$(20$p$.)$ The mean inter$-$arrival times of professors and students to a restaurant inside the campus is $4$ and $2$ minutes, respectively. There are two people serving the customers at the place where the foods are selected by the customers. If both servers are busy, a newly arrived customer wait in the queue. The mean service time is $2$ minutes.

a$.$ Is this queue stable? If so$,$ solve below questions.

b$.$ Find the expected waiting time of customers in the queue in steady state.

c$.$ Find the expected waiting times of professors and students in the queue, if professors have the $($nonpreemptive$)$ priority.

d$.$ Find the expected waiting times of professors and students in the queue, if students have the $($nonpreemptive$)$ priority.