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...

This is primarily because an evaluation of car-following behavior by individual drivers across various cycles of oscillations demonstrates that drivers' behaviors are consistent or constant across the spectrum, which makes it easy to detect them using a simple model. Throughout the various cycles of traffic oscillations, a driver's response to these oscillations is directly linked and influenced by his/her behavior during the pre-oscillation period. This is evidenced in the fact that the standard value for the difference in time, which is commonly known as time gap in this model, is 1 second whereas the wave speed is within a standardized range that corresponds to a standardized length of the vehicle.
The other way through which this simplified model works is that the individual driver's behavior is likely to be influenced by traffic oscillations, especially in overcrowded traffic. However, the effect of traffic oscillations on changing driver behavior is not prevalent and remains largely minimal. This is mainly because drivers already have a pre-determined reaction to these oscillations because of their behaviors prior to their occurrence. This essentially means that the spontaneous occurrence of traffic oscillations, particularly in overcrowded scenarios, is a by-product of both nervous and forceful behaviors of drivers (Laval & Leclercq, 2010, p.4519). Therefore, the stop-and-go waves that annoy drivers across the globe because of increased consumption of fuel and subsequent emissions emerge regardless of the specific instances of the individual behaviors of drivers during oscillations. However, drivers react to the oscillations based on their behaviors before they occurred. This theory works on the premise that if a car is following another on a standardized highway, they have similar time-space trajectory (Newell, 2002, p.195). However, the trajectory may be different with regards to interpretation and translation in time and space. The similar time-space trajectory acts as an indicator of the fact that driver reaction during oscillation is influenced by his/her behavior prior to the wavering.

Limitations of the Model

Despite being a simplified representative of existing car-following models in the past five decades, Newell's Simplified Car-Following Model is characterized by several limitations. The first limitation of the model is that cars that are speeding do not generate waves that fanned outward. This is a major limitation despite the view that wave speed remains the same across numerous flow or density values within standardized ranges. Secondly, it is relatively difficult to verify whether non-linear effects don't emerge in lined-up traffic when car velocities increase towards realization of the anticipated velocities. This is primarily because queued vehicles do not necessarily attain high velocities while on standardized approaches to the various intersections. The third limitation of the model is its vulnerability to lane-changing initiatives by drivers such as over-taking since such activities end up interfering with car following. Consequently, the proposed model or theory largely fails with regards to lined up freeway traffic that is characterized by increased lane-changing activities and initiatives by drivers. Finally, Newell's model is limited in the sense that it is not applicable in non-standardized traffic situations since it only focuses on homogenous highways.

Overcoming Limitations

Given these limitations, it is increasingly important to identify suitable measures of overcoming the weaknesses in order to enhance the applicability of Newell's Simplified Car-Following Model to all situations. The first measure for addressing these limitations would entail conducting a study on its applicability to situations characterized by high vehicle velocities. This will help provide insights of effects generated by linear density-flow curves in queued traffic, especially when the vehicles match anticipated velocities. This measure will help address in verifying the probable emergence of non-linear effects in lined up traffic when vehicles have high velocities. Secondly, this theory needs to be transformed to incorporate lane-changing effects in order to lessen its vulnerability to such activities that interfere with car following. The inclusion should entail situations with heavy lane-changing activities in order to provide better understanding of the effect of geometric non-standardized traffic on the behaviors of drivers (Ahn, Cassidy & Laval, 2004, p.438).

In conclusion, Newell's car-following model is arguably a simplified model of existing car models, which reflects dynamics of traffic flow. The model is based on several assumptions including consideration of traffic flow as a consequence of formation and propagation, effect of driver response time on traffic oscillation, basis on two congested branches, and consistent driver behaviors. While the model is formulated on the premise of driver response time and the effective length of the car, it works as constant-in-time…