标题： 大规模分布式同步系统，使用完成取消冗余机制 显示英文标题

标题： Large-scale distributed synchronization systems, using a cancel-on-completion redundancy mechanism

摘要： 我们考虑一类多智能体分布式同步系统，这些系统被建模为在实线上移动的$n$个粒子。 这一类系统推广了文献[15]中考虑的多服务器排队系统的模型，采用了所谓的完成取消（c.o.c.）冗余机制，但同时也受到其他应用的启发。 文献[15]中的模型是一个在左边界点受控的粒子系统。 本文更一般的模型是允许在任一侧、两侧或完全不进行控制的边界条件。 我们考虑的是均场渐近情形，当粒子数$n$和作业到达率趋于无穷大，而每个粒子的作业到达率保持不变时的情形。 结果包括：均场极限（ML）固定点的存在性/唯一性，这些固定点描述了系统的极限动态；稳态渐近独立性的条件（当$n \to\infty$时，平稳分布集中在单个状态上，该状态必然是ML的固定点）；以及当$n \to\infty$时，无约束（自由）粒子系统平均速度的极限。 特别是，我们对左控制系统的结论统一并推广了文献[15]中的相应结果。 我们的技术发展使得不同类型的控制系统能够在统一的框架下进行分析。 特别是，这些系统被用作彼此分析的工具。 显示英文摘要

摘要： We consider a class of multi-agent distributed synchronization systems, which are modeled as $n$ particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in [15], employing so-called cancel-on-completion (c.o.c.) redundancy mechanism, but is motivated by other applications as well. The model in [15] is a particle system, regulated at the left boundary point. The more general model of this paper is such that we allow regulation boundaries on either side, or both sides, or no regulation at all. We consider the mean-field asymptotic regime, when the number of particles $n$ and the job arrival rates go to infinity, while the job arrival rates per particle remain constant. The results include: the existence/uniqueness of fixed points of mean-field limits (ML), which describe the limiting dynamics of the system; conditions for the steady-state asymptotic independence (concentration, as $n \to\infty$, of the stationary distribution on a single state, which is necessarily an ML fixed point); the limits, as $n \to\infty$, of the average velocity at which unregulated (free) particle system advances. In particular, our results for the left-regulated system unify and generalize the corresponding results in [15]. Our technical development is such that the systems with different types of regulation are analyzed within a unified framework. In particular, these systems are used as tools for analysis of each other.