Question

Cars arrive at a service station according to Poisson's distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 minutes. At steady state, the average waiting time in the queue is

• A. 50 minutes
• B. 10 minutes
• C. 25 minutes
• D. 20 minutes

Answer 1

The correct option is A 50 minutes

$\text{Given data:}$

$\lambda =\text{arrival rate = 5/hour}$

$\mu =\text{service rate = 6/hour}$

$\therefore \text{Average waiting time in queue}$

$W_q=\frac{\lambda }{\mu (\mu -\lambda )}=\frac{5}{6(6-5)}hr$

$\text{= 0.833 hr = 50 minutes}$