In this work, the M|G|? queue system transient probabilities, with time origin at the beginning of a busy period, are determined. It is emphasized the obtained distribution mean and variance study as time functions. In this study, for which it is determinant the hazard rate function service time, arise some differential equations which solutions lead to some particular service time distributions for which those parameters present a particular behavior.

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M|G ?, Transient probabilities, Hazard rate function, Differential equations