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Study about a Differential Equation in an Infinite Servers Queue System with Poisson Arrivals Busy Cycle Distribution Study
Document Title
arXiv:2204.00621
Year (definitive publication)
2022
Language
English
Country
United States of America
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Abstract
In the infinite servers queue with Poisson arrivals real life practical applications, the busy period and the busy cycle probabilistic study is of main importance. But it is a very difficult task. In this text, we show that by solving a Riccati equation induced by this queue transient probabilities monotony study as time functions, we obtain a collection of service length distribution functions, for which both the busy period and the busy cycle have lengths with quite simple distributions, generally given in terms of exponential distributions and the degenerate at the origin distribution.
Acknowledgements
This work is financed by national funds through FCT - Fundação para a Ciência e
Tecnologia, I.P., under the project FCT UIDB/04466/2022. Furthermore, the author
thanks the ISCTE-IUL and ISTAR-IUL, for their support.
Keywords
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Computer and Information Sciences - Natural Sciences
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