# Two M/M/1 queues working independently

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 $$2\mu$$?

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