Students arrive at Hande Hoca's office every $6$ minutes on the average. When there is no one waiting in front of her room, the meeting takes about $10$ minutes on average. However, if there are $1$ or $2$ students walting in front of the room, Hande Hoca makes a shorter session with the current student in the room and decreases the meeting time to $5$ minutes on average. When there are $2$ students in front of the room waiting, new students coming to the $5"$ floor see the crowd in the corridor and decide to cancel. their meeting $($they don't even join in the queuel$).$ Assuming that all the interarrival times and advising session durations are following exponential distribution, answer the following questions:

a$-)$ Determine the arrival $($R$./$ and service rates $($pa$)$ for n$=0,1,2..(3$ pts$)$

b$-)$ Draw a graph representing the queueing system where the nodes show the number of students in the system? $(3$ pts$)$

c$)$ What is the probability that no student comes to Hande Hoca's room for $15$ minutes? $(3$ pts$)$

d$-)$ What is the steady$-$state probability that there is no one in the corridor $($queue$)?(8$ pts$)$

e$)$ What is the steady$-$state probability that a student balks? $(3$ pts$)$