Authors:
Ismail A. Mageed
and
Demetres D. Kouvatsos
Affiliation:
Department of Computer Science, Faculty of Engineering and Informatics, University of Bradford, Bradford, BD7 1DP, U.K.
Keyword(s):
Stable M/G/1 Queue, Maximum Entropy (ME), Information Geometry (IG), Statistical Manifold (SM), Queue Manifold (QM), Ricci Curvature (RC), Riemannian Metric (RM), Fisher Information Matrix (FIM), Kullback’s Divergence (KD), J-divergence (JD), Information Matrix Exponential (IME).
Abstract:
Information geometry (IG) provides the characterization of thestructure of statistical models froma differential geometric point of view. By considering families of probability distributions as mani-folds 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 mode-lling study of information geometrics of a queueing system. In this context, the manifold of stableM/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 hasa zero 0 -Gaussian curvature a non-zero Ricci Curvature Tensor (RCT). Unifying IG with Que-ueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geo-metry (RG) point of vi
ew, leading to the analysis of the stable M/G/1 queue, based on Theory of Relativity (TR)
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