On the interchangeability and stochastic ordering of ·/M/1 queues in tandem

A probabilistic proof is given of the fact that the departure process from two initially empty. ·/M/1 queues in tandem is unaffected when the service rates are interchanged. As a consequence of this, we show that when the sum of the service rates at the two queues is held constant the departure process stochastically increases as the service rates become equal. The proofs are based on coupling of reflected random walks.