Question

A 11-car platoon is approaching a traffic light with vehicle actuated control, and the light turns green when the head car of the platoon is 120ft away from the stop

bar. Suppose that the headway between cars in the platoon is 2 seconds, the cars are traveling at 30ft/sec, and the duration of the green light follows a negative exponential distribution with a mean of 30 seconds. What is the probability that all the 11-cars in the platoon can travel through the intersection if the platoon keeps traveling at 30ft/sec (the platoon is considered having crossed the intersection when the last car in the platoon crosses the stop bar).

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