2. A business man wants to open a barber shop in a busy business area. He expects that his customers will arrive in a poison distribution with an average of 10 customers per hour. He is not sure how many chairs of service and barbers he should have (a barber for a chair). If all barbers are busy, an arriving customer has to wait. He knows that on average each barber can handle 3 customers per hour with exponential distribution. He uses an M/M/S queue model with 4 barbers (M/M/4) with max. queue length of 5 . He gets the following results. Answer "N/A" if answer is not available or unknown. Give your brief reason how you reach your answer for each answer. Use M/M/4 result to answer the following questions. 2.1 Is utilization of each barber the same? What is an average utilization of a barber? Explain your answer. 2.2 What is the probability of all 4 barbers is idle at the same time? 2.3 What is the probability of a customer does NOT have to wait for a haircut service? 2.4 What is the average number of customer(s) in the shop? 2.5 What is the average number of customer(s) in the shop waiting in line? 2.6 What is the minimum time a customer spends in the line? 2.7 What is the maximum time a customer spends in the shop? 2.8 What is the average time a customer spends in the shop? 2.9 What is the average time a customer spends waiting in line? 2.10 If a barber works 10 hours a day, how many hours a day on average does he spend time with his customer? 2.11 What is the meaning of "a customer balks"? How does it happen? 2.12 If maximum queue length is changed to 3, will new utilization of each barber be higher, lower, or the same? Explain your