Version 1
: Received: 27 January 2024 / Approved: 29 January 2024 / Online: 29 January 2024 (08:44:46 CET)
How to cite:
A Mageed, D.I. Information Geometric Analysis of the Dynamics of M/M/∞ Transient Queue Manifold. Preprints2024, 2024011994. https://doi.org/10.20944/preprints202401.1994.v1
A Mageed, D.I. Information Geometric Analysis of the Dynamics of M/M/∞ Transient Queue Manifold. Preprints 2024, 2024011994. https://doi.org/10.20944/preprints202401.1994.v1
A Mageed, D.I. Information Geometric Analysis of the Dynamics of M/M/∞ Transient Queue Manifold. Preprints2024, 2024011994. https://doi.org/10.20944/preprints202401.1994.v1
APA Style
A Mageed, D.I. (2024). Information Geometric Analysis of the Dynamics of <em>M/M/∞</em> Transient Queue Manifold. Preprints. https://doi.org/10.20944/preprints202401.1994.v1
Chicago/Turabian Style
A Mageed, D.I. 2024 "Information Geometric Analysis of the Dynamics of <em>M/M/∞</em> Transient Queue Manifold" Preprints. https://doi.org/10.20944/preprints202401.1994.v1
Abstract
From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .
Keywords
Transient , information geometry (IG), statistical manifold (SM), M/M/ Infinity queue manifold (QM), Geodesic equations of motion, Ricci Curvature (RC), Einstein Tensor, Stress Energy Tensor, Riemannian metric (RM), Fisher Information matrix (FIM), Inverse Fisher Information matrix (IFIM), threshold theorem
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
