An average of 10 cars per hour arrive at a drive-thru with a single ATM. Assume the average service time per customer is 4 minutes. Assume that the inter-arrival times and the service times are exponential. a) What is the probability that the ATM is unoccupied? b) What is the average number of cars in the queue at the ATM? c) What is the average time that a car spends in the parking lot?
Added by Rebecca A.
Step 1
Given that the arrival rate is 10 cars per hour and the service rate is 15 cars per hour, we have λ = 10 and μ = 15. Using the formula for the probability that the system is empty: P(0) = 1 - λ/μ, we get: P(0) = 1 - 10/15 = 1 - 0.666 = 0.334. Show more…
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