An Information Theoretic Unified Global Theory For a Stable $M/G/1$ Queue With Potential Maximum Entropy Applications to Energy Works

This paper establishes comprehensive description of the theory of maximum entropy global formalism to analyze a stable
$\boldsymbol{M/G/1}$
queue, novel state probability
$\boldsymbol{p_{q, UG}(n)},\boldsymbol{n=0,1,}$
2,… as inductive inference approach for systems. This revolutioanry approach is based on the provision of maximizing Ismail's entropy(IE), namely,
$\boldsymbol{H_{(q, UG)}}$
, which is the ultimte generalization to all the entropy measures in the literature, subject to prescribed contraints. Numerical portraits are provided to capture the influential effect of the derived formalism,
$\boldsymbol{p_{q, UG}(n),\ n=} \boldsymbol{0,1,2, \ldots}$
on the stable
$\boldsymbol{M/GE_{q, UG}/1}$
queue with heavy tails. An expxposition to several potential applictaions of maximum entropy(ME) to energy works is undertaken. Conclusion with possible future research pathways are given.