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1 ) ZBank is currently having teller counters to serve the need of the customers

ID: 353496 • Letter: 1

Question

1 )ZBank is currently having teller counters to serve the need of the customers. The customers arrive at the rate of 20 customers per hour. The Teller takes in an average 2 minutes per customer.

What type of queuing system they have currently?

How many of customers wait in line and what is the average wait time?

If the bank replaces the teller by a ATM machine which takes exactly 2 minutes every time to serve a customer What type queuing system the bank will have?

How many customers will wait at ATM and what is the average wait time?

Explanation / Answer

a) M/M/1 since there is one teller handling the requests as per our question.

b) arrival rate lamda = 20 customers /hr

service rate u=60/2=30 customers/hr

customers waiting in line Lq= lamda Wq

Wq=average wait time =lamda/(u(u-lamda) =20/(30*(30-20) =0.067 hours or 4.02 mins

Lq=20*0.067=1.33 or 1 customer

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when the teller is changed by ATM still the model is M/M/1 since there is one server

other answers are same for ATM since it also takes 2min to serve

Wq=0.067 hr or 4.02 mins

Lq=1 customer