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 system state for a given $n$ is the empirical distribution of the particles' locations. 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 of the stationary distribution on a single ML fixed point); the limits 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 approach is such that the systems with different types of regulation are analyzed within a unified framework.

翻译：本文研究一类多智能体分布式同步系统，其建模为在实轴上运动的$n$个粒子。该类系统推广了文献[15]中采用所谓取消完成（c.o.c.）冗余机制的多服务器排队系统模型，但其应用背景更为广泛。文献[15]中的模型是在左边界点受调控的粒子系统。本文提出的更一般化模型允许在单侧边界、双侧边界或无边界调控的情况下进行分析。我们考虑平均场渐近机制，即当粒子数量$n$与任务到达率趋于无穷时，每个粒子的任务到达率保持恒定。对于给定的$n$，系统状态由粒子位置的实证分布表示。主要研究成果包括：描述系统极限动力学的平均场极限（ML）不动点的存在性与唯一性证明；稳态渐近独立性（平稳分布集中于单个ML不动点）的判定条件；无调控（自由）粒子系统平均推进速度的极限解析。特别地，针对左边界调控系统的研究结果统一并推广了文献[15]中的相应结论。本研究所采用的技术方法使得不同类型调控的系统能在统一框架下进行分析。