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M|M|∞ Busy Period and Busy Cycle Distribution Functions Bounds
Document Title
EasyChair Preprint Nº 7932
Year (definitive publication)
2022
Language
English
Country
United Kingdom
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Abstract
The busy period length distribution function knowledge is important for any queue system, and in particular for the M|G|∞ 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 M|M|∞ 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 M|M|∞ system busy cycle length distribution function are presented.
Acknowledgements
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Keywords
bounds,busy period,distribution function,M|M|∞
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Computer and Information Sciences - Natural Sciences
Funding Records
| Funding Reference | Funding Entity |
|---|---|
| PEst-OE/EGE/UI0315/2011 | FCT-Fundação para a Ciência e Tecnologia, I.P. |
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