Year: 2025
Type: article
Abstract: In gossip networks, a source node forwards time-stamped updates to a network of observers according to a Poisson process. The observers then update each other on this information according to Poisson processes as well. The Age of Information (AoI) of a given node is the difference between the current time and the most recent time-stamp of source information that the node has received. We provide a method for evaluating the AoI of a node in terms of first passage percolation. We then use this distributional identity to prove matching upper and lower bounds on the AoI in terms of connectivity properties of the underlying network. In particular, if one setsXvto be the AoI of nodevon a finite graphGwithnnodes, then we definem*= min{m:m· |Bm(v)| ≥n} whereBm(v) is the ball of radiusminG. In the case when the maximum degree ofGis bounded by Δ we prove EXv= ΘΔ(m*). As corollaries, we solve multiple open problems in the literature such as showing the age of information on a subset of Zdis Θ(n1/(d+1)). We also demonstrate examples of graphs with AoI scaling likenαfor each α ∈ (0, 1/2). These graphs are not vertex-transitive and in fact we show that if one considers the AoI on a graph coming from a vertex-transitive infinite graph then either EXv= Θ(n1/k) for some integerk≥ 2 or EXv=no(1).
Authors: Thomas Jacob Maranzatto, Marcus Michelen
Institutions: University of Maryland, College Park, Northwestern University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Institute for Data, Econometrics, Algorithms and Learning (IDEAL), CAREER: Analytic and High-dimensional Methods in Probability, Random structures in high dimensions: Matrices, polynomials and point processes, G6671297155, LEAPS-MPS: Analytic Approaches to Limit Theorems and Random Structures
OpenAlex ID: W4414463330