Biomedical subjects

Martin Treiber

Publications and source records attributed to Martin Treiber.

5 recordsLinked to original sources

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.

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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.

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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.

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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.

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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.

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