Modeling dynamic transportation networks. An intelligent transportation system oriented approach. 2nd rev. ed.

*(English)*Zbl 0898.90004
Berlin: Springer. xx, 356 p. (1996).

The book deals with various models of dynamic processes that take place on a road network. The processes are formed by flows of vehicles traversing the network between their origin and destination along a chosen route. The vehicles are driven by drivers with different experience, features and information. In a general case, a traveller chooses a route from his origin to destination, a time of departure and a mode of transport. The choice is influenced by current or historical information, which is available to the traveller. Serious phenomena on the network, namely congestion, spillback effects and incidents, arise from the interaction of the travellers and the associated flows. To implement intelligent transportation system, for example a complex of Advanced Traveller Information System and Advanced Traffic Management System, a tool for the phenomena prediction is necessary.

The authors developed several models to describe various traveller behaviour in the road network according to some of common rules as Ideal or Instantaneous Dynamic User Optimal State or Ideal or Instantaneous Stochastic Dynamic User Optimal State. They derived link-based models containing boundary, flow conservation and flow propagation constraints and logit rules from the original route-based model following the above mentioned rules. The flows in the models are described using time dependent variables for link inflow and link exit flow.

To get the information of the flow quantities and following phenomena corresponding to a given dynamic user optimal state, it is necessary to solve the discrete optimization problem associated with the model. For that purpose, the authors developed a method consisting of the Frank-Wolfe method (the gradient method for constrained range of feasible solutions) and the diagonalization technique. The method and the consequences including the appropriate theory are broadly discussed in the second part of the book. To enable the study of the problems, which are dealt with in the book, the authors provide a number of examples and exercises at the end of each chapter.

The authors developed several models to describe various traveller behaviour in the road network according to some of common rules as Ideal or Instantaneous Dynamic User Optimal State or Ideal or Instantaneous Stochastic Dynamic User Optimal State. They derived link-based models containing boundary, flow conservation and flow propagation constraints and logit rules from the original route-based model following the above mentioned rules. The flows in the models are described using time dependent variables for link inflow and link exit flow.

To get the information of the flow quantities and following phenomena corresponding to a given dynamic user optimal state, it is necessary to solve the discrete optimization problem associated with the model. For that purpose, the authors developed a method consisting of the Frank-Wolfe method (the gradient method for constrained range of feasible solutions) and the diagonalization technique. The method and the consequences including the appropriate theory are broadly discussed in the second part of the book. To enable the study of the problems, which are dealt with in the book, the authors provide a number of examples and exercises at the end of each chapter.

Reviewer: J.Janáček (Žilina)

##### MSC:

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

90B06 | Transportation, logistics and supply chain management |

90B10 | Deterministic network models in operations research |

90B20 | Traffic problems in operations research |