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

### Ismail A. Mageed, Demetres Kouvatsos

#### Abstract

Information geometry (IG) seeks to characterize the structure of statistical geodesic 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 Kullbackâ€™s divergence (KD) and J-divergence (JD) are determined. Also, it is revealed that the stable M/G/1 queue manifold is developable (i.e., has a zero Gaussian curvature) and has 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 the Theory of Relativity (TR).

Download#### Paper Citation

#### in Harvard Style

A. Mageed I. and Kouvatsos D. (2021). **The Impact of Information Geometry on the Analysis of the Stable M/G/1 Queue Manifold**.In *Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-485-5, pages 153-160. DOI: 10.5220/0010206801530160

#### in Bibtex Style

@conference{icores21,

author={Ismail A. Mageed and Demetres Kouvatsos},

title={The Impact of Information Geometry on the Analysis of the Stable M/G/1 Queue Manifold},

booktitle={Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2021},

pages={153-160},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010206801530160},

isbn={978-989-758-485-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

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

SN - 978-989-758-485-5

AU - A. Mageed I.

AU - Kouvatsos D.

PY - 2021

SP - 153

EP - 160

DO - 10.5220/0010206801530160