Echo Chamber Analysis: Matrix Geometric Method for Aggregated Model of GI/G/s in Discrete Time

This study focuses on the discrete-time general-distribution aggregation network queueing system, which was the subject of our previous study with using the Matrix Geometric Method (MGM), and discusses the micro characterization methods and results of the processing nodes of the model. The MGM in our previous studies were found difficult to validate in some areas owing to the lack of resources in the computing environment during the validation phase. Therefore, in this paper, we use the random matrix theory to perform a spectral analysis to investigate the nature of fluctuations in the eigenvalues and discuss their properties. We assume an undirected graph type and an effective graph type network. For each link type, the behavior of the maximum eigenvalue as the number of agents increases is investigated and its dynamics is clarified. We also present a system modeling methodology to connect the same analysis method to the aggregation network queueing system, and discuss the validity of the methodology.