The Robot Company owns car wash stations throughout the United States. Robot sta

Question

The Robot Company owns car wash stations throughout the United States. Robot stays open 14 hours per day. Robot has a power unit that can wash cars at the rate of one every 5 minutes on average. The company estimates that customers will not wait in line more than 5 minutes for a car wash. A longer time will cause Robot to lose car wash sale. If the estimate of customer arrivals resulting in washes is 10 per hour, how many lost sales does Robot have each day? Assuming customer interarrival time and service time both follow exponential distribution.

Explanation / Answer

Here, customer arrival rate = 10 cars / hr = 1/6 cars per min = 0.166

system service rate µ = 1/5 cars per min =0.2

Waiting time of customer in queue = maximum 5 min.

When you calculate waiting time ( Wq) in queue based on given arrival and service rate,

Wq = / µ ( µ -  )

= 0.166 / 0.2 ( 0.2 - 0.166 )

= 24.41 minutes

Hence total waiting time in queue for customer is 24.41 min. Now as company has estimated that customer is not willing to stay in system for more than 5 min. of waiting, estimated lost of sales per day = aproximately 5 cars.

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