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The busy period length distribution function knowledge is important for anyqueue system, and for the MGINF queue. But the mathematical expressions are ingeneral very complicated, with a few exceptions, involving usually infinitesums and multiple convolutions. So, in this work are deduced some bounds forthe MMINF system busy period length distribution function, meaning the second Mexponential service time, which analytic expressions are simpler than the exactone. As a consequence, also some bounds for the MMINF system busy cycle lengthdistribution function are presented.

Poisson Arrivals, Exponential Service Time, and Infinite Servers Queue Busy Period and Busy Cycle Distribution Function Bounds