This book introduces readers to the main traffic flow modelling approaches and discusses their features and applications. It provides a comprehensive and cutting-edge review of traffic flow models, from their roots in the 1930s to the latest developments in the field. In addition, it presents problem sets that offer readers further insights into the models and hands-on experience with simulation approaches. The simulations used in the exercises can be built upon for readers’ own research or other applications.
The models discussed in this book are applied to describe, predict and control traffic flows on roads with the aid of rapid and accurate estimations of current and future states. The book shows how these models are developed, what their chief characteristics are, and how they can be effectively employed.@en

The capacity drop forms a major reason why the prevention of congestion is targeted by traffic management, as lower capacities are detrimental to traffic throughput. Various reasons describing the dynamics behind the capacity have been described, however one of these, reaction times, has had less explicit attention when modelling on a macroscopic flow level. In this contribution, a method to include the effect of reaction times for the capacity drop in heterogeneous traffic is proposed. The applied method further overcomes difficulties in including reaction times in a discrete time model through relaxation of the updating process in the discretization. This approach is novel for application in the considered first order approach, which is practise ready, contrary to many other models that propose similar approaches. The combination of the introduced method and the model form a solid development and method to apply the capacity drop based on this causation of the capacity drop. The results of the experiment case showed that the influence of traffic heterogeneity had a limited effect on the severity of the capacity drop, while it did influence the time of congestion onset. The influence of the reaction time on traffic showed greater capacity drop values for greater reaction time settings. The findings showed the method effective and valid, while the model application is also practise ready.

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An efficient simulation method for two-dimensional continuum pedestrian flow models is introduced. It is a two-dimensional adaptation of the Godunov scheme for one-dimensional road traffic flow models. It is further extended to include multiple classes, representing groups of pedestrians with different behavior, origin, and destination. The method can be applied to continuum pedestrian flow models in a wide range of applications from the design of train stations and other travel hubs to the study of crowd behavior and safety at sports, religious, and cultural events. The combination of the efficient simulation method with continuum models enables the user to get simulation results much quicker than before. This opens doors to real-time crowd control and to more advanced optimization of planning and control. Test results show the importance of choosing appropriate numerical settings, including grid cell and time step size for realistic simulation results.@en

Continuum traffic flow models are essentially nonlinear hyperbolic systems of partial differential equations. Except for limited specific cases, these systems must be solved numerically. Mathematical structure of continuum models can be different for each class of models. As a result, suitable numerical schemes for some classes may not be efficient for others. In this study, an improved numerical method is proposed for a class of second-order traffic flow models. The method is based on McCormack scheme, which is a widely-used method for non-homogeneous second-order traffic flow models, but fails to produce reasonable results for homogeneous models including Aw-Rascle type models which are the focus of this paper. It is shown that this is mainly due to spurious numerical oscillations. Smoothing methods to overcome these issues are studied and applied. Central dispersion and artificial viscosity (AV) methods are incorporated into the standard McCormack scheme and tested. To reduce numerical diffusion, a total variation diminishing Runge-Kutta time stepping scheme is applied. Results show the capability of the proposed methods, and especially the AV method, to eliminate the oscillations of the standard McCormack scheme as well as controlling numerical diffusion.@en

Since the beginning of this millennium many multi-class continuum traffic flow models have been proposed. We present a set of qualitative requirements for this type of models, including nonincreasing density-speed relations and anisotropy. The requirements are cast into a framework that applies a generalised deterministic multi-class kinematic wave traffic flow model. A step-by-step plan is developed to apply the framework to models that fit into the generalised model. The plan could only be developed using the Lagrangian formulation of the generic model, but it can also be applied to models in the traditional Eulerian formulation. We conclude that only few models known from literature satisfy all requirements unconditionally. The step-by-step plan can further more be applied in the development of new models, the adaptation of existing models and the calibration of model parameters.@en

Since the beginning of this millennium, many models of multiclass continuum traffic flow have been proposed. A set of qualitative requirements is presented for this type of model, including nonincreasing density–speed relationships and anisotropy. The requirements are cast into a framework that applies a generalized model of deterministic multiclass kinematic wave traffic flow. A step-by-step plan is developed to apply the framework to models that fit into the generalized model. The plan could be developed only with the Lagrangian formulation of the generic model but could also be applied to models in the traditional Eulerian formulation. It was concluded that only a few models known from the literature satisfied all requirements unconditionally. The step-by-step plan can furthermore be applied in the development of new models, the adaptation of existing models, and the calibration of model parameters.@en