M|M|∞ Busy Period and Busy Cycle Distribution Functions Bounds

EasyChair Preprint 7932

Abstract

The busy period length distribution function knowledge is important for any queue system, and in particular 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 the M|M|∞  system busy cycle length distribution function are presented.

Keyphrases: M|M|∞, bounds, busy period, distribution function

@booklet{EasyChair:7932,
  author    = {Manuel Alberto M. Ferreira and Marina Andrade},
  title     = {M|M|∞ Busy Period and Busy Cycle Distribution Functions Bounds},
  howpublished = {EasyChair Preprint 7932},
  year      = {EasyChair, 2022}}