Spatial Distribution of the Mean Peak Age of Information in Wireless Networks

This paper considers a large-scale wireless network consisting of source-destination (SD) pairs, where the sources send time-sensitive information, termed status updates, to their corresponding destinations in a time-slotted fashion. We employ Age of information (AoI) for quantifying the freshness of the status updates measured at the destination nodes for two different queuing disciplines, namely Type I and II queues. Type I queue is assumed to transmit the status updates in a first-come-first-served (FCFS) fashion with no storage facility. However, Type I queue may not necessarily minimize AoI because a new update will not be allowed to enter a server until the current update has been successfully transmitted. To overcome this shortcoming, we consider Type II queue in which the most recent status update available at a given transmission slot is transmitted in order to minimize the AoI. As the update delivery rate for a given link is a function of the interference field seen from the receiver, the temporal mean AoI can be treated as a random variable over space. Our goal in this paper is to characterize the spatial distribution of the mean AoI observed by the SD pairs by modeling them as a Poisson bipolar process. Towards this objective, we first derive accurate bounds on the moments of success probability while efficiently capturing the interference-induced coupling in the activities of the SD pairs. Using this result, we then derive tight bounds on the moments as well as the spatial distribution of peak AoI. Our numerical results verify our analytical findings and demonstrate the impact of various system design parameters on the mean peak AoI.