Biomedical subjects

Dirk Helbing

Publications and source records attributed to Dirk Helbing.

11 recordsLinked to original sources

PubMed2006

Analytical approach to continuous and intermittent bottleneck flows.

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.

Journal Article↗

PubMed2006

Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps.

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and simulate traffic breakdowns in open systems with an on-ramp as bottleneck and in a closed ring road. Single-vehicle data and one-minute aggregated data generated by several virtual detectors show a semiquantitative agreement with microscopic and flow-density data from the Dutch freeway A9. This includes the observed distributions of the net time headways for free and congested traffic, the velocity variance as a function of density, and the fundamental diagram. The modal value of the time headway distribution is shifted by a factor of about 2 under congested conditions. Macroscopically, this corresponds to the capacity drop at the transition from free to congested traffic. The simulated fundamental diagram shows free, synchronized, and jammed traffic, and a wide scattering in the congested traffic regime. We explain this by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons even for a deterministic dynamics on a single lane.

Journal Article↗

PubMed2005

Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic.

In two intersecting many-particle streams, one can often find the emergence of oscillatory patterns. Here, we investigate the interaction of pedestrians with vehicles, when they try to cross a road. A numerical study of this coupled pedestrian-vehicle delay problem has been presented in a previous paper. Here, we focus on the analytical treatment of the problem, which requires us to use a simplified car-following model. Our analytical results for the transition to oscillatory pedestrian and traffic flows and the average waiting times are well supported by numerical evaluations and give a detailed picture of the collective dynamics emerging when pedestrians try to cross a road. The mathematical expressions allow one to identify the dependence on model parameters such as the vehicle or pedestrian arrival rate, and the safety factor of pedestrian gap acceptance. We also calculate a formula for the vehicle time gap distribution, which corresponds to the departure time contribution of a M/D/1 queue characterized by Poissonian distributed Markovian arrivals, 1 service channel, and deterministic departures.

Journal Article↗

PubMed2005

Analytical investigation of innovation dynamics considering stochasticity in the evaluation of fitness.

We investigate a selection-mutation model for the dynamics of technological innovation, a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success ("fitness"), they are an essential prerequisite for innovation. Together with a selection of above-average technologies due to imitation behavior, they are the "driving force" for the continuous increase in fitness. We will give analytical solutions for the probability distribution of technologies for special cases and in the limit of large times. The selection dynamics is modeled by a "proportional imitation" of better technologies. However, the assessment of a technology's fitness may be imperfect and, therefore, vary stochastically. We will derive conditions under which a wrong assessment of fitness can accelerate the innovation dynamics, as has been found in some surprising numerical investigations.

Journal Article↗

PubMed2004

Physics, stability, and dynamics of supply networks.

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bullwhip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Journal Article↗

PubMed2004

Network-induced oscillatory behavior in material flow networks and irregular business cycles.

Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of power grids remains to be explored. Based on a simple model of supply networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most supply networks display damped oscillations, even when their units--and linear chains of these units--behave in a nonoscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a different interpretation of business cycles and of oscillating or pulsating processes. The network structure of material flows itself turns out to be a source of instability, and cyclical variations are an inherent feature of decentralized adjustments.

Journal Article↗

PubMed2004

Experiment, theory, and simulation of the evacuation of a room without visibility.

We study the evacuation process from a smoky room by means of experiments and simulations. People in a dark or smoky room are mimicked by "blind" students wearing eye masks. The evacuation of the disoriented students from the room is observed by video cameras, and the escape time of each student is measured. We find that the disoriented students exhibit a distinctly different behavior compared to a situation in which people can see their environment. Our experimental results are related to a theoretical approach and reproduced by an extended lattice gas model taking into account the empirically observed behavior. Our particular focus is on the mean value and distribution of escape times. For a large number of people in the room, the escape time distribution is wide because of jamming. Surprisingly, adding more exits does not improve the situation in the expected way, since most people use the exit that is discovered first, which may be viewed as a kind of herding effect based on nonlocal, but direct acoustic interactions. Moreover, the average escape time becomes minimal for a certain finite number of people in the dark or smoky room. These nonlinear effects have practical implications for emergency evacuation and the planning of safer buildings.

Journal Article↗

PubMed2004

Optimal traffic organization in ants under crowded conditions.

Efficient transportation, a hot topic in nonlinear science, is essential for modern societies and the survival of biological species. Biological evolution has generated a rich variety of successful solutions, which have inspired engineers to design optimized artificial systems. Foraging ants, for example, form attractive trails that support the exploitation of initially unknown food sources in almost the minimum possible time. However, can this strategy cope with bottleneck situations, when interactions cause delays that reduce the overall flow? Here, we present an experimental study of ants confronted with two alternative routes. We find that pheromone-based attraction generates one trail at low densities, whereas at a high level of crowding, another trail is established before traffic volume is affected, which guarantees that an optimal rate of food return is maintained. This bifurcation phenomenon is explained by a nonlinear modelling approach. Surprisingly, the underlying mechanism is based on inhibitory interactions. It points to capacity reserves, a limitation of the density-induced speed reduction, and a sufficient pheromone concentration for reliable trail perception. The balancing mechanism between cohesive and dispersive forces appears to be generic in natural, urban and transportation systems.

Animals↗

PubMed2003

Interpreting the wide scattering of synchronized traffic data by time gap statistics.

Based on the statistical evaluation of experimental single-vehicle data, we propose a quantitative interpretation of the erratic scattering of flow-density data in synchronized traffic flows. A correlation analysis suggests that the dynamical flow-density data are well compatible with the so-called jam line characterizing fully developed traffic jams, if one takes into account the variation of their propagation speed due to the large variation of the netto time gaps (the inhomogeneity of traffic flow). The form of the time gap distribution depends not only on the density, but also on the measurement cross section: The most probable netto time gap in congested traffic flow upstream of a bottleneck is significantly increased compared to uncongested freeway sections. Moreover, we identify different power-law scaling laws for the relative variance of netto time gaps as a function of the sampling size. While the exponent is -1 in free traffic corresponding to statistically independent time gaps, the exponent is about -2/3 in congested traffic flow because of correlations between queued vehicles.

Journal Article↗

PubMed2003

Memory effects in microscopic traffic models and wide scattering in flow-density data.

By means of microscopic simulations we show that noninstantaneous adaptation of the driving behavior to the traffic situation together with the conventional method to measure flow-density data provides a possible explanation for the observed inverse-lambda shape and the wide scattering of flow-density data in "synchronized" congested traffic. We model a memory effect in the response of drivers to the traffic situation for a wide class of car-following models by introducing an additional dynamical variable (the "subjective level of service") describing the adaptation of drivers to the surrounding traffic situation during the past few minutes and couple this internal state to parameters of the underlying model that are related to the driving style. For illustration, we use the intelligent-driver model (IDM) as the underlying model, characterize the level of service solely by the velocity, and couple the internal variable to the IDM parameter "time gap" to model an increase of the time gap in congested traffic ("frustration effect"), which is supported by single-vehicle data. We simulate open systems with a bottleneck and obtain flow-density data by implementing "virtual detectors." The shape, relative size, and apparent "stochasticity" of the region of the scattered data points agree nearly quantitatively with empirical data. Wide scattering is even observed for identical vehicles, although the proposed model is a time-continuous, deterministic, single-lane car-following model with a unique fundamental diagram.

Journal Article↗

PubMed2003

Lattice gas simulation of experimentally studied evacuation dynamics.

We study the evacuation process from a classroom by means of experiments and simulations. The evacuation of students from a classroom is observed by video cameras, and the escape time of each student is measured. Our experimental results are compared with simulations based on a lattice gas model of pedestrian flows. We find that the empirically identified inefficiencies of the evacuation process can be well reproduced. Our particular focus is on the spatial dependence of the escape times on the initial positions, which is highly significant. The escape time distribution turns out to be rather broad due to a jamming (queuing) of the students at the exit, which determines not only the saturation flow (capacity) but also the temporal characteristics of the evacuation dynamics.

Journal Article↗