M|M|∞ Busy Period and Busy Cycle Distribution Functions Bounds - Ferreira, M. A. M.; Andrade, M. A. P. (EasyChair Preprint Nº 7932, 2025)
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.