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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
16th Conference on Applied Mathematics, APLIMAT 2017
Year (definitive publication)
2017
Language
English
Country
Slovakia
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Abstract
The M|G|? queue system 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
Exact differential equations,First order differential equations,Hazard rate function,M|G|?,Queue,Service time length,Transient probabilities
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Other Engineering and Technology Sciences - Engineering and Technology
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