BONUS $(12$ pts$.)$ Customers arrive at a single$-$server system at a Poisson rate of $4$ per hour and the service time is exponential with a mean of $12$ minutes per customer.

$($a$)(4$ pts$.)$ What are the long$-$run average number of customers in service $(L_s)$ and in the queue $(L_Q)$ equal to$?$

$($b$)(4$ pts$.)$ What are the long$-$run average time in service $(W_S)$ and in the queue $(W_Q)$ equal to$?$

$($c$)(2$ pts$.)$ What is the utilization of the server?

$($d$)(2$ pts$.)$ What are the long$-$run average number of customers in the system $(L)$ and the long$-$run average time in system $(W)$ if the arrival rate increases to $5$ per hour?