First Order Differential Equations Induced by the Infinite Servers Queue with Poisson Arrivals Transient Behavior Probability Distribution Parameters Study as Time Functions
Probability
2021-09-29 v1
Abstract
The infinite servers queue with Poisson arrivals state transient probabilities, considering the time origin at the beginning of a busy period, mean and variance monotony as time functions is studied. These studies, for which results it is determinant the hazard rate function service time length, induce the consideration of two differential equations, one related with the mean monotony study and another with the variance monotony study, which solutions lead to some particular service time distributions, for which those parameters present specific behaviors as time functions.
Keywords
Cite
@article{arxiv.2109.13591,
title = {First Order Differential Equations Induced by the Infinite Servers Queue with Poisson Arrivals Transient Behavior Probability Distribution Parameters Study as Time Functions},
author = {Manuel Alberto M. Ferreira},
journal= {arXiv preprint arXiv:2109.13591},
year = {2021}
}
Comments
10 pages and no figures