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arXiv · 2209.05312

Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds

Manuel Alberto M. Ferreira
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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.

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BibTeXRIS

Manuel Alberto M. Ferreira. 2022-09-09. Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds. https://arxiv.org/abs/2209.05312

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