Maximum Ismail’s Second Entropy(HI q )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

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, pq,I (Sn ), n=0,1,2,… on the stable M/GEq,I /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