This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. The heavy-traffic limit with a single bottleneck queue is especially tractable because it yields limit processes involving one-dimensional reflected Brownian motion. That limit plays an important role in our new nonparametric decomposition approximation of the steady-state performance using indices of dispersion and robust optimization.

中文翻译：

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固定网络流的大流量限制

本文研究了开放排队网络中的固定客户流。流是对从一个队列流向另一个队列或流出网络的客户进行计数的过程。我们在广义杰克逊网络中建立了独特的平稳流的存在，并随着时间的增加收敛到平稳流。我们为固定流建立了大流量限制，允许对队列的任意子集进行临界加载。单个瓶颈队列的大流量限制特别容易处理，因为它会产生涉及一维反射布朗运动的限制过程。该限制在我们使用分散指数和稳健优化的稳态性能的新非参数分解近似中起着重要作用。