Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds
Probability
2022-09-13 v1
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.
Cite
@article{arxiv.2209.05312,
title = {Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds},
author = {Manuel Alberto M. Ferreira},
journal= {arXiv preprint arXiv:2209.05312},
year = {2022}
}
Comments
7 pages and no figures