Module 3 : Microscopic Traffic Flow Modeling

Lecture 14 : Car Following Models

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	Car following models Car following theories describe how one vehicle follows another vehicle in an uninterrupted flow. Various models were formulated to represent how a driver reacts to the changes in the relative positions of the vehicle ahead. Models like Pipes, Forbes, General Motors and Optimal velocity model are worth discussing. Notation Before going in to the details, various notations used in car-following models are discussed here with the help of figure 1. The leader vehicle is denoted as $n$ and the following vehicle as $(n+1)$. Two characteristics at an instant $t$ are of importance; location and speed. Location and speed of the lead vehicle at time instant $t$ are represented by $x_n^t$ and $v_n^t$ respectively. Similarly, the location and speed of the follower are denoted by $x_{n+1}^t$ and $v_{n+1}^t$ respectively. The following vehicle is assumed to accelerate at time $t+\Delta T$ and not at $t$, where $\Delta T$ is the interval of time required for a driver to react to a changing situation. The gap between the leader and the follower vehicle is therefore $x_n^t-x_{n+1}^t$. Figure 1: Notation for car following model