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Question Two At a particular Automatic Teller Machine (ATM), customer’s arrival follows a Poisson distribution with...

Question Two

At a particular Automatic Teller Machine (ATM), customer’s arrival follows a Poisson distribution with an average time of 6 minutes between arrivals. The time- intervals between services at ATM is 3 minutes. On the basis of this information, answer the following questions:

  1.       What would be the expected average queue length and the average number of customers in the queuing system?      
  1. How long on average does a customer have to wait in the queue?            
  2. How much time on average does a customer spend in the system?                      

Homework Answers

Answer #1

(i)

Arrival Rate = = 1/6 arrivals per minute

Service Rste = = 1/3 services per inutes

So,

Utility Factor =

(a)

the expected average queue length = Lq is given by:

So,

Answer is:

the expected average queue length = 0.5

(b)

Wait in the queue = Wq is given by:

Wait in the system = WS is given by:

the average number of customers in the queuing system = LS is given by:

So,

Answer is:

The average number of customers in the queuing system = 1

(i)

Wait in the queue = Wq is given by:

So,

Answer is:

Wait in the queue = 3

(ii)

Wait in the system = WS is given by:

So,

Answer is:

Wait in the system = 6

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