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 under the preemptive and non-preemptive queueing disciplines with no storage facility. The non-preemptive queue drops the newly arriving updates until the update in service is successfully delivered, whereas the preemptive queue replaces the current update in service with the newly arriving update, if any. 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 bipolar Poisson point process (PPP). 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 (PAoI). Our numerical results verify our analytical findings and demonstrate the impact of various system design parameters on the mean PAoI.