On the Trio Unification of Information Geometry, Einsteinian Relativity, and Transient Queues the Parthasarathian Case

Ismail A Mageed

doi:10.20944/preprints202402.0038.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 31 January 2024 / Approved: 1 February 2024 / Online: 2 February 2024 (06:34:40 CET)

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses the relationship between stability and the Gaussian curvature, as well as the connections between queueing theory, information geometry, , Riemannian geometry, and the Theory of Relativity.

Transient M/M/1; IG, statistical manifold (SM); QM; Geodesic equations of motion; Riemannian metric (RM); Fisher Information matrix (FIM); Inverse Fisher Information matrix (IFIM); threshold theorem

Computer Science and Mathematics, Probability and Statistics

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On the Trio Unification of Information Geometry, Einsteinian Relativity, and Transient Queues the Parthasarathian Case

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