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).

中文翻译：

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受比特币启发的具有随机流体限制的无限服务器模型

摘要 比特币网络固有的同步过程产生了一个无限服务器模型，它具有客户交互的不寻常特征。我们为该模型推导出的封闭形式特征之一是繁忙时段分布，与直觉相反，它不依赖于到达率。我们通过利用两个特定服务学科之间的等价性来解释这一点，这也用于推导出模型的平稳分布。除了这些封闭形式的结果之外，第二个主要贡献涉及渐近结果：存在服务延迟时的流体限制。由于流体极限是在大数定律类型的标度下出现的，它们通常是确定性的，但在本文讨论的模型设置中，流体极限是随机的（更具体地说，是增长崩溃类型）。