We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this system, we determine the mean conditional waiting time for an arriving customer using a sample path analysis approach. The approach classifies system state upon arrival into scenarios and exploits an inherent structure in the sequence of events that occur till the customer departs to obtain conditional waiting time estimates. We conduct numerical studies to show both the accuracy of our conditional waiting time estimates and their practical importance.

中文翻译：

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串联轮询队列中的条件等待时间分析

我们分析具有两个产品类型和两个站点的轮询队列的串联网络。我们假设网络的外部到达遵循泊松过程，并且每个站点的服务时间呈指数分布。对于此系统，我们使用样本路径分析方法确定到达客户的平均条件等待时间。该方法将到达时的系统状态分类为各种场景，并利用事件的顺序中的固有结构，这些事件的发生顺序一直持续到客户离开以获得条件等待时间估计为止。我们进行数值研究，以显示我们的有条件等待时间估计的准确性及其实际重要性。