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Management of Waiting Lines at a Truck Weighing Station

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Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour.

a. How many trucks would you expect to see at the weighing station, including those being inspected?
b. If a truck was just arriving at the station, about how many minutes could the driver expect to be at the station?
c. What is the probability that both inspectors would be busy at the same time?
d. How many minutes, on average, would a truck that is not immediately inspected have to wait?
e. What condition would exist if there was only one inspector?
f. What is the maximum line length for a probability of .97?

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Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty during those hours, each of whom can ...

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