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Drivers who come to get their licenses at the Department of Motor Vehicles have their photograph...

Drivers who come to get their licenses at the Department of Motor Vehicles have their photograph taken by an automated machine that develops the photograph onto the license card. The machine requires 6 minutes to prepare a license. Drivers arrive at the machine at the mean rate of 7.8 per hour. Assume it is a single-server waiting line model.

(a) Determine the mean arrival rate and the mean service rate.

(b) Determine the probability that a driver will have an empty queue.

(c) Determine the probability that 3 drivers are in the queuing system.

(d) Determine the average number of drivers in the queue and the average number of drivers in the system.

(e) Determine the average waiting time in the queue and the average total time in the system for a driver.

(f) Find the utilization factor of the automated machine.

Math   Statistics-And-Probability   
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