ABSTRACT
CONTENTS 8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.1 Summary This book presented the derivation of conservation laws for scalar case as well as vector models. Then, more details based on physics and traffic behavior were provided for specific models, for gas dynamics and traffic dynamics. The reason for that was that traffic models are developed following the compressible gas behavior. Pedestrian models were developed by extending the one-dimensional traffic models to two dimensions and also by adding multidirectional motion. The system of PDE models for traffic were developed using relaxation models, which, in the limit of the relaxation parameter going to zero, turn into the corresponding scalar traffic models.
