Age of Information with Unreliable Transmissions in Multi-Source Multi-Hop Status Update Systems

This paper studies the "age of information" (AoI) in multi-hop networks with time-slotted transmissions and packet loss in a setting where each node is both a source and monitor of information. Nodes take turns broadcasting their information to other nodes while also maintaining tables of updates for the information received from other nodes. It is assumed that transmission errors in the network occur with a fixed error probability and that transmission errors are independent across links. Using tools from graph theory, two algorithms are developed based on sequential flooding with repetitive transmissions when transmission errors occur. These algorithms generate status update dissemination schedules for any network with a connected topology. The two algorithms differ in terms of whether the root nodes in each sequential flooding tree resample their local information when transmission errors occur. A lower bound on the average peak AoI as a function of fundamental graph properties is also derived for schedules generated by the algorithm without resampling by the root nodes. Numerical results are presented to evaluate the achieved average peak AoI for some canonical graph topologies.