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If two M/M/1 queues with arrival rate $\lambda$ and service rate $\mu$ are working independently. Is the system equivalent to a single M/M/1 queue with arrival rate $2\lambda$ and service rate $2\mu$?

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    $\begingroup$ What happens when the first customer arrives? Does that customer get served twice as fast? $\endgroup$ – Mark L. Stone Jul 11 '20 at 12:33
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    $\begingroup$ Another hint: In both scenarios, think about what it takes for a server to be idle. $\endgroup$ – prubin Jul 11 '20 at 22:41

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