Question: Consider an M/M/1/1 queueing system (i.e., a single-server queue with customers arriving according to a Poisson process with rate a > 0, exponentially distributed service

Consider an M/M/1/1 queueing system (i.e., a single-server queue with customers

arriving according to a Poisson process with rate a > 0, exponentially distributed

service times with rate b > 0, an upper bound of one customer in the system at any

time, and all random variables being independent of each other). Suppose that each

customer who is served by this system pays $r for the service. Compute the long-run

average hourly revenue as a function of a and b. Make sure to compute the steady-state

distribution of the number of customers in the system. Explain.

Let r = 8.

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