We study a discrete-time queueing network with blocking that is primarily motivated by outpatient network management. To tackle the curse of dimensionality in performance analysis, we develop a refined mean-field approximation that deals with changing population size, a nonconventional feature that makes the analysis challenging within the existing literature. We explicitly quantify the convergence rate for this approximation as $O(1/N)$ with $N$ being the system size. Not only is this convergence better than the $O(1/\sqrt{N})$ convergence proven in prior work, but our approximation shows a significant improvement in performance prediction accuracy when the system size is small, compared to the conventional (unrefined) mean-field approximation. This accuracy makes our approximation appealing to support decision-making in practice.

中文翻译：

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带阻塞的离散时间排队网络的精细平均场近似

我们研究了一个具有阻塞的离散时间排队网络，其主要动机是门诊网络管理。为了解决性能分析中的维数灾难，我们开发了一种改进的平均场近似来处理不断变化的人口规模，这是一种非常规特征，使得现有文献中的分析具有挑战性。我们明确地将这种近似的收敛速度量化为$氧（1/氮）$和$氮$是系统大小。这种收敛性不仅优于$氧（1/\sqrt{氮}）$收敛性已在之前的工作中得到证明，但与传统的（未经细化的）平均场近似相比，我们的近似表明，当系统尺寸较小时，性能预测精度有显着提高。这种准确性使得我们的近似值对于支持实践中的决策具有吸引力。