Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds - Ferreira, M. A. M. (arXiv:2209.05312, 2025)
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.