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We study the version age of information in a multi-hop multi-castcache-enabled network, where updates at the source are marked with incrementingversion numbers, and the inter-update times on the links are not necessarilyexponentially distributed. We focus on the set of non-arithmetic distributions,which includes continuous probability distributions as a subset, with finitefirst and second moments for inter-update times. We first characterize theinstantaneous version age of information at each node for an arbitrary network.We then explicate the recursive equations for instantaneous version age ofinformation in multi-hop networks and employ semi-martingale representation ofrenewal processes to derive closed form expressions for the expected versionage of information at an end user. We show that the expected age in a multi-hopnetwork exhibits an additive structure. Further, we show that the expected ageat each user is proportional to the variance of inter-update times at all linksbetween a user and the source. Thus, end user nodes should request packetupdates at constant intervals.

Timely Tracking of a Remote Dynamic Source Via Multi-Hop Renewal Updates