Download PDFOpen PDF in browserM|M|∞ Busy Period and Busy Cycle Distribution Functions BoundsEasyChair Preprint 79327 pages•Date: May 8, 2022AbstractThe 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
|