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

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Document pages: 33 pages

Abstract: This paper considers a large-scale wireless network consisting ofsource-destination (SD) pairs, where the sources send time-sensitiveinformation, termed status updates, to their corresponding destinations in atime-slotted fashion. We employ Age of information (AoI) for quantifying thefreshness of the status updates measured at the destination nodes for twodifferent queuing disciplines, namely Type I and II queues. Type I queue isassumed to transmit the status updates in a first-come-first-served (FCFS)fashion with no storage facility. However, Type I queue may not necessarilyminimize AoI because a new update will not be allowed to enter a server untilthe current update has been successfully transmitted. To overcome thisshortcoming, we consider Type II queue in which the most recent status updateavailable at a given transmission slot is transmitted in order to minimize theAoI. As the update delivery rate for a given link is a function of theinterference field seen from the receiver, the temporal mean AoI can be treatedas a random variable over space. Our goal in this paper is to characterize thespatial distribution of the mean AoI observed by the SD pairs by modeling themas a Poisson bipolar process. Towards this objective, we first derive accuratebounds on the moments of success probability while efficiently capturing theinterference-induced coupling in the activities of the SD pairs. Using thisresult, we then derive tight bounds on the moments as well as the spatialdistribution of peak AoI. Our numerical results verify our analytical findingsand demonstrate the impact of various system design parameters on the mean peakAoI.

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