Info- Geometric Analysis of the Stable Queue Manifold Dynamics With Queue Applications to E-health

A Mageed, Dr Ismail

doi:10.20944/preprints202401.1813.v1

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…This strategy connected information matrix theories with IG, opening new insights into queueing theory. According to [3,6], Ricci curvature quantifies the distinction between the standard Euclidean metric (EM) and the Riemannian metric (RM) in the setting of the article. In contrast, the difference in volume between a geodesic ball and a Euclidean ball with the same radius is measured by scalar curvature.…”

Section: Introductionmentioning

confidence: 99%

Towards An Info-Geometric Theory Of The Analysis Of Non-Time Dependent Queueing Systems

A. Mageed

2024

Preprint

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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 a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 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. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.

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Section: Introductionmentioning

confidence: 99%

Towards An Info-Geometric Theory Of The Analysis Of Non-Time Dependent Queueing Systems

A. Mageed

2024

Preprint

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“…The entropy functional stops being exhaustive due to logarithm linearization. To examine a range of non-extensive systems, Tsallisian followers have extensively utilised this quality [12][13][14][15][16][17][18][19][20]. In doing so, the constraint |1 − 𝑞| ≪ 1 mentioned above is typically ignored.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

On the Rényi Entropy Functional, Tsallis Distributions and Lévy Stable Distributions

A Mageed

2024

Preprint

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The Rényi entropy functional was optimised for the novel findings of this investigation under various conditions. Their research's findings suggest that the complete spectrum of Lévy stable distributions is covered by generalised t-distributions. Additionally, an exposition was undertaken to prove that the Lévy distribution generalizes Tsallisian distribution, rather than the reverse. The current study is a strong generalization of an existing research work in the literature.

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Info- Geometric Analysis of the Stable Queue Manifold Dynamics With Queue Applications to E-health

Cited by 2 publications

References 5 publications

Towards An Info-Geometric Theory Of The Analysis Of Non-Time Dependent Queueing Systems

Towards An Info-Geometric Theory Of The Analysis Of Non-Time Dependent Queueing Systems

On the Rényi Entropy Functional, Tsallis Distributions and Lévy Stable Distributions

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