In directed acyclic graph (DAG)-based distributed ledgers, unreferenced blocks (tips) form the backlog of a distributed queueing system. Each new block creates one tip and attempts to remove up to $k$ existing tips by referencing them. With heterogeneous propagation delays, these service decisions are made from delayed local information, so nodes may disagree on the backlog and some reference attempts are wasted. We study a continuous-time Poisson model with bounded heterogeneous delays and uniform tip selection. We prove that the embedded tip-configuration chain is irreducible, aperiodic, and positive Harris recurrent, and hence admits a unique stationary regime. The observer and local tip-pool sizes have stationary exponential moments, converge to their stationary limits, and satisfy almost-sure ergodic averages. We also derive a Little-type identity relating the stationary mean observer tip count to the mean time until a typical block is first referenced. Simulations are included as qualitative illustrations of the effects of delay variability and issuance heterogeneity.

翻译：在基于有向无环图（DAG）的分布式账本中，未被引用的区块（即"提示信息"）构成分布式排队系统的积压队列。每个新区块会产生一个提示信息，并试图通过引用最多$k$个现有提示信息来移除它们。由于存在异构传播延迟，这些服务决策基于延迟的本地信息做出，因此节点可能对积压状态存在分歧，部分引用尝试因而失效。我们研究了具有有界异构延迟和均匀提示信息选择的连续时间泊松模型。证明表明，嵌入的提示信息配置链是不可约、非周期且正Harris递归的，因此存在唯一的平稳状态。观察者与本地提示信息池规模具有平稳指数矩，收敛于其平稳极限，并满足几乎必然遍历平均性质。我们还推导出类似Little定律的关系式，将平稳平均观察者提示信息数量与典型区块首次被引用的平均时间联系起来。仿真结果作为定性说明，展示了延迟异质性与发布非均匀性的影响。