Q4. Women arrive at a hairdresser that operates in Withington, Manchester with a single haircut and single manicure services according to a Poisson process. The arrival rate of customers is 2 per hour. Service times for haircut and manicure are represented by exponential random variables with rates 4 and 6 per hour, respectively. Since getting a haircut takes longer than a manicure, the arriving customer directly sits for a haircut if the seat is not occupied. If another person is getting a haircut once the new customer arrives and manicure seat is free, she begins her manicure. If both of the seats are busy, the new arrival is cannot enter the system. A customer who completes her haircut goes for a manicure if it is empty else, leaves the hairdresser. Customers leave the hairdresser after receiving manicure. Show all your work step-by-step while answering the following: a i. Define states and draw the transition state diagram. ii. Calculate long-run probabilities of all states. iii. Determine the fraction of women who cannot enter the system? iv. How many minutes on average a woman spends at the hairdresser? v. What is the fraction of entering women that can get a haircut? vi. The hairdresser modifies its operations by cancelling manicure services. Q4. Women arrive at a hairdresser that operates in Withington, Manchester with a single haircut and single manicure services according to a Poisson process. The arrival rate of customers is 2 per hour. Service times for haircut and manicure are represented by exponential random variables with rates 4 and 6 per hour, respectively. Since getting a haircut takes longer than a manicure, the arriving customer directly sits for a haircut if the seat is not occupied. If another person is getting a haircut once the new customer arrives and manicure seat is free, she begins her manicure. If both of the seats are busy, the new arrival is cannot enter the system. A customer who completes her haircut goes for a manicure if it is empty else, leaves the hairdresser. Customers leave the hairdresser after receiving manicure. Show all your work step-by-step while answering the following: a i. Define states and draw the transition state diagram. ii. Calculate long-run probabilities of all states. iii. Determine the fraction of women who cannot enter the system? iv. How many minutes on average a woman spends at the hairdresser? v. What is the fraction of entering women that can get a haircut? vi. The hairdresser modifies its operations by cancelling manicure services