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This exposition presents a novel approach to solving an M/M/m queue for thewaiting time and the residence time. The motivation comes from an algebraicsolution for the residence time of the M/M/1 queue. The key idea is theintroduction of an ansatz transformation, defined in terms of the Erlang Bfunction, that avoids the more opaque derivation based on applied probabilitytheory. The only prerequisite is an elementary knowledge of the Poissondistribution, which is already necessary for understanding the M/M/1 queue. Theapproach described here supersedes our earlier approximate morphingtransformation.

Erlang Redux: An Ansatz Method for Solving the M/M/m Queue