Answered

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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)?

Sagot :

JeanaShupp

Answer: The customer spends 10 minutes at a booth.

Step-by-step explanation:

Let n= number of booths, [tex]\rho[/tex] = utilization, [tex]\lambda[/tex] = arrival rate, [tex]\mu=[/tex]Service rate

We know that

[tex]\rho=\dfrac{\lambda}{\mu\times n}[/tex]

As per given,

[tex]0.5=\dfrac{15}{\mu\times5}\\\\\Rightarrow\ \mu=\dfrac{15}{5\times0.5}\\\\\Rightarrow\ \mu=6[/tex]

Service rate = 6 customers per hour.

Time taken by each customer = [tex]\frac{1}{\mu}[/tex]

[tex]=\frac{1}{6} \ hours \ or\ \dfrac{60}{6}\ minutes\\\\=10 \ minutes[/tex]

Hence, the customer spends 10 minutes at a booth.

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