Question

The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will be

• A. 4
• B. 3.2
• C. 4.2
• D. 3

Answer 1

The correct option is B 3.2

$\text{Arrival rate,}\lambda =8perhour$

$\text{Service rate:}\mu =\frac{60}{6}=10perhour$

$\text{Average number of customers in the queue}$

$L_q=\frac{{\lambda }^2}{\mu (\mu -\lambda )}=\frac{(8{)}^2}{10(10-8)}=3.2$