Kinematics of Traffic Congestion

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This simple model of traffic congestion on an expressway calculates the optimum speed for a given flow of vehicles. First the model calculates the stopping distance , which is the sum of the length of the car
, the distance that the car moves while the driver reacts
, and the braking distance
based on the deceleration.
Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA
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Details
We are using basic formulas of kinematics , where
is the initial velocity, and
. The capacity is defined as
, where
is the number of cars and
is the stopping time. On the other hand,
. It can be shown that
, which is the function plotted.
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