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:

- What would be the expected average queue length and the average number of customers in the queuing system?

- How long on average does a customer have to wait in the queue?
- 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**

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