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6 years ago
A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is 16 per hour and the average service time is three minutes. If the dry cleaner wants to accommodate (have enough room for) all of the waiting cars at least 96 percent of the time, how many car-lengths should they make the driveway leading to the window?
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Quantitative Analysis for Management

Quantitative Analysis for Management


Edition: 12th
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6 years ago
The probability of having more than 14 cars in the system is (16/20)14+1 = 0.035, so they should make the driveway approximately 13 car-lengths long (because one car will be at the service window). (The probability of having more than 13 cars in the system is 0.044 (which is too high), and the percentage only gets worse as the queue length is shortened.)
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