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Publication Detailed Description
POISSOIN ARRIVALS, EXPONENTIAL SERVICE TIME, AND INFINITE SERVERS QUEUE BUSY PERIOD AND BUSY CYCLE DISTRIBUTION FUNCTIONS BOUNDS
Journal Title
Acta Scientiae et Intellectus
Year (definitive publication)
2022
Language
English
Country
Azerbaijan
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Abstract
The busy period length distribution function knowledge is important for any queue system, and 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 theM/M/∞ system busy cycle length distribution function are presented.
Acknowledgements
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Keywords
M/M/∞,busy period,distribution function,bounds
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
- Computer and Information Sciences - Natural Sciences
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