Many of a bank’s customers use its automatic teller machine to transact business
ID: 460137 • Letter: M
Question
Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain ATM location at a rate of one every three minutes. An average of 42 customers per hour can be served by the ATM.
a. What is the utilization of this ATM?
b. What is the average wait time in minutes?
c. What is the average time in minutes spent in the system?
d. What is the average number of customers waiting for service?
e. What is the average number of customers in the system?
Explanation / Answer
Solution :
Arrival Rate = 20 custoemers / hour
Service Rate = 42 custoemers / hour
a. Utilization of this ATM :
Arrival rate / service rate = 20 / 42 =0.48
b. Average wait time in minutes :
Arrival rate / service rate ( service rate - Arrival rate ) = 20 /42 (42-20) = 0.021
c. Average time in minutes spent in the system
= 1 /(service rate - Arrival rate) = 1/(42-20) =0.045
d. Average number of customers waiting for service
= Arrival rate ^ 2 / service rate ( service rate - Arrival rate ) = 20*20/42(42-20) = 0.43
e. Average number of customers in the system
= Arrival rate / service rate ( service rate - Arrival rate ) = 20 / 42 (42 - 20 ) = 0.022
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