English

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.

Keywords

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