Question

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?      

2. How long on average does a customer have to wait in the queue?            
3. How much time on average does a customer spend in the system?                      

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 = L_q is given by:

So,

Answer is:

the expected average queue length = 0.5

(b)

Wait in the queue = W_q is given by:

Wait in the system = W_S is given by:

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

So,

Answer is:

The average number of customers in the queuing system = 1

(i)

Wait in the queue = W_q is given by:

So,

Answer is:

Wait in the queue = 3

(ii)

Wait in the system = W_S is given by:

So,

Answer is:

Wait in the system = 6