# Question with regard to queueing theory

I am just in the midst of examn preparation and ask myself if somebody could help me with the following queueing problem:

A local country garage has one petrol pump. On average, customers are served at a rate of 6 per minute. On normal days, customers arrive at the rate of 30 every 10 minutes. Arrivals follow a Poisson distribution and service times follow an exponential distribution.

a. What is the average number of customers in the queue?

## 1 Answer

Hint:

Relevant formula: $$\rho = \frac{\lambda}{\mu}$$ $$N(M/M/1)=\frac{\rho}{1-\rho}$$

• Thanks a lot. That hint helped me getting on the right track. – dazzle Jun 26 '17 at 19:45