  This exposition presents a novel approach to solving an M/M/m queue for the
waiting time and the residence time. The motivation comes from an algebraic
solution for the residence time of the M/M/1 queue. The key idea is the
introduction of an ansatz transformation, defined in terms of the Erlang B
function, that avoids the more opaque derivation based on applied probability
theory. The only prerequisite is an elementary knowledge of the Poisson
distribution, which is already necessary for understanding the M/M/1 queue. The
approach described here supersedes our earlier approximate morphing
transformation.
