Question

If the average arrival rate is 10 per hour, and the average time it takes to help a customer is 5 minutes, then:

Group of answer choices

No customer will ever have to wait: we can help more customers per hour than arrive

Utilization is less than 100%: we can help more customers per hour than arrive, but we may have a queue form and customers might have to wait..

None of the other answers are correct

There can never be queue: we can help more customers per hour than arrive

Answer #1

**Assuming M/M/1
Queuing Model**

Average arrival rate = 10/hr

Average Service rate = 1 per minutes = 20/hr

Server Utilization = 10/20 = 0.5 = 50%

Which means system is stable

Probability of 1 customer in system is P_{1}=
= 0.5 x 0.5 = 0.25

Probability more than 1 customer in queue = 1-P_{1} =
1-0.25 = 0.75

Now let us look at options

**Option 1:** As there is a probability of 0.75,
that there can be 2 or more customers in queue. Customer may have
to wait, hence option 1 is *false*.

**Option 2:** Yes, utilzation is less than 100% we
got 50% and we can help more customers per hour than current
situation but they may have to wait which is also true. *Hence,
over all we can conclude that this statement is Correct.*

*Remaining options are also incorrect*

With an average service rate of 15 customers per hour and an
average customer arrival rate of 12 customers per hour, calculate
the probability that actual service time will be less than or equal
to five minutes.

Arrival Rate = 1/50 = 0.02 calls hour.
Service Rate= 1 hour (travel time) + 1.5 hour (repair
time) =2.5 hours
With m = 1/ 2.5 = 0.4 hours per customers
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