Newell's Simplified Car-Following Model
Drivers tend to display oscillatory paths that are characterized with cycles of regular acceleration or deceleration because of traffic oscillations. The term traffic oscillations are used to describe the stop-and-go driving situations that are common in overcrowded traffic. Generally, conventional wisdom postulates that traffic oscillations are brought by instabilities in longitudinal car interactions. As a result of increased traffic oscillations, especially in congested traffic, numerous car-following models have been developed and proposed in the recent past. These models have been developed to duplicate oscillations through assumption of probabilistic headways during accelerations. In addition, car following models are the most significant reflections of traffic flow dynamics based on single vehicles. An example of the recently proposed or developed car-following model is the Simplified Car-Following Model by Newell.
The Model's Assumptions
Newell's car-following model is arguably the simplest model that was recently developed as part of the microscopic models whose dynamics of traffic flow is based on single vehicles. The simplicity of the model is attributable to the fact that it's based on time-discrete concepts and speed function (Treiber & Kesting, 2012, p.173). The two major components of Newell's Simplified Car-Following Model are time difference or response time and the vehicle length. Actually, Newell's Simplified Car-Following Model can be considered as a special type of current models though it comprises smaller number of parameters and utilizes a different logic unlike the existing ones (Newell, 2002, p.195). This simplified representative of existing car-following models is based on several assumptions.
First, the model assumes that traffic oscillation is basically a by-product of formation and propagation. While formation is brought by drivers' initiatives towards changing lanes, the causes of propagation are relatively unknown. In essence, the model is developed on assumption that the causes of propagation are unclear despite the increase in oscillations even when drivers are not involved in lane-changing activities. Secondly, the model assumes that driver response time is a major factor in the increase of traffic oscillation though the reaction time takes place within very small time intervals of a few seconds (Laval & Leclercq, 2010, p.4520).
Third, Newell proposed this model on the premise that two congested branches exist in the flow-density fundamental diagram without systems relating to driver behavior. One of these congested branches is the upper branch, which refers to the state of traffic when cars slow down and the lower branch, which is the state of traffic when cars increase speed. Fourth, Newell's Simplified Car-Following Model is based on the assumptions that drivers' behaviors are constant across a spectrum of oscillation cycles. This assumption is based on findings of an analysis of car-following behaviors of individual drivers in nearly all cycles of oscillation. Finally, this simplified representative of existing elementary car-following models assumes that drivers have an ongoing response time as part of the time delay.
Formulations
As previously mentioned, the premise upon which this model is developed and proposed is driver response time and the effective length of the car. The formulations of this model includes the consideration that the standard value for the difference in time is 1 second whereas the wave speed is within the range -20 km/h and -15 km/h. These parameters match an effective length of the vehicle of approximately five meters. Through these parameters, the car-following model has the capability of duplicating instant formation and subsequent propagation of sot-and-go waves during overcrowded traffic. As a result, this simplified car following model formulates the finding that there is a strong link between the behavior of drivers and pre- and post- oscillation. This is primarily because behaviors are relatively consistent among drivers and can be detected or determined through the use of a simple model like this (Chen, Laval, Zheng & Ahn, 2012, p.744).
The other formulation of Newell's Simplified Car-Following Model is the established correlation between theory and fluid models. This connection is established in attempts to transform the model into a macroscopic one through which the consistent behavior across drivers can be explained. Due to the transformation that focuses on generating macroscopic outputs that demonstrate the use of a simpler model with few parameters, there is a linear link or correlation between lined up flows and densities. Therefore, in lined up traffic, flow is essentially a linear declining function of density, which is also influenced by driver behavior and response time. In this case, the average wave speed remains autonomous regardless of the velocities of the car (Ahn, Cassidy & Laval, 2004, p.433).
How the Model Works
Newell's Simplified Car-Following Model works as a constant-in-time framework with...
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