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

Abstract

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.