Stochastic Geometry-based Analysis of the Distribution of Peak Age of Information
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In this paper, we consider a large-scale wireless network consisting of source-destination (SD) pairs where the source nodes frequently send status updates about some underlying physical processes (observed by them) to their corresponding destination nodes. The status updates of each source node are transmitted based on a first-come-first-served (FCFC) queueing discipline with no storing facility (i.e., zero buffer). For this setup, we employ Age of information (AoI) as a performance metric to quantify freshness of the status updates when they reach the destination nodes. While most of the existing works are focused on the analysis of mean AoI in deterministic network topologies, we aim to characterize the distribution of AoI in a large-scale stochastic setting. Towards this objective, we first characterize the distribution of the successful transmission of a status update using stochastic geometry by modeling the locations of the SD pairs as a bipolar Poisson point process (PPP). Using this distribution, we then derive tight bounds on the moments as well as the distribution of peak AoI. Our results provide useful design guidelines on the appropriate selection of different system parameters to minimize the mean peak AoI.
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