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]中采用所谓完成即取消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]中的模型是一个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、双侧或完全不施加边界调控。我们考虑平均场渐近机制，即当粒子数$n$与任务到达率趋于无穷时，单位粒子的任务到达率保持恒定。对于给定$n$，系统状态由粒子位置的经验分布描述。研究成果包括：描述系统极限动力学的平均场极限不动点的存在唯一性；稳态渐近独立性条件（平稳分布集中于单个平均场极限不动点）；无调控自由粒子系统平均推进速度的极限。特别地，我们对左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可在统一框架内进行分析。