Aug 19, 2017

How long should an arriving customer expect to wait before vacuuming begins on her car?

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Cars arriving at Bunkey’s Car Wash follow a Poisson distribution with a mean interarrival time of 10 minutes. These cars are successively vacuumed, washed, and hand-dried, and the time to perform each of the three tasks is exponentially distributed with a mean of 3 minutes. How long should an arriving customer expect to wait before vacuuming begins on her car? Bunkey realizes that this is excessive and hires additional help so that the time to vacuum and hand-dry a car is reduced to 1 minute each. By how much does this reduce the customer’s waiting time?


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