Between 4:00PM and 6:00PM the vehicles arrive to the entrance ramp of a regional toll road...

Between 4:00PM and 6:00PM the vehicles arrive to the entrance ramp of a regional toll road at a constant rate of 1740 vehicles per hour. The toll plaza at the entrance ramp has five toll booths, which combined can process up to 34 vehicles per minute. At 4:30PM one of the toll booths is disabled due to electronics malfunction, which reduces the vehicle processing capacity of the toll plaza to 27 vehicles per minute. At 5:00 PM the toll booth is repaired and the toll plaza capacity is restored back to 34 vehicles per minute. Assuming that the vehicle arrivals and departures at the toll plaza have uniform deterministic distributions, determine the total duration of the queue that had formed due to the toll booth closure, in minutes.

Expert Solution

Initial from 4:00 pm to 4:30 pm arrival rate (29veh/min) is less than departure rate (34 veh/ min), so there is no queue between this time, queue starts from 4:30 pm and ends at 5:12 pm that means duration of queue is 42 minutes.

Ally Wells answered 9 months ago

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