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Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds
Document Title
arXiv:2209.05312
Year (definitive publication)
2022
Language
English
Country
United States of America
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Abstract
The busy period length distribution function knowledge is important for any queue system, and for the MGINF queue. But the mathematical expressions are in general very complicated, with a few exceptions, involving usually infinite sums and multiple convolutions. So, in this work are deduced some bounds for the MMINF system busy period length distribution function, meaning the second M exponential service time, which analytic expressions are simpler than the exact one. As a consequence, also some bounds for the MMINF system busy cycle length distribution function are presented.
Acknowledgements
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Keywords
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Computer and Information Sciences - Natural Sciences
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