Question

Imagine a simple process in which 5 ticket booths are selling tickets for an opera. If customers are coming at a rate of 15 / hour, and the utilization of the 5 booths is 50%, then how long does a customer spend at a booth (each customer goes to only one booth)?

Answer 1

Answer: The customer spends 10 minutes at a booth.

Step-by-step explanation:

Let n= number of booths, $\rho$ = utilization, $\lambda$ = arrival rate, $\mu=$Service rate

We know that

$\rho=\dfrac{\lambda}{\mu\times n}$

As per given,

$0.5=\dfrac{15}{\mu\times5}\\\\\Rightarrow\ \mu=\dfrac{15}{5\times0.5}\\\\\Rightarrow\ \mu=6$

Service rate = 6 customers per hour.

Time taken by each customer = $\frac{1}{\mu}$

$=\frac{1}{6} \ hours \ or\ \dfrac{60}{6}\ minutes\\\\=10 \ minutes$

Hence, the customer spends 10 minutes at a booth.