Information Geometric Analysis of the Dynamics of Transient M/M/∞ Queue Manifold
DOI:
https://doi.org/10.31181/sa22202433Keywords:
Transient M/M/ ∞ queueuing system, Information geometry, Statistical manifold, Queue manifold, Geodesic equations of motion, Ricci curvature, Einstein tensor, Stress energy tensor, Riemannian metric, Fisher information matrix, Inverse fisher information matrix, Threshold theoremAbstract
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 IG of a queuing system. From the perspective of IG, the manifold of the temporary M/M/∞ queue is described in this context. The Fisher Information Matrix (FIM) as well as the Inverse of FIM, (IFIM) of transient M/M/∞ Queue Manifold (QM) are devised. In addition to that, new results that uncovered the significant impact of stability of M/M/∞ QM on the existence of IFIM are obtained. Moreover, the Geodesic Equations (GEs) of motion of the coordinates of the underlying transient M/M/∞ are obtained. Also, it is revealed that stable M/M/∞ QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero 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/∞ QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed. A summary combined with future research work are given.
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