When a jam occurs, the vehicle quickly piled up. For example, in highway vehicles drive at a rate of 80 km/h and the distance between the vehicles 80m. The distance here is between the rear end of the vehicle in front to the front end of the rear vehicle. Suppose the average length of the queue is calculated form the front end of the first vehicle to the rear end of the last vehicle?
To calculate the average length of the queue in this scenario, you need to consider the rate at which vehicles are entering the queue and the rate at which they are leaving.
In this case, let's assume that the rate at which vehicles are entering is 1 vehicle per second. This means that every second, a new vehicle is joining the end of the queue.
Now, we need to determine the rate at which vehicles are leaving the queue. Since the vehicles are driving at a rate of 80 km/h, and the distance between them is 80m, we can calculate the time it takes for a vehicle to pass a given point.
To convert the speed from km/h to m/s, we divide it by 3.6. So, 80 km/h is equivalent to (80/3.6) m/s, which is approximately 22.22 m/s.
Therefore, it takes (80m / 22.22 m/s) = 3.6 seconds for a vehicle to pass a point.
Now, let's consider the average length of the queue. Assuming the queue is in a steady-state condition, the rate of vehicles entering the queue must equal the rate of vehicles leaving the queue.
Based on our earlier assumption, 1 vehicle is entering the queue per second. And since it takes 3.6 seconds for a vehicle to pass a point, the rate of vehicles leaving the queue is 1/3.6 = 0.28 vehicles per second.
To calculate the average length of the queue, we divide the rate of vehicles entering by the rate of vehicles leaving. So, the average length of the queue is 1 vehicle / 0.28 vehicles per second = 3.57 seconds.
Therefore, in this example, the average length of the queue is approximately 3.57 seconds, which corresponds to the distance between the front end of the first vehicle to the rear end of the last vehicle in the queue.