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Question: Cynthia Knott’s Car Wash is open

Cynthia Knott’s Car Wash is open 6 days a week, but its busiest day is always Saturday. From historical data, Cynthia estimates that dirty cars arrive at the rate of 20 per hour all day Saturday. With a full crew working the hand-wash line, she figures that cars can be cleaned at the rate of one every 2 minutes. One car at a time is cleaned in this example of a single-channel waiting line.
Assuming Poisson arrivals and exponential service times, find the following:
a) The average number of cars in line.
b) The average time that a car waits before it is washed.
c) The average time that a car spends in the service system.
d) The utilization rate of the car wash.
e) The probability that no cars are in the system.
f) Cynthia is thinking of switching to an all-automated car wash that uses no crew. The equipment under consideration washes one car every minute at a constant rate. How will your answers to parts (a) through (e) change with the new system?


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