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Kigarya
Kigarya
17.08.2021 • 
Mathematics

Visitor's parking at Ozark College is limited to five spaces only. Cars making use of this space arrive according to a Poisson distribution at the rate of six cars per hour. Parking time is exponentially distributed with a mean of 30 minutes. Visitors who cannot find an empty space on arrival may temporarily wait inside the lot until a parked car leaves. That temporary space can hold only three cars. Other cars that cannot park or find a temporary waiting space must go elsewhere. Determine the following: (a) The probability, pn, of n cars in the system. (b) The effective arrival rate for cars that actually use the lot. (c) The average number of cars in the lot. (d) The average time a car waits for a parking space inside the lot. (e) The average number of occupied parking spaces. (f) The average utilization of the parking lot.

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