Customers arrive at a bakery at an average rate of $18$ ?per hour on weekday mornings. The arrival distribution can be described by a Poisson distribution with a mean of $18.$ ?Each clerk can serve a customer in an average of three minutes. This time can be described by an exponential distribution with a mean of $3\mathrm{.}0$ ?minutes.

a $.$ ?What are the arrival and service rates?

b $.$ ?Compute the average number of customers being served at any time.

c $.$ ?Suppose it has been determined that the average number of customers waiting in line is $8\mathrm{.}1.$ ?Compute the average number of customers in the system $($ i $.$ e $.,$ ?waiting in line or being served $),$ ?the average time customers wait in line, and the average time in the system.

d $.$ ?Determine the system utilization for $M=1,2,$ ?and $3$ ?servers.