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Stop-and-go waves are commonly observed in traffic and pedestrian flows. In most traffic models they occur through a phase transition after fine tuning of parameters when the model has unstable homogeneous solutions. Inertia effects are believed to play an important role in this mechanism. Here, we present a novel explanation for stop-and-go waves based on stochastic effects in the absence of inertia. The introduction of specific coloured noises in a stable microscopic first order model allows to describe realistic stop-and-go behaviour without requiring instabilities or phase transitions. We apply the approach to pedestrian single-file motion and compare simulation results to real pedestrian trajectories. Plausible values for the model parameters are discussed., Comment: 10 pages, 8 figures. This is an extended version of the contribution arXiv:1801.09791

In this study a simple speed-based model is employed to simulate an experiment of pedestrian bottleneck flow. The experiment revealed that the density near the bottleneck is influenced by the motivation of the pedestrians and the corridor width. In narrow corridors, distinct lanes are formed for pedestrians with low motivation. These lanes can disappear when the pedestrians have a high motivation to reach their target. We show that a speed-based model is - despite its relative simplicity- capable to reproduce the observed phenomena to a high degree.

In recent years, the measures to interfere the crowds movement with physical facilities (such as channelizing, separation railing) have become more and more common, but how they affect the crowd movement and what moving risks exist in the entrance confluence area have not been fully revealed. Therefore, this paper analyzes the moving risk of the crowds before the bottleneck entrance area, in the presence of the channelizing barriers by controllable laboratory experiments. The visual color cloud charts of the local density, speed and confusion degree of moving directions within the entrance confluence area are analyzed in the presence of different gaps (1.05m and 0.7m) channelizing barriers, to further quantify the motion risk of the crowds. The study finds that the narrower gaps of the channelizing railings, the larger area of high-risk zones, and they have clear ‘lane formation’ effect in shaping the risk zones. The both ends of the channelizing barriers are higher moving risk zones for multi-entry sides conditions, but the area before the middle channels also needs to be closely concerned when the participants entering from two opposite entering sides. The study will provide theoretical basis for evaluating the safety of the setting conditions of the channelizing barriers and conducting scientific crowd management decisions.

We apply the concept of time-to-collision (TTC) to the modeling of pedestrian dynamics. The TTC combines the spatial distances with the velocities to quantify the 'distance' to a collision. Therefore, it is a promising candidate for modeling the interactions between pedestrians. Empirical studies also indicate that the interaction between pedestrians can be described by the TTC: While the pair distribution of the distances, i.e. the probability of two pedestrians to have a certain spatial distance, was found to strongly depend on the relative velocity, the TTC accurately parametrizes its pair distribution. However, there are still few pedestrian models that use the TTC. After giving a general definition of the TTC, we present the widely used approximations for its calculation, especially in a one-dimensional setting. Combined with a desired time-gap, these give rise to different models, namely an Optimal-Velocity model and a new Time-to-Collision model. The TTC model exhibits, however, generic inconsistencies which are related to the estimates we use to approximate the speed of the predecessor. The estimates have a large impact on the dynamics and must therefore be interpreted as reflecting the pedestrians behavior, i.e. as anticipation strategies. We propose new estimates for the predecessor's speed. These give rise to a rich family of models based on the TTC which are analyzed by means of linear stability analysis and simulations.

The Braess paradox describes the counterintuitive situation that the addition of new roads to road networks can lead to higher travel times for all network users. Recently we could show that user optima leading to the paradox exist in networks of microscopic transport models. We derived phase diagrams for two kinds of route choice strategies that were externally tuned and applied by all network users. Here we address the question whether these user optima are still realized if intelligent route choice decisions are made based upon two kinds of traffic information. We find that the paradox still can occur if the drivers 1) make informed decisions based on their own past experiences or 2) use traffic information similar to that provided by modern navigation apps. This indicates that modern traffic information systems are not able to resolve Braess' paradox., 37 pages, 15 figures

Prof. Dr. H. C. Dietrich Stauffer passed away on August 6, 2019 after a long battle with cancer. He was for many years the Managing Editor of International Journal of Modern Physics C. The scientific community of statistical and computational physics has lost one of its prominent figures, who has shaped the field for over almost five decades.

It is interesting to investigate the effect of background music on pedestrian movement. This paper investigates the properties of crowd motion with external rhythms. With rhythm, pedestrians stop more frequently than without any rhythm. The stopping also increases with the increment of the tempo. Velocity and flow with rhythms are lower than that without any rhythm at high densities due to the more frequent stopping. Stepping behavior analysis shows that the step frequency with rhythms is smaller than that without any rhythm, especially at high densities. Dynamic coordinated behavior is weakened by music, which also affectsthe stepping behavior. Our study will be helpful for understanding the effect of background music on pedestrian movement.

This contribution presents a realistic cellular automaton model for multi-lane traffic, based on the model proposed by Lee et al. (2004). In contrast to current approaches, a limited deceleration capability, i.e., a mechanical restriction, has been assigned to the vehicles. Moreover, the velocity of the vehicles was determined on the basis of the local neighborhood, and the drivers were thus divided into optimistic or pessimistic drivers. The former were prone to underestimating their safety distance if their neighborhood admitted it, whereas the latter always kept a safe distance, thus over-reacting. This resulted in a convincing reproduction of the microscopic and macroscopic features of synchronized traffic. The anticipation of the leader’s velocity was thereby essential for the reproduction of synchronized traffic. Nevertheless, accidents occurred in the stationary state, and thus, the model approach required modification so as to be capable of simulating multi-lane traffic. The adapted model was enhanced by a realistic lane-change algorithm, and a multi-lane model, reproducing the empirical data even better than the single-lane approach, was formulated. In open systems with bottlenecks, such as an on-ramp or a speed-limit, the empirically observed complex structures of the synchronized traffic could be reproduced in great detail.

We study the Brownian motion of a particle in a bounded circular 2-dimensional domain, in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it travels along the one-dimensional boundary. During the diffusion, the Brownian particle resets to its initial position with a constant rate $r$. The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results., 11 pages, 10 figures

Pedestrian behaviours tend to depend on the type of facility. Therefore accurate predictions of pedestrians movements in complex geometries (including corridor, bottleneck or intersection) are difficult to achieve for classical models with few parameters. Artificial neural networks have multiple parameters and are able to identify various types of patterns. They could be a suitable alternative for forecasts. We aim in this paper to present first steps testing this approach. We compare estimations of pedestrian speed with a classical model and a neural network for combinations of corridor and bottleneck experiments. The results show that the neural network is able to differentiate the two geometries and to improve the estimation of pedestrian speeds when the geometries are mixed., 8 pages, 5 figures; Traffic and Granular Flow 2017 Conference (TGF'17)

Stop-and-go waves are commonly observed in traffic and pedestrian flows. In traffic theory they are described by phase transitions of metastable models. The self-organization phenomenon occurs due to inertia mechanisms but requires fine tuning of the parameters. Here, a novel explanation for stop-and-go waves based on stochastic effects is presented for pedestrian dynamics. We show that the introduction of specific coloured noises in a stable microscopic model allows to describe realistic pedestrian stop-and-go behaviour without requirement of metastability and phase transition. We compare simulation results of the stochastic model to real pedestrian trajectories and discuss plausible values for the model's parameters., 8 pages, 5 figures; Traffic and Granular Flow 2017 Conference (TGF'17)

Pedestrian crowds often include social groups, i.e. pedestrians that walk together because of social relationships. They show characteristic configurations and influence the dynamics of the entire crowd. In order to investigate the impact of social groups on evacuations we performed an empirical study with pupils. Several evacuation runs with groups of different sizes and different interactions were performed. New group parameters are introduced which allow to describe the dynamics of the groups and the configuration of the group members quantitatively. The analysis shows a possible decrease of evacuation times for large groups due to self-ordering effects. Social groups can be approximated as ellipses that orientate along their direction of motion. Furthermore, explicitly cooperative behaviour among group members leads to a stronger aggregation of group members and an intermittent way of evacuation., 17 pages, 11 figures

In this paper, the stability of the uniform solutions is analysed for microscopic flow models in interaction with $K\ge1$ predecessors. We calculate general conditions for the linear stability on the ring geometry and explore the results with particular pedestrian and car-following models based on relaxation processes. The uniform solutions are stable if the relaxation times are sufficiently small. The analysis is focused on the relevance of the number of predecessors in the dynamics. Unexpected non-monotonic relations between $K$ and the stability are presented., Comment: 18 pages, 14 figures

We obtain the exact solution of the one-loop mode-coupling equations for the dynamical structure function in the framework of non-linear fluctuating hydrodynamics in one space dimension for the strictly hyperbolic case where all characteristic velocities are different. All solutions are characterized by dynamical exponents which are Kepler ratios of consecutive Fibonacci numbers, which includes the golden mean as a limiting case. The scaling form of all higher Fibonacci modes are asymmetric L\'evy-distributions. Thus a hierarchy of new dynamical universality classes is established. We also compute the precise numerical value of the Pr\"ahofer-Spohn scaling constant to which scaling functions obtained from mode coupling theory are sensitive., Comment: PACS classification: \pacs{05.60.Cd, 05.20.Jj, 05.70.Ln, 47.10.-g}

To better design safe and comfortable urban spaces, understanding the nature of human crowd movement is important. However, precise interactions among pedestrians are difficult to measure in the presence of their complex decision-making processes and many related factors. While extensive studies on pedestrian flow through bottlenecks and corridors have been conducted, the dominant mode of interaction in these scenarios may not be relevant in different scenarios. Here, we attempt to decipher the factors that affect human reactions to other individuals from a different perspective. We conducted experiments employing the inflow process in which pedestrians successively enter a confined area (like an elevator) and look for a temporary position. In this process, pedestrians have a wider range of options regarding their motion than in the classical scenarios; therefore, other factors might become relevant. The preference of location is visualized by pedestrian density profiles obtained from recorded pedestrian trajectories. Non-trivial patterns of space acquisition, e.g., an apparent preference for positions near corners, were observed. This indicates the relevance of psychological and anticipative factors beyond the private sphere, which have not been deeply discussed so far in the literature on pedestrian dynamics. From the results, four major factors, which we call flow avoidance, distance cost, angle cost, and boundary preference, were suggested. We confirmed that a description of decision-making based on these factors can give a rise to realistic preference patterns, using a simple mathematical model. Our findings provide new perspectives and a baseline for considering the optimization of design and safety in crowded public areas and public transport carriers., Comment: 23 pages, 6 figures

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with unstable homogeneous states are identified. In this unstable regime it is then checked whether phase transitions or stop-and-go waves occur. Results based on numerical simulations show, however, that the investigated models lead to unrealistic behavior in form of backwards moving pedestrians and overlapping. This is one reason why stop-and-go waves have not been observed in these models. The unrealistic behavior is not related to the numerical treatment of the dynamic equations but rather indicates an intrinsic problem of this model class. Identifying the underlying generic problems gives indications how to define models that do not show such unrealistic behavior. As an example we introduce a new force-based model which produces realistic jam dynamics without the appearance of unrealistic negative speeds for empirical desired walking speeds., 20 pages, 15 figures, published in PRE

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent $z=2$ another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with $z=3/2$. It appears e.g. in low-dimensional dynamical phenomena far from thermal equilibrium which exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of non-equilibrium universality classes. Remarkably their dynamical exponents $z_\alpha$ are given by ratios of neighbouring Fibonacci numbers, starting with either $z_1=3/2$ (if a KPZ mode exist) or $z_1=2$ (if a diffusive mode is present). If neither a diffusive nor a KPZ mode are present, all dynamical modes have the Golden Mean $z=(1+\sqrt{5})/2$ as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric L\'evy distributions which are completely fixed by the macroscopic current-density relation and compressibility matrix of the system and hence accessible to experimental measurement., Comment: 8 pages, 5 Figs (2 Figure revised, one new Figure added), revised introduction

We reconsider the long-standing question of the critical defect hopping rate $r_c$ in the one-dimensional totally asymmetric exclusion process (TASEP) with a slow bond (defect). For $r< r_c$ a phase separated state is observed due to queuing at the defect site whereas for $r\geq r_c$ the defect site has only local effects on the stationary state of the homogeneous system. Mean-field theory predicts $r_c=1$ (when hopping rates outside the defect bond are equal to 1) but numerical investigations seem to indicate $r_c \approx 0.80(2)$. Here we improve the numerics to show that $r_c > 0.99$ and give strong evidence that indeed $r_c=1$ as predicted by mean-field theory, and anticipated by recent theoretical findings., 5 pages, 6 Figs, version as accepted by Europhysics Letters

We propose a microscopic stochastic model to describe 1D pedestrian trajectories obtained in laboratory experiments. The model is based on optimal velocity (OV) functions and an additive noise determined by the inertial Ornstein-Uhlenbeck process. After statistical estimation of the OV function and noise parameters, we explore the model by simulation. The results show that the stochastic approach gives a good description of the characteristic relation between speed and spacing (fundamental diagram) and its variability. Moreover, it can reproduce the observed stop-and-go waves, bimodal speed distributions, and nonzero speed or spacing autocorrelations.

The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by the M/M/1 queue that neglects the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered on a microscopic level. It is equivalent to a Totally Asymmetric Exclusion Process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability alpha and the service probability beta. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used. In this article, we review the main properties of the EQP. We also mention extensions and applications of the EQP and some related models., 20 pages, 11 figures, to appear in Mathematical Models and Methods in Applied Sciences, Special Issue "Traffic, Crowds and Swarms 2015"; contains a review of results from arXiv:1012.4525, arXiv:1109.0425, arXiv:1210.1482, arXiv:1308.2417, arXiv:1409.0329 and some new results

We propose a simple microscopic model for arching phenomena at bottlenecks. The dynamics of particles in front of a bottleneck is described by a one-dimensional stochastic cellular automaton on a semicircular geometry. The model reproduces oscillation phenomena due to the formation and collapsing of arches. It predicts the existence of a critical bottleneck size for continuous particle flows. The dependence of the jamming probability on the system size is approximated by the Gompertz function. The analytical results are in good agreement with simulations.

The relation between flow and density is an essential quantitative characteristic to describe the efficiency of traffic systems. We have performed experiments with single-file motion of bicycles and compare the results with previous studies for car and pedestrian motion in similar setups. In the space-time diagrams we observe three different states of motion (free flow state, jammed state and stop-and-go waves) in all these systems. Despite of their obvious differences they are described by a universal fundamental diagram after proper rescaling of space and time which takes into account the size and free velocity of the three kinds of agents. This indicates that the similarities between the systems go deeper than expected., 5 pages, 5 figures

The exclusive queueing process (EQP) is a generalization of the classical M/M/1 queue. It is equivalent to a totally asymmetric exclusion process (TASEP) of varying length. Here we consider two discrete-time versions of the EQP with parallel and backward-sequential update rules. The phase diagram (with respect to the arrival probability \alpha\ and the service probability \beta) is divided into two phases corresponding to divergence and convergence of the system length. We investigate the behavior on the critical line separating these phases. For both update rules, we find diffusive behavior for small output probability (\beta\beta_c it becomes sub-diffusive and nonuniversal: the exponents characterizing the divergence of the system length and the number of customers are found to depend on the update rule. For the backward-update case, they also depend on the hopping parameter p, and remain finite when p is large, indicating a first order transition., Comment: v2: published version

In this study, we provide results of controlled experiments of single file bicycle movement on a circuit. We compare the fundamental characteristics of bicycle traffic with that of car and pedestrian traffic, which have been studied extensively in previous research under similar condition. From the comparison of the time-space diagrams of these three one-dimensional traffic flows, different states of motion (free flow state, the jammed state and stop-and-go waves) can be observed in all these systems. The fundamental diagrams are compared in two different ways. Without considering the size and free velocity of these three kinds of objects, the data points occupy different density ranges in the diagram. However, when we use the concept of scaling by considering the free velocity and size of the moving objects, the fundamental diagrams show the same structure and values. This implies that the transport properties in these three different types of single file traffic flow could be unified in a certain range by simple scaling. These results provide insights into the dynamics but also may be relevant for the improvement of mixed traffic systems.

The exclusive queuing process (EQP) incorporates the exclusion principle into classic queuing models. It is characterized by, in addition to the entrance probability ? and exit probability ?, a third parameter: the hopping probability p. The EQP can be interpreted as an exclusion process of variable system length. Its phase diagram in the parameter space (?,?) is divided into a convergent phase and a divergent phase by a critical line which consists of a curved part and a straight part. Here we extend previous studies of this phase diagram. We identify subphases in the divergent phase, which can be distinguished by means of the shape of the density profile, and determine the velocity of the system length growth. This is done for EQPs with different update rules (parallel, backward sequential and continuous time). We also investigate the dynamics of the system length and the number of customers on the critical line. They are diffusive or subdiffusive with non-universal exponents that also depend on the update rules.

Recently, the stationary state of a parallel-update totally asymmetric simple exclusion process with varying system length, which can be regarded as a queueing process with excluded-volume effect (exclusive queueing process), was obtained [C Arita and D Yanagisawa, J. Stat. Phys. 141, 829 (2010)]. In this paper, we analyze the dynamical properties of the number of particles [N(t)] and the position of the last particle (the system length) [L(t)], using an analytical method (generating function technique) as well as a phenomenological description based on domain-wall dynamics and Monte Carlo simulations. The system exhibits two phases corresponding to linear convergence or divergence of [N(t)] and [L(t)]. These phases can both further be subdivided into high-density and maximal-current subphases. The predictions of the domain-wall theory are found to be in very good agreement quantitively with results from Monte Carlo simulations in the convergent phase. On the other hand, in the divergent phase, only the prediction for [N(t)] agrees with simulations.

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments., Comment: 10 pages, 14 figures, accepted for publication as a Regular Article in Physical Review E. This version contains minor changes

The asymmetric simple exclusion process with additional Langmuir kinetics, i.e. attachment and detachment in the bulk, is a paradigmatic model for intracellular transport. Here we study this model in the presence of randomly distributed inhomogeneities ('defects'). Using Monte Carlo simulations, we find a multitude of coexisting high- and low-density domains. The results are generic for one-dimensional driven diffusive systems with short-range interactions and can be understood in terms of a local extremal principle for the current profile. This principle is used to determine current profiles and phase diagrams as well as statistical properties of ensembles of defect samples., submitted for publishing

We investigate the effects of disorder on driven lattice gases with open boundaries using the totally asymmetric simple exclusion process as a paradigmatic example. Disorder is realized by randomly distributed defect sites with reduced hopping rate. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We study the current as function of the entry and exit rates and the realization of disorder and find that it is, in leading order, determined by the longest stretch of consecutive defect sites (single-bottleneck approximation, SBA). Using results from extreme value statistics the SBA allows to study ensembles with fixed defect density which gives accurate results, e.g. for the expectation value of the current. Corrections to SBA come from effective interactions of bottlenecks close to the longest one. Defects close to the boundaries can be described by effective boundary rates and lead to shifts of the phase transitions. Finally it is shown that the SBA also works for more complex models. As an example we discuss a model with internal states that has been proposed to describe transport of the kinesin KIF1A., submitted to J. Stat. Mech

A new public conveyance model applicable to buses and trains is proposed in this paper by using stochastic cellular automaton. We have found the optimal density of vehicles, at which the average velocity becomes maximum, significantly depends on the number of stops and passengers behavior of getting on a vehicle at stops. The efficiency of the hail-and-ride system is also discussed by comparing the different behavior of passengers. Moreover, we have found that a big cluster of vehicles is divided into small clusters, by incorporating information of the number of vehicles between successive stops., 8 pages, 15 figures

Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyday life. Experimental, theoretical and computational investigations in the last few years have led to a deeper understanding of the generic or common physical principles involved in these phenomena. In particular, some of the methods of non-equilibrium statistical mechanics, pioneered almost a hundred years ago by Einstein, Langevin and others, turned out to be powerful theoretical tools for quantitaive analysis of models of these traffic-like collective phenomena as these systems are intrinsically far from equilibrium. In this review we critically examine the current status of our understanding, expose the limitations of the existing methods, mention open challenging questions and speculate on the possible future directions of research in this interdisciplinary area where physics meets not only chemistry and biology but also (nano-)technology., 33 page Review article, REVTEX text, 29 EPS and PS figures

The understanding of traffic dynamics on highway networks is essential for traffic control. Nowadays realistic microscopic models exist that allow highly efficient (faster-than-real-time) simulations of large networks. These simulations can be used not only to determine the state of the network from incomplete information, but also for traffic forecasting. We also discuss an analysis of the highway network in Germany to identify bottlenecks and possible optimization strategies. Language: en

We study discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations. Results from computer simulations of the floor field model are compared with empirical findings. Furthermore the influence of increasing the maximal walking speed $v_{{\rm max}}$ is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to $v_{{\rm max}}>1$ turns out to be a severe challenge which can be solved in different ways. Four major variants are discussed that take into account different dynamical aspects. The variation of $v_{{\rm max}}$ has strong influence on the shape of the flow-density relation. We show that walking speeds $v_{{\rm max}}>1$ lead to results which are in very good agreement with empirical data., Comment: 22 pages, 15 figures, to appear in J. Stat. Mech.: Theor. Exp

A recently introduced cellular automaton model for Internet traffic is investigated in the context of boundary induced phase transitions and the appropriate phase diagrams. Since the model allows multi allocation of sites there are some deviations in the internal dynamics as well as in global properties compared to known driven lattice gas models. As a consequence the yielding phase diagram derived by numerical simulations reveals some interesting new features like a capacity shift in dependence to the allocation number.

Many insects like ants communicate chemically via chemotaxis. This allows them to build large trail systems which in many respects are similar to human-build highway networks. Using a recently proposed stochastic cellular automaton model 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. We also discuss the effect of counterflow on the trails., 12 pages, 7 figures, uses Springer macros; to appear in the proceedings of "Traffic and Granular Flow '03"

We investigate a large class of antiferromagnetic spin-1 chains with nearest neighbour interaction and exactly known matrix product ground state. The spectrum of low-lying excitations is calculated numerically by DMRG and exact diagonalisation. Spin liquid behaviour with an excitation gap is observed meeting the Haldane scenario. Further, we compare properties of the anisotropic model with the well-known isotropic AKLT model and use the analytical single mode approximation to obtain a quantitative understanding of the excitation gap. The low-lying excited states can be interpreted in terms of a magnon-like elementary excitation., 9 pages, 6 figures, accepted for publication in Eur. Phys. J. B, uses svjour.cls

A microscopic description of packet transport in the Internet by using a simple cellular automaton model is presented. Therefore we introduced a generalized exclusion process which allows to study travel times of the particles (‘data packets’) along a path in the network. Computer simulations reveal the appearance of a free flow and a jammed phase separated by a (critical) transition regime. The power spectra are compared to empirical data for the RTT (Round Trip Time) obtained from measurements in the Internet. We find that the model is able to reproduce the characteristic statistical behavior in agreement with the empirical data for free flow and congested phase. Moreover the model shows, as observed in reality, critical behavior (1/f-noise) for paths with critical load.

The impact of global traffic light control strategies for city networks is analyzed in a recently proposed cellular automaton model. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets.