Stefan Lämmer

Scaling laws in the spatial structure of urban road networks

The urban road networks of the 20 largest German cities have been analysed, based on a detailed database providing the geographical positions as well as the travel-times for network sizes up to 37,000 nodes and 87,000 links. As the human driver recognises travel-times rather than distances, faster roads appear to be ‘shorter’ than slower ones. The resulting metric space has an effective dimension δ>2, which is a significant measure of the heterogeneity of road speeds. We found that traffic strongly concentrates on only a small fraction of the roads. The distribution of vehicular flows over the roads obeys a power law, indicating a clear hierarchical order of the roads. Studying the cellular structure of the areas enclosed by the roads, the distribution of cell sizes is scale invariant as well.

Self-Organized Control of Irregular or Perturbed Network Traffic

We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking into account congestion-responsive traffic assignment and adaptive traffic control. We observe dynamic traffic patterns which significantly depend on the respective network topology. Synchronization is only one interesting example and implies the emergence of green waves. In this connection, we will discuss adaptive strategies of traffic light control which can considerably improve throughputs and travel times, using self-organization principles based on local interactions between vehicles and traffic lights. Similar adaptive control principles can be applied to other queueing networks such as production systems. In fact, we suggest to turn push operation of traffic systems into pull operation: By removing vehicles as fast as possible from the network, queuing effects can be most efficiently avoided. The proposed control concept can utilize the cheap sensor technologies available in the future and leads to reasonable operation modes. It is flexible, adaptive, robust, and decentralized rather than based on precalculated signal plans and a vulnerable traffic control center.

Urban road networks — spatial networks with universal geometric features?

Abstract Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for the time evolution of urban road networks.

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.

SELF-ORGANIZED NETWORK FLOWS

A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and load-dependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find self-organized oscillations in the flows similar to the operation of traffic lights.

On Stability Problems of Supply Networks Constrained With Transport Delay

Transportation is one of the most crucial components in supply networks. In transportation lines, there exists a finite time between products leaving a point and arriving to another point in the supply network. This period of time is the delay, which accompanies all transportation lines present in the entire network. Delay is a well-known limitation, which is inevitable and pervasive in the network causing synchronization problems, fluctuating or excessive inventories, and lack of robustness of inventories against cyclic perturbations. The end results of such undesirable effects directly reflect to costs. This paper is motivated to reveal the mechanisms leading to these problems by analytically characterizing qualitative behavior of supply network dynamics modeled by continuous-time differential equations. The presence of delay forms the main challenge in the analysis and this is tackled by developing/utilizing the tools emerging from delay systems and control theory. While the backbone of the paper addresses the qualitative behavior in presence of a single delay representing delays in all transportation paths, it also reveals how to choose production rates and transportation delay without inducing any undesirable effects mentioned. Thorough cases studies with single and multiple delays are presented to demonstrate the effectiveness of the approaches proposed.

Managing Complexity: An Introduction

Many of us have been raised with the idea of cause and effect, i.e. some stimulus-response theory of the world. Particularly, small causes would have small effects and large causes would have large effects. This is, in fact, true for “linear systems”, where cause and effect are proportional to each other. Such behavior is often found close to the equilibrium state of a system. However, when complex systems are driven far from equilibrium, non-linearities dominate, which can cause many kinds of “strange” and counter-intuitive behaviors. In the following, we will mention a few. We all have been surprised by these behaviors many times. While linear system have no more than one stationary state (equilibrium) or one optimal solution, the situation for non-linear systems is different. They can have multiple stationary solutions or optima (see Fig. 1), which has several important implications:

On Stability Analysis and Parametric Design of Supply Networks Under the Presence of Transportation Delays

Management of interconnected manufacturing units, supply networks, constitutes a timely, but challenging problem in Physics, Operations Research and Mathematics, as it carries very rich dynamics. At the first stage, a very well understanding of the underlying mechanisms and interactions within the hierarchical construct of such networks is required. For this pursuit, a more realistic approach is proposed in this paper, which takes into account the presence of naturally existing transportation delays of supplies in between individual production units. In general, the presence of delays in the dynamics imports another source of instability, which needs to be addressed. However, it is well-known that a thorough stability analysis against delays carries complications, thus it is non-trivial. We present analytical techniques to tackle such difficulties, surfacing allowable transportation delays within the supply network that guarantees stable stock levels. This, in parallel, enables the selection of production rates assuring the supply network to operate in a stable regime. Moreover, we show that under certain parametric settings, the supply network dynamics may become highly sensitive against the presence of delays, which in turn, initiates an undesirable phenomenon called bullwhip effect. We present case studies demonstrating the bullwhip effect and suggesting parametric selections to avoid this undesired behavior within supply networks.Copyright

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.

Power Laws in Urban Supply Networks, Social Systems, and Dense Pedestrian Crowds

The classical view of the spatio-temporal evolution of cities in developed countries is that urban spaces are the result of (centralized) urban planning. After the advent of complex systems’ theory, however, people have started to interpret city structures as a result of self-organization processes. In fact, although the dynamics of urban agglomerations is a consequence of many human decisions, these are often guided by optimization goals, requirements, constraints, or boundary conditions (such as topographic ones). Therefore, it appears promising to view urban planning decisions as results of the existing structures and upcoming ones (e.g. when a new freeway will lead close by in the near future). Within such an approach, it would not be surprising anymore if urban evolution could be understood as a result of self-organization (Batty & Longley, 1994; Frankhauser, 1994; Schweitzer, 1997).