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.

中文翻译：

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Erlang Redux：一种解决M/M/m队列的Ansatz方法

该说明提出了一种解决等待时间和停留时间的 M/M/m 队列的新方法。动机来自 M/M/1 队列停留时间的代数解。关键思想是引入 ansatz 变换，根据 Erlang B 函数定义，避免了基于应用概率论的更不透明的推导。唯一的先决条件是泊松分布的基本知识，这对于理解 M/M/1 队列已经是必要的。这里描述的方法取代了我们之前的近似变形变换。