Oil Change Center Queue

Cars arrive at an oil change center following a Poisson process, at the rate of four per hour. There is a single available mechanic, and the time taken to perform an oil change is exponentially distributed, with an average of 12 minutes. Approximate an unlimited car space.

    
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Steady-state distribution for the system:
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Distribution for the number of cars in the system:
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Probability that there are more than three cars at the oil change center:
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Mean and variance for the number of cars in the system:
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