Estimation of Car-following Behavior using Fundamental of Differential Equations

Majority of traffic engineering analyses are based on traffic flow micro-simulation tools. Car-following model is one of the most significant micro-simulation sub-models that control driver's behavior with respect to the preceding vehicle in the same lane. Multiplicity of the car-following models is so high that there is therefore an obvious need for recognition of these models prior to picking up for utilization. In this research, the special case of well-known General Motors (GM) car-following model, is considered and characteristics of this model are described. The considered model is GM model as well as the assumption of driver's reaction time to be zero for all drivers, namely, Quick Response Driver Model. To achieve this purpose, some usual scenarios are defined in car-following process and these scenarios are simulated with Quick Response Driver Model. Also, utilization of differential equations approach is proposed for prediction and estimation of following vehicle behavior in car-following process that preceding vehicle behavior is given. Furthermore, Quick Response Driver Model is calibrated using real car-following time series data to identify model characteristics. The analyses of model evaluation with real data show the good capability of the model to reproduce real world considerations with RMSPE=1.7%. Additionally, results demonstrate that employment of differential equations is a robust approach in analysis of quick response driver model and decrease computational costs.