PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Maximum Ismail’s Second Entropy Formalism of Heavy-Tailed Queues with Hurst Exponent Heuristic Mean Queue Length Combined with Potential Applications of Hurst Exponent to Social Computing and Connected Health
Version 1
: Received: 29 January 2024 / Approved: 29 January 2024 / Online: 30 January 2024 (08:45:46 CET)
How to cite:
A Mageed, D.I. Maximum Ismail’s Second Entropy Formalism of Heavy-Tailed Queues with Hurst Exponent Heuristic Mean Queue Length Combined with Potential Applications of Hurst Exponent to Social Computing and Connected Health. Preprints2024, 2024012055. https://doi.org/10.20944/preprints202401.2055.v1
A Mageed, D.I. Maximum Ismail’s Second Entropy Formalism of Heavy-Tailed Queues with Hurst Exponent Heuristic Mean Queue Length Combined with Potential Applications of Hurst Exponent to Social Computing and Connected Health. Preprints 2024, 2024012055. https://doi.org/10.20944/preprints202401.2055.v1
A Mageed, D.I. Maximum Ismail’s Second Entropy Formalism of Heavy-Tailed Queues with Hurst Exponent Heuristic Mean Queue Length Combined with Potential Applications of Hurst Exponent to Social Computing and Connected Health. Preprints2024, 2024012055. https://doi.org/10.20944/preprints202401.2055.v1
APA Style
A Mageed, D.I. (2024). Maximum Ismail’s Second Entropy Formalism of Heavy-Tailed Queues with Hurst Exponent Heuristic Mean Queue Length Combined with Potential Applications of Hurst Exponent to Social Computing and Connected Health. Preprints. https://doi.org/10.20944/preprints202401.2055.v1
Chicago/Turabian Style
A Mageed, D.I. 2024 "Maximum Ismail’s Second Entropy Formalism of Heavy-Tailed Queues with Hurst Exponent Heuristic Mean Queue Length Combined with Potential Applications of Hurst Exponent to Social Computing and Connected Health" Preprints. https://doi.org/10.20944/preprints202401.2055.v1
Abstract
The theory of Ismail's non-extensive maximum entropy solution (NME) is described in detail. It is used as an inductive inference technique for heavy-tailed queues with a non-robust mean queue length and a non-extensive "long-range" interaction. In our novel method, we substitute the non-robust mean queue length for the conventional Pollaczeck-Khinchin mean queue length. In other words, the new non-extensivity parameter q will be included in the resulting state probability function.Numerical portraits are provided to capture the influential effect of the derived formalism, , on the stable M//1 queue with heavy tails. More potentially, some applications of Hurst Exponent to social computing and connected health are provided. Conclusion with some challenging open problems and possible future research pathways are given.
Keywords
Queue, Noros Mean Queue Length, stable M/G/1 queue, Ismail’s second entropy.
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.
