Car Following

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The car-following model is used to calculate an acceleration value for a vehicle in a follower mode. SwashSim employs the Modified-Pitt car-following model (Cohen, 2002a and 2002b). The Modified-Pitt car-following model has been demonstrated (Cohen, 2002a and 2002b; Washburn and Cruz-Casas, 2007) to work well for multiple traffic flow regimes (e.g., uninterrupted flow and queue arrival/discharge flow). The Modified-Pitt car-following equation calculates the acceleration value for a trailing vehicle based on intuitive parameters such as the speed and acceleration of the lead vehicle, the speed of the trailing vehicle, the relative position of the lead and trail vehicles, as well as a desired headway. This equation also incorporates a sensitivity factor, K, which is discussed in the next subsection. This equation allows for relatively easy calibration. Car-following models are generally based on a ‘driving rule’, such as a desired following distance or following headway. The Modified-Pitt model is based on the rule of a desired following headway. The main form of the model is as follows.

$$ {a_f}(t+T)=\frac{K{\begin{array}{l} {s_l}(t+R)-{s_f}(t+R)-{L_l}-h{v_f}(t+R)+\\ [{v_f}(t+R)-{v_l}(t+R)]T-\frac{1}{2}{a_l}(t+T){T^2} \end{array}{T(h+\frac{1}{2T})} $$

where



The (K) value is a sensitivity parameter used to adjust the acceleration calculated by the car-following model. This factor is analogous to a spring constant used to describe how tightly or loosely a coupled system (a platoon of vehicles in this case) operates. This factor essentially adjusts how quickly or slowly acceleration changes, for one or more vehicles, propagate through the platoon. By default, two separate values for the sensitivity parameter, K, are used in the car-following model—one for uninterrupted flow and one for queue arrival/discharge flow. Cohen stated that a larger K value should be used in interrupted flow conditions (a more tightly coupled system) due to over-damping effects (Cohen, 2002a). This assumption was tested in the car-following model and yielded the best results. Vehicles had a smoother interaction in the work zone (uninterrupted flow, a more loosely coupled system) with K = 0.75 and for the queue arrival and queue discharge processes performed well with K = 1.1. The definition of the queue arrival area is 300 feet upstream of the last vehicle in queue, and the definition of the queue discharge area is 300 feet downstream of a stop bar (see Figure below).