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First Order Differential Equations Induced by the Infinite Servers Queue with Poisson Arrivals Transient Behavior Probability Distribution Parameters Study as Time Functions
Document Title
arXiv:2109.13591
Year (definitive publication)
2021
Language
English
Country
United States of America
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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.
Acknowledgements
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Keywords
M|G|,queue,transient probabilities,service time length,hazard rate function,first order differential equations,exact differential equations.
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
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