Answer to Question #172962 in Operations Research for Gayathri

Question

In a public telephone booth the arrivals are on the average 15 per hour. A call on the average takes 3minutes.If there is just one phone,find

a)expected number of callers in the booth at anytime

b)The portion of the time the booth is expected to be idle

Answer 1

$\lambda=\frac{1}{15},$

$\mu=\frac 13,$

1)

$L=\frac{\mu}{\mu-\lambda}=\frac{\frac 13}{\frac 13-\frac{1}{15}}=1.25,$

2)

$P=1-\frac{\lambda}{\mu}=1-\frac{\frac{1}{15}}{\frac 13}=0.8.$