Calculate the reduction in waiting time in the queue for customers (if any) in minutes that can be expected by replacing the current crew by the robotic oil change unit. Enter your answer in minutes rounded to 2 decimal places.
Bob runs a car oil change shop. His oil change crew can change the oil of a car in 10 minutes on average. Since he has only 1 oil change crew working on 1 oil change pit, only 1 car is processed at a time.
Cars arrive at his oil change facility at the rate of 5.45 cars per hour.
Assume the arrivals are Poisson distributed and the oil change service times by his crew follow an exponential distribution.
Bob, after taking a class, has become interested in automation. He is thinking of investing in an automated robotic oil change unit that can replace his current crew. Bob learns that this automated robotic oil change machine takes precisely 10 minutes on every car to change the oil (i.e. there is no variability in this service time). Bob is a bit disappointed that this robotic oil change unit on average does not appear to be faster than his crew. Bob wants to reduce the customer waiting time at his shop. He wants you to help him figure out if the robotic oil change unit can reduce customer waiting time in the queue (waiting for the oil change).
Calculate the reduction in waiting time in the queue for customers (if any) in minutes that can be expected by replacing the current crew by the robotic oil change unit. Enter your answer in minutes rounded to 2 decimal places.
Hint: If W1 is the waiting time in the queue in the current system and W2 is the waiting time in the queue with the robotic oil change unit installed, then the reduction in waiting time can be computed as W1 - W2.
Queuing theory is an important concept in service-providing organizations. This concept helps the managers evaluate the time taken to provide services without any lag to satisfy the customers. They aim to minimize the waiting time and number of customers by increasing the service rates.
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