After a brief survey of traffic models I will discuss three questions: Existence and univalence (or multivalence) of the fundamental diagram, the link between kinetic and macroscopic models, and the emergence of moving traffic jams in dense traffic.
The latter phenomenon will be discussed for a macroscopic model derived from a Vlasov type kinetic model (with reasonable nonlocalities) which possesses classes of traveling wave solutions.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

We consider Enskog-Boltzmann models for traffic flows and derive under a suitable scaling the corresponding Fokker-Planck equations.
Connections with the Vlasov-Fokker-Planck model recently introduced by Illner & coauthors are discussed. Some numerical results are also presented.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Ants build and use a transport system that has many similarities with human-build highway networks. The main mechanism for the formation of these ant trails is a special form of communication on a chemical basis, called chemotaxis.
Using a stochastic cellular automaton model which is an extension of the Asymmetric Simple Exclusion Process (ASEP) that takes into account the effects of chemotaxis we discuss the basic properties of the traffic flow on existing trails.
Surprisingly it is found that in certain regimes the average speed of the ants can vary non-monotonically with their density. This is in sharp contrast to highway traffic. The observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.
The predictions of the model approach are in qualitative agreement with empirical observations on natural ant trails for which we have determined fundamental diagrams, velocity and headway distributions etc. by video analysis.

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• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Can we reliably predict and quantitatively describe how large groups of people move? One approach to this problem is based on the quantitative methods of statistical physics. In cases when the interactions between the members of a group are relatively well defined (e.g, pedestrian traffic) the corresponding models reproduce relevant aspects of the observed phenomena.
People moving in the same environment typically develop specific patterns of collective motion including the formation of lanes, flocking or jamming at bottlenecks. We simulate such phenomena assuming realistic interactions between particles representing humans.
The two specific cases to be discussed in more detail are waves produced by crowds at large sporting events and the main features of pedestrian escape panic under various conditions. Our models allow the prediction of crowd behavior even in cases when experimental methods are obviously not applicable and, thus, are expected to be useful in assessing the level of security in situations involving large groups of excited people.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Understanding the dynamical properties of large crowds is of great practical importance. Emergency situations require efficient evacuation strategies to avoid casualties and reduce the number of injured persons.
In many cases legal requirements have to be fulfilled, e.g. for aircraft or cruise ships. For tests already in the planning stage reliable simulation models are required to avoid additional costs for changes in the construction.
From a physics point of view pedestrian dynamics is challenging due to the large variety of collective phenomena that can be observed, e.g. formation of lanes in counterflow.
In this talk we give an overview on the empirical and theoretical results on pedestrian dynamics. The focus will be on a cellular automaton model (the floor field model) in which interactions are implemented in analogy to the process of chemotaxis.

You may download the slides of the talk

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

In this talk, I will show how to derive a gas-kinetic equation from an underlying simple microscopic model, and, in turn, a non-local macroscopic model from the gaskinetic model. In contrast to other approaches, the collision term will be explicitely evaluated in the transition from the kinetic to the macroscopic model. This enables to relate the macroscopic "pressure term" or "anticipation term" to microscopic statistical properties.
In the second part, I will derive analytic criteria for the flow stability for nonlocal macroscopic models in closed and open systems, and show that the flow stability is equivalent to the microscopic string stability of the intelligent-driver model and related modell classes. Finally, I will define a set of general stability classes applicable for both microscopic and macroscopic models. By simulation of open systems with a bottleneck, I will demonstrate that micro and macromodels of the same stability class produce identical sets of spatiotemporal states, i.e., the same "phase diagrams".

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• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

We present a network model for supply chains with policy attributes using kinetic equations. The proposed network model is an extension of the single lane model with policy attributes presented by Degond et. al.
The single lane model is extended to the network case using suitable moment closures. Numerical results are presented for several different examples.

You may download the slides of the talk

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)

Networks are widely used in complex systems, for example, to identify closely related groups of participants in the system (called modules, clusters or communities). The network clustering program CFinder identifies densely internally connected groups of nodes (modules) in networks and allows explicitly for overlaps among the identified modules. Recently, we have extended CFinder to weighted and directed networks.
In both graph models and directed real graphs we identify two types of directed network modules: in- and out-modules based on whether the overlaps of the modules contain mainly in- or out-hubs. We find in-modules in: the directed graph of Google's own webpages and a large word association net of English words. We find out-modules in an e-mail web and the transcription regulatory network of yeast.
In biological and other networks, too, modules and the "background" are often hard to tell apart, and one cannot draw sharp boundaries for the modules. The extension of CFinder to weighted graphs allows one to identify densely internally connected groups of nodes (proteins in a PPI network) with higher confidence.

• Event: Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' (2008)