分布式账本模型中随机延迟的流极限
Fluid limit of a distributed ledger model with random delay
AI总结：
本文研究了考虑批量到达和随机延迟的分布式账本DAG模型，通过流极限理论分析其渐近行为，并通过模拟验证了稳定状态。
摘要：
分布式账本，包括区块链和其他去中心化数据库，设计用于在线存储信息，其中所有受信任的网络成员都可以透明地更新数据。账本发展的动态可以用有向无环图（DAG）数学地表示。在本文中，我们研究了一个考虑批量到达和附件随机延迟的DAG模型。我们通过让到达率趋于无穷大和到达间隔时间趋于零来分析该模型的渐近行为。我们证明了DAG中叶子的数量以及各种表征DAG顶点的随机变量可以近似为其流极限，表示为一组延迟偏微分方程的解。此外，我们建立了该流极限的稳定状态，并通过模拟验证了我们的发现。
英文摘要：
Distributed ledgers, including blockchain and other decentralized databases, are designed to store information online where all trusted network members can update the data with transparency. The dynamics of ledger's development can be mathematically represented by a directed acyclic graph (DAG). In this paper, we study a DAG model which considers batch arrivals and random delay of attachment. We analyze the asymptotic behavior of this model by letting the arrival rate go to infinity and the inter-arrival time go to zero. We establish that the number of leaves in the DAG and various random variables characterizing the vertices in the DAG can be approximated by its fluid limit, represented as the solution to a set of delayed partial differential equations. Furthermore, we establish the stable state of this fluid limit and validate our findings through simulations.
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