We investigate the Age of Information (AoI) of Jackson Networks with finite buffer size. We provide a closed form expression of an upper bound of the average AoI by using Stochastic Hybrid Systems (SHS) along with linear algebra tools. Since the computation of the bound requires inverting a ${N}\,\,\times \,\,{N}$ matrix, where ${N}$ is the number of queues in the network, we provide a simple iterative algorithm and prove its convergence with geometric convergence rate. Numerical results allow us to assess the accuracy of our model in various settings.

中文翻译：

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具有有限缓冲区大小的Jackson网络的信息时代

我们调查了具有有限缓冲区大小的杰克逊网络的信息时代（AoI）。通过使用随机混合系统（SHS）和线性代数工具，我们提供了平均AoI上限的封闭形式表示。由于边界的计算需要将a取反 $ {N} \，\，\ times \，\，{N} $ 矩阵，在哪里 $ {N} $ 是网络中的队列数，我们提供一种简单的迭代算法，并以几何收敛速度证明其收敛性。数值结果使我们能够评估各种设置下模型的准确性。