Royal Institute of Technology Degree Project in Engineering Physics Numerical Analysis at the Department of Mathematics Microscopic Models for Traffic Dynamics

As the volume of vehicular traffic has been increasing ever since its advent in the early 20th century, traffic dynamics has become a popular topic of study amongst physicists and mathematicians. This paper aims to explain different ways of modeling and simulating traffic and traffic dynamics. In general, modeling of traffic can be divided into two types of models, microscopic and macroscopic. In this paper, primary focus is on microscopic models. Examples are shown on how to implement simulations of so called car-following models as well as models based on cellular automata. Certain problems and scenarios regarding traffic are studied as well. These include how to efficiently distribute a roadblock, how to set the green/red time periods of a traffic light in order to achieve a high traffic flow or a low vehicle density, and how traffic flow can be maximized with respect to density or other parameters. Results show that simulations using cellular automata models generally compute faster than simulations using car-following models. However, the results obtained from cellular automata models tend to be more difficult to interpret and apply to real-world scenarios. A high level of stochasticity in the cellular automata models was also found to be necessary for the models to give applicable results. Car-following models, on the other hand, were found to have the advantage of being more deterministic.