Vehicles arrive at a border crossing and must be inspected by a single inspection station before proceeding. The vehicles arrive at the station according to a Posson disribution at a rate of 882 vehicles/hour (time between arrivals is exponentially distributed). The times for vehicles to be processes are exponentially distributed with an average inspection time of 4 seconds per vehicle, no matter what type of vehicle it is. 45% of the vehicles are passenger cars and 55% are commercial trucks. The average amount of road space taken up by a car (car length plus buffer space) while waiting in line is 20 feet. The average amount of road space taken by a truck is 60 feet. Calculate the average length, in miles, of the waiting line of vehicles.
Vehicles arrive at a border crossing and must be inspected by a
single inspection station before proceeding. The vehicles arrive at the station according to a Posson disribution at a rate of 882 vehicles/hour (time between arrivals is exponentially distributed). The times for vehicles to be processes are exponentially distributed with an average inspection time of 4 seconds per vehicle, no matter what type of vehicle it is. 45% of the vehicles are passenger cars and 55% are commercial trucks. The average amount of road space taken up by a car (car length plus buffer space) while waiting in line is 20 feet. The average amount of road space taken by a truck is 60 feet. Calculate the average length, in miles, of the waiting line of vehicles.
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