Mixed Traffic Modelling: An Overview of Car Following and Lane Change Models

2. Traffic Modelling

Traffic is defined with help of three fundamental variables namely Speed, Density and Flow. Traffic was defined by first-order models which were based on continuity equations. These equations defined the rate of change of the density in terms of gradients or differences of flow (Trieber & Kesting 2013). As these models were closed by specifying flow or local speeds they failed to replicate the field traffic flows which usually had dispersed values of speed and flow. In other words, speed has its dynamic equation. This class of models, called Lighthill-Whithman-Richards (LWR) models, were known as models of first-class order (Lebacque et al., 1998). In such models, instant speed changes for different road conditions led to unlimited accelerations which in turn led to unrealistic traffic flows. Deficiencies of first-order models were addressed by second-order models as they have dynamic speed. Local speed has its dynamic acceleration equation. Speed is defined as a function of density. This gives the ability to model traffic flow instabilities, capacity drop, traffic waves and scattered flow density. Payne’s Model, Kerner Konhäuser's (KK) Model, and Gas-kinetic Based Traffic Model (GKT) belong to this class of models (Treiber et al., 1999). In these models rate of change of local speed is equal to an acceleration function. They can define the dynamic nature of velocity wherein the speed detected by the detector as well as speed change due to movement to a new location is defined. These models however have a disadvantage in terms of anticipation of traffic conditions ahead of them. These shortcomings were addressed by adding anticipation terms in the modelling equations (Pandey et al., 2023).