Question

In a self service store with one cashier, 8 customers arrive on an average of every 5 mins. And the cashier can serve 10 in 5 mins. If both arrival and service time are exponentially distributed, then determine
a.Average number of customer waiting in the queue for average.
b.Expected waiting time in the queue.
c.What is the probability of having more than 6 customers in the system.

Answer 1

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Answer⬇️⬇️

a.Average number of customer waiting in the queue for average. ✔️

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Answer 2

Answer:

2 minutes

Explanation:

Time spend in the queue

The waiting time will be $W_{q} =\frac{\alpha }{\beta (\alpha -\beta )}$

System's waiting time $W_{s}=\frac{1}{(\alpha -\beta )}$

where $\alpha$ is the service rate and $\beta$ is the arrival rate of the customer.

8 customers arrive on an average every 5 mins i.e. $\beta =8*12=96$ customer per hour

10 customers can be served every 5 mins i.e. $\alpha =10*12=120$ customers per hour

Now,

$W_{q} = \frac{\beta }{(\alpha )(\alpha -\beta )} = \frac{96}{120(120-96)} = \frac{1}{30} hr=2min$

#SPJ2