Homework problem: Sunset Airlines is concerned about the level of service for its check-in procedure. Currently, a single clerk spends an average of 3 minutes per passenger checking luggage and issuing boarding passes. Passengers arrive at the rate of 15 per hour. Make all the assumptions of M/M/1 model. Submit your answers to the following questions. Show your work.

(a) What is the utilization of the clerk?

(b) What is the average number of passengers in service?

(c) What is the average number of passengers in the waiting line?

(d) What is the average waiting time in line of a passenger?

(e) What is the average time spent in the system of a passenger?

(f) What is the average number of passengers in the system?

(g) What is the probability of having more than 2 passengers in the system?

(h) What is the probability of having no passenger in the waiting line?

(i) If the clerk is replaced by a self-serve ATM with a constant service time of 3 minutes, what would be the average waiting time in line of a passenger?