Problem 18-2 A vending machine dispenses hot chocolate or coffee. Service time i

Question

Problem 18-2 A vending machine dispenses hot chocolate or coffee. Service time is 40 seconds per cup and is constant. Customers arrive at a mean rate of 60 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average numbercustomers

Explanation / Answer

Arrival rate = 60 per hour

Service rate = 60*60/40 = 90 per hour

A.

Average number of customers waiting in line = 60^2/(90*(90-60))

Average number of customers waiting in line = 1.33

B.

Average time customer spending in the system = 1/(90-60) = 1/30

Average time customer spending in the system = .033 hrs. or 2 minutes

C.

Average number of customers in the system = 60/(90-60)

Average number of customers in the system = 2

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