On the Age of Information in Multi-Source Multi-Hop Wireless Status Update Networks

This paper studies a multi-source "age of information" problem in multi-hop wireless networks with packetized status updates and explicit channel contention. Specifically, the scenario considered in this paper assumes that each node in the network is a both a source and a monitor of information. Nodes take turns broadcasting their information to other nodes in the network while also maintaining tables of status updates for the information received from all other nodes in the network. Lower bounds on the peak and average age of information are derived and are found to be a function of fundamental graph properties including the connected domination number of the graph and the average shortest path length. In addition to these converse results, achievability results are developed through the presentation of an explicit algorithm for constructing near-optimal status update schedules along with an analytical upper bound for the average and peak age of these schedules. Finally, numerical results are presented that compute the bounds, construct schedules, and compute the achieved average and peak ages of these schedules exhaustively over every connected network topology with nine or fewer nodes. The results show that the the developed schedules achieve a peak age exactly matching the lower bounds and an average age within a multiplicative factor of 1.035 of the lower bound in all tested cases.