We show how to calculate the Age of Information in an overtake-free network of quasi-reversible queues, with exponential exogenous interarrivals of multiple classes of update packets and exponential service times at all nodes. Results are provided for any number of M/M/1 First-Come-First-Served (FCFS) queues in tandem, and for a network with two classes of update packets, entering through different queues in the network and exiting through the same queue. The main takeaway is that in a network with different classes of update packets, individual classes roughly preserve the ages they would achieve if they were alone in the network, except when shared queues become saturated, in which case the ages increase considerably. The results are extensible for other quasi-reversible queues for which sojourn time distributions are known, such as M/M/c FCFS queues and processor-sharing queues.

中文翻译：

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准可逆队列无超车网络中的信息时代

我们展示了如何在准可逆队列的无超车网络中计算信息时代，其中多类更新数据包的指数外生间隔和所有节点的指数服务时间。为任意数量的 M/M/1 先到先服务 (FCFS) 队列以及具有两类更新数据包的网络提供结果，这些数据包通过网络中的不同队列进入并通过同一队列退出. 主要结论是，在具有不同类别的更新数据包的网络中，各个类别大致保留了它们单独在网络中时会达到的年龄，除非共享队列变得饱和，在这种情况下，年龄会显着增加。结果可扩展到其他已知逗留时间分布的准可逆队列，