Discrete Models of Traffic Flow (0-1)

Introduction

This electronic lecture note on the cellular automaton models of traffic flow is an outgrowth of the materials pepared for the seminars and study meetings of the Mathematical Engineering Laboratory (aka, Theoretical Physics Group) at the Graduate School of Kochi University of Technology.

It has been made accessible to KUT students who might be interested in joining us. Now it is open to general public who might have overheard such terms as "fundamental diagram" and "Nagel-Schreckenber model" and developped an interest to the science of traffic flow.

Here, I have placed greater emphasis on the phsyical background and on the model building than the technical details of actual numerics of traffic flow simulations. Constructing a rasonable model with sufficient parameters that reproduce certain set of reality is of course important. But to learn the process of model building that crystalizes the physical essence of phenomena is of far greater importance for further devolopment.

The discrete model of traffic flow can be regarded as a part of that once popular subject of "complexity". I plan a section entirely on the subject of the historical role of the science of complexity in late 20th century. However, the cellular automata model of traffic flow is a single example of unquestionable success among various attempts in the field. This is evident in the fact that it forms a basis of, and is now incorporated into the realistic traffic simulators. As such discrete traffic flow model is an ideal introduction for the science of complexity.

Apart from the standard materials on cellular automata and Nagel Shreckenber model, many of the materials found here are based on the original research by author's group. Readers are free to use all the materials in unaltered form for research and educational purpose with proper and clear quotation of the source. Use for other purposes such as commercial and political ar strickly prohibited.

This e-lecture exists only with the contribtion, first and formost, of Dr. Petr Seba, my always inspiring friend, who has brought this subject to our group in the first place, and also of Mr. Tetsuya Abe and Mr. Yutaka Nishimura who were the engines for many of the actual works at the field, to whom I express sincere gratitudes.