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At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.
a. What is the average length of the waiting line? (Round your answer to 2 decimal places.)
Average length customers
b. What is the average time that a vehicle must wait to get through the system? (Round your answer to 2 decimal places.) Hint: Here you are looking for total time spent in the system, not the time spent waiting in the line alone.
Average time minutes
c. What is the utilization of the inspector? (Round your answer to 1 decimal place.)
Utilization %
d. What is the probability (percentage) that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)
Probability
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