A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and make reservations. Consumers arrive at a rate of 8 per hour and the clerk can service 12 customers on an average per hour.

i) What is the average number of customers waiting for the service of the clerk?

ii) What is the average time a customer has to wait before getting service?

i) The average number of customers waiting for the service of the clerk can be calculated using the formula for the M/M/1 queue model:

\[
L_q = \frac{{\lambda^2}}{{\mu (\mu - \lambda)}}
\]

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