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A M|M|m|m Queue System Transient Behavior Study
Document Title
arXiv:2312.03870
Year (definitive publication)
2023
Language
English
Country
United States of America
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Abstract
It is a very hard task to compute an exact solution for the differential equations, with differences, system that allows the determination of the M|M|m|m system transient probabilities. The respective complexity grows with m. The computations are extremely fastidious and the length and the fact that the expressions obtained are often approximate, and not exact, will not allow the transient probabilities behavior as time functions characterization. To overcome these problems, in this work it is analyzed how that system can supply approximate values to the M|M|m|m queue system. It is also presented an asymptotic method to solve the system that becomes possible in many cases to obtain simple approximated expressions for those probabilities using the M|M|Inf transient probabilities, very well-known and very much easier to study.
Acknowledgements
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Keywords
M|M|m|m,M|M|∞,transient probabilities
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Computer and Information Sciences - Natural Sciences
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