In-A-Jiffy Lube Inc offers both car wash and oil change services to its customers. It has 3 car wash bays, 1 service person working on oil changes, 1 person working on minor repairs and 1 cashier. Suppose arrival rate to the car wash facility is according to a Poisson Process with rate 10/hr. The arrival rate for the oil change is also a Poisson process with a rate of 2/hr. While the oil change is being done, the service person also checks for some minor problems in the car. 20% of the cars tend to have a minor problem and these cars are sent to the minor repair facility. After the service is completed, all cars join a common queue to make their payment at ITOM 6277 Operations and Supply Chain Management the cashier. The diagram below represents the service process at In-A-Jiffy. Car wash, Oil change and Minor repairs are exponentially distributed and take 15 minutes, 20 minutes and 30 minutes respectively. The payment process is also exponentially distributed and it takes 4 minutes for the cashier to collect payment from a customer. Figure 1: Jiffy Lube Process Diagram

a. What is the average time a car coming for car wash spends in the system?

b. What is the average time a car that comes to get an oil change spends in the queue? 

A= 10/hr X = 2/hr Car wash bays Bay 1 Bay 2 Bay 3 Oil Change 20min 20% Minor Repair 30min 80% Cashier 4 min