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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?

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Hint:

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

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

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