Physical Sciences and Mathematics Commons^™

On Superposition Of Heterogeneous Edge Processes In Dynamic Random Graphs, Zhongmei Yao, Daren B. H. Cline, Dmitri Loguinov

Computer Science Faculty Publications

This paper builds a generic modeling framework for analyzing the edge-creation process in dynamic random graphs in which nodes continuously alternate between active and inactive states, which represent churn behavior of modern distributed systems. We prove that despite heterogeneity of node lifetimes, different initial out-degree, non-Poisson arrival/failure dynamics, and complex spatial and temporal dependency among creation of both initial and replacement edges, a superposition of edge-arrival processes to a live node under uniform selection converges to a Poisson process when system size becomes sufficiently large. Due to the convoluted dependency and non-renewal nature of various point processes, this result significantly …