The Impact of Information Geometry on the Analysis of the Stable M/G/1 Queue Manifold

Abstract

Information geometry (IG) provides the characterization of the structure of statistical models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of stable M/G/1queue is characterised from the viewpoint of IG, the Kullback’s divergence (KD) and J-divergence (JD) are determined. Also, it is revealed that the stable M/G/1 queue manifold has a zero 0 -Gaussian curvature a non-zero Ricci Curvature Tensor (RCT). Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometry (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on Theory of Relativity (TR).