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Question 3 (20%)

 

A bank installs an ATM and observes that the customers arrive at

a rate of 15 per hour and the arrivals follow a Poisson distribution. The ATM has a fixed non-random service time of 3 minutes per customer. (Hint: this is a M/D/1 process, and.)

 

(a) Calculate the average time spent by a customer in this system. (10 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) What is the percentage of time that the ATM is idle? (5 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) Over time, the ATM machine becomes slower. If the ATM machine slows down and requires 5 minutes per customer, what happens to the utilization? (5 points)

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