标题： 广义杰克逊网络在多尺度重负载情况下的功能极限 显示英文标题

标题： Functional Limits of Generalized Jackson Networks in Multi-scale Heavy Traffic

摘要： 我们研究在多尺度重负载情况下广义杰克逊网络的功能极限，其中各站点以不同且分离的速率接近完全利用。 我们的主要结果表明，经过适当缩放的队列长度过程弱收敛到一个坐标相互独立的极限过程。 这一发现提供了基本的动态机制，解释了之前仅在平稳分布中观察到的渐近独立性。 极限过程的具体形式被证明依赖于初始条件。 此外，我们引入并分析了一个分块多尺度重负载情况。 在此情况下，网络的站点被划分为块，不同块中的站点以不同的速率接近重负载，而同一块内的站点共享一个共同的速率。 我们同样获得了此情况下的功能极限，表明极限过程表现出分块独立性。 显示英文摘要

摘要： We investigate the functional limits of generalized Jackson networks in a multi-scale heavy traffic regime where stations approach full utilization at distinct, separated rates. Our main result shows that the appropriately scaled queue length processes converge weakly to a limit process whose coordinates are mutually independent. This finding provides the fundamental dynamic mechanism that explains the asymptotic independence previously observed only in stationary distributions. The specific form of the limit processes is shown to depend on the initial conditions. Moreover, we introduce and analyze a blockwise multi-scale heavy traffic regime. In this regime, the network's stations are partitioned into blocks, where stations in different blocks approach the heavy traffic at different rates, while stations within the same block share a common rate. We obtain the functional limits in this regime as well, showing that the limit process exhibits blockwise independence.