We study age of information in multi-hop multi-cast cache-enabled networks where the inter-update times on the links are not necessarily exponentially distributed. We focus on the set of non-arithmetic distributions for inter-update times, which includes continuous probability distributions as a subset. We first characterize instantaneous age of information at each node for arbitrary networks. We then explicate the recursive equations for instantaneous age of information in multi-hop networks and derive closed form expressions for expected age of information at an end-user. We show that expected age in multi-hop networks exhibits an additive structure. Further, we show that the expected age at each user is directly proportional to the variance of inter-update times at all links between a user and the source. We expect the analysis in this work to help alleviate the over-dependence on Poisson processes for future work in age of information.

翻译：我们研究了多跳多播缓存网络中的信息年龄，其中链路上的更新间隔时间不一定服从指数分布。我们重点关注更新间隔时间的非算术分布集合，该集合包含连续概率分布作为其子集。首先，我们描述了任意网络中每个节点的瞬时信息年龄。随后，我们阐明了多跳网络中瞬时信息年龄的递归方程，并推导出终端用户期望信息年龄的闭式表达式。我们证明了多跳网络中的期望信息年龄具有可加结构。此外，我们表明每个用户的期望信息年龄与用户与源之间所有链路上更新间隔时间的方差成正比。我们期望本文的分析有助于减轻未来信息年龄研究中对于泊松过程的过度依赖。