Newell's car-following model

In traffic flow theory, Newell’s car-following model is a method used to determine how vehicles follow one another on a roadway. The main idea of this model is that a vehicle will maintain a minimum space and time gap between it and the vehicle that precedes it. Thus, under congested conditions, if the leading car changes its speed, the following vehicle will also change speed at a point in time-space along the traffic wave speed, -w. In traffic flow theory, Newell’s car-following model is a method used to determine how vehicles follow one another on a roadway. The main idea of this model is that a vehicle will maintain a minimum space and time gap between it and the vehicle that precedes it. Thus, under congested conditions, if the leading car changes its speed, the following vehicle will also change speed at a point in time-space along the traffic wave speed, -w. Assuming the fundamental diagram (flow-density) is a triangular function, a traffic state A with speed vA and density kA can be assumed in the congestion region. The density on the roadway can be determined using the spacing between vehicles and is computed simply the equation: kA = 1/sA Geometric relations from the fundamental diagram can be used to calculate the density as well, given by the equation: kA = (kj w)/(vA+w) In the time-space diagram, the trajectories of the leading (top) and following (bottom) vehicle are separated by the distance δ and time τ. The spacing between vehicles at traffic state A can be found using a geometric relationship found in the time-space diagram: sA = vA(τ)+δ Using relationships between the previous equations, variables τ and δ can be solved for: