The busy period length distribution function knowledge is important for any queue system, and in particular for the M/M/? 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

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Bounds; Busy period; Distribution function; M/M/?