M/G/1 queue with Balking Shannonian Maximum Entropy Closed Form Expression with Some Potential Queueing Applications to Energy

Abstract

The investigation of stable M/G/1 and queue with balking, characterized by a Poisson prospective arrival process and i.i.d. general (G) service periods, is being done to examine linkages between discrete maximum entropy (ME) distribution (i.e., the derived solutions resulting from the Lagrangian optimization of the proposed entropy function under prior and main constraints conditions) judgements and Markov chains. Increasing moment limitations are expected to keep exposing distinct state probability for single and many server queues with new information theoretic distributional structures. In this setting, the stationary queue length distributions (QLDs) of the queues-specifically, the generalized discrete Half Normal (GdHN) distributions-are more precisely inferred. The underlying service time distribution function and the cumulative service time distribution function both describe the M/GE/1 queue with balking (by balking, we mean the situation when customers refuse to join a queue) bearing the GdHN ME. Significant applications of queuing theory have been demonstrated to reveal the potential role of queueing techniques to energy works and other related fields. Fundamentally, the sky is open for revolutionary advancements by employing novel emerging queueing techniques in energy works and many unexplored disciplines.