Karsten Peters

Transient dynamics increasing network vulnerability to cascading failures.

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws. It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. The robustness of networks showing cascading failures is generally given by a complex interplay between the network topology and flow dynamics.

Efficient response to cascading disaster spreading.

We study the effectiveness of recovery strategies for a dynamic model of failure spreading in networks. These strategies control the distribution of resources based on information about the current network state and network topology. In order to assess their success, we have performed a series of simulation experiments. The considered parameters of these experiments are the network topology, the response time delay, and the overall disposition of resources. Our investigations are focused on the comparison of strategies for different scenarios and the determination of the most appropriate strategy. The importance of prompt response and the minimum sufficient quantity of resources are discussed as well.

Modelling of cascading effects and efficient response to disaster spreading in complex networks

In order to assess cascading effects in directed networks, we present a model for the dynamics of failure spreading. The model combines network nodes as active, bistable elements and delayed interactions along directed links. Through simulations, we study the dynamics behaviour of generic sample networks. Besides evaluating the failure cascades, for which we observe a critical threshold for the undamped spreading of failures in a network, we simulated the effect of different strategies for the management of spreading disasters. Our recovery strategies are based on the assumption that the interaction structure of the challenged network remains unchanged, while additional resources for mitigation actions, improving the recovery capacities of system components, can be distributed over the network. The simulations clearly demonstrate that the topology of a network is a crucial factor both for the behaviour under external disturbances and for the optimality of different strategies to cope with an evolving disaster. Our model may be used to improve disaster preparedness and anticipative disaster response management.

Decentralised control of material or traffic flows in networks using phase-synchronisation

We present a self-organising, decentralised control method for material flows in networks. The concept applies to networks where time sharing mechanisms between conflicting flows in nodes are required and where a coordination of these local switches on a system-wide level can improve the performance. We show that, under certain assumptions, the control of nodes can be mapped to a network of phase-oscillators.

ANALYTICAL AND NUMERICAL INVESTIGATION OF ANT BEHAVIOR UNDER CROWDED CONDITIONS

Swarm intelligence is widely recognized as a powerful paradigm of self-organized optimization, with numerous examples of successful applications in distributed artificial intelligence. However, the role of physical interactions in the organization of traffic flows in ants under crowded conditions has only been studied very recently. The related results suggest new ways of congestion control and simple algorithms for optimal resource usage based on local interactions and, therefore, decentralized control concepts. Here, we present a mathematical analysis of such concepts for an experiment with two alternative ways with limited capacities between a food source and the nest of an ant colony. Moreover, we carry out microscopic computer simulations for generalized setups, in which ants have more alternatives or the alternative ways are of different lengths. In this way and by variation of interaction parameters, we can get a better idea of how powerful congestion control based on local repulsive interactions may be. Finally, we discuss potential applications of this design principle to routing in traffic or data networks and machine usage in supply systems.

Logistics Networks: Coping with Nonlinearity and Complexity

Nowadays the complexity of logistics is a buzzword spreading in business, media and everyday practice. However, the study of logistics networks from the point of view of complex dynamical systems theory has started only recently. In the past decade, physicists have been more and more interested in interdisciplinary fields such as biophysics, traffic physics, econophysics, or sociophysics. Also, the study of production processes and logistics networks has become attractive, although the title of the book “Factory Physics” suggests that there should be some connection. In fact, it is quite natural to study production and logistics from the point of view of material flows. Therefore, many-particle approaches such as Monte-Carlo simulations and fluid-dynamic models should be applicable to logistics systems. As we will discuss in the following, this is really the case.