Probabilistic proof of the interchangeability of ./M/1 queues in series

Given a finite number of empty ./M/1 queues, let customers arrive according to an arbitrary arrival process and be served at each queue exactly once, in some fixed order. The process of departing customers from the network has the same law, whatever the order in which the queues are visited. This remarkable result, due to R. Weber 4], is given a simple probabilistic proof.