What is the probability that a car does not have to wait


Car wash facility operates with only one bay. Cars arrive according to a Poisson distribution with a mean of 5 cars per hour and may wait in the facility's parking lot if the bay is busy. The time for washing and cleaning a car is exponential, with a mean of 6 minutes. Cars that cannot park in the lot can wait in the street bordering the wash facility. There is no limit on the size of the parking space. What is the probability that a car does not have to wait for service? On the average, how many cars have to wait in line? With the construction of another bay, on the average how many cars have to wait in line? Which is the best alternative (one or two bays) and why?

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