Question

For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?

• A. 24 per hour
• B. 12 per hour
• C. 6 per hour
• D. 10 per hour

Answer 1

The correct option is A 24 per hour

$\lambda =\text{Arrival rate,}\mu =\text{Service rate}$

$\therefore \text{When}\lambda >\mu ,$

queue length will keep on increasing and alternatively the system will fail.

When the $\lambda <\mu ,$ system works and provides a steady state, finite queue length.

So $\mu >\lambda$ then only option (d) $\mu =24$ per hour is correct.