Languages: English
• ISSNs: 1532-6349

Abstract

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 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).