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Summary There is discussion if traffic displays spontaneous breakdown. This paper presents computational evidence that stochastic car following models can have a control parameter that moves the model between displaying and not displaying spontaneous phase separation for some densities. Those phases can be called “laminar” and “jammed”. Models with spontaneous phase separation show three states as...
Summary Resolution of LWR model is considered. The method proposed in this paper differs from (continuous) characteristic based analytical resolutions or from (discretized) finite difference schemes. It is based on an approximation of the flow-density relationship which yields a solution with piecewise constant density. This solution is then exactly calculated by tracking waves and handling their...
Summary This paper is an analysis of the various scales at which traffic flow can be represented, from vehicular to continuum flow models, with various time and space resolutions. The paper first investigates the question of scales and scale separation in traffic flow, both in modelling and measurement, using analogy with other disciplines. It then evaluates the representation of vehicles heterogeneities...
Summary Based on a microscopic theory of spatial-temporal congested traffic patterns at freeway bottlenecks, diagrams and features of the congested patterns at bottlenecks due to on-ramps, merge bottlenecks (a reduction in freeway lanes), and off-ramps are studied and compared.
Summary Congested traffic patterns at a symmetric merger of two single-lane roads into one road are studied in the KKW-model, a cellular automaton that traces all observed congestion patterns back to two basic concepts: A typical distance below which a driver decides to adjust his speed to the one of the car in front, and the minimal distance between cars that is compatible with secure driving. The...
Summary The transport of products between different suppliers or production units can be described similarly to driven many-particle and traffic systems. We introduce equations for the flow of goods in supply networks and the adaptation of production speeds. Moreover, we present two examples: The case of linear (sequential) supply chains and the case of re-entrant production. In particular, we discuss...
Summary We present a macroscopic traffic flow model that explicitly builds on continuous individual driving behaviour. Not only do we start from classical car-following rules (like the kind that are used in microscopic simulators), the model also explicitly accounts for the finite reaction times of drivers, anticipation behaviour, anisotropy in driver responses and the finite space requirement of...
Summary In this paper we describe a relation between a microscopic stochastic traffic cellular automaton model (i.e., the STCA) and the macroscopic first-order continuum model (i.e., the LWR model). The innovative aspect is that we explicitly incorporate the STCA's stochasticity in the construction of the fundamental diagram used by the LWR model. We apply our methodology to a small case study, giving...
Summary From probabilistic point of view we investigate a quite classical dynamical system given by stochastic differential equations, i. e. ordinary differential equations driven by multiplicative noise. Based on this Langevin approach the probability density distributions of vehicular velocities as well as headway distances are calculated and discussed. Our work is a continuation of a stochastic...
Summary A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system $$ \left\{ {x,v = \dot x} \right\} $$ with additive white noise is analyzed numerically. A chain of such oscillators is also studied in brief.
Summary Since the year 2000, the Centre of Applied Informatics and the Institute for Transport Research at the German Aerospace Centre develops a microscopic road traffic simulation package named ’SUMO’ — an acronym for “Simulation of Urban MObility”. Meanwhile, the simulation is capable to deal with realistic scenarios such as large cities and is used for these purposes within the institute's projects...
Summary We show that some simple urban traffic flow equations can be approximated by equations which are equivalent to a Schrödinger equation. For a simulation of the Schrödinger equation as well as for analytical computations it is useful that waves of traffic which travel along a road are not reflected at the boundaries of the simulated region. We present the non-reflecting boundary condition for...
Summary Continuum models for traffic flows may serve as a tool for the optimal management of traffic. From the mathematical point of view, the development of a control theory for conservation laws is still at its beginning. From the engineering point of view, both the optimality criteria and the selection of the controllable parameters seem far from being standardized. This note presents first...
Summary This note discusses the role of source terms in the modeling of vehicular traffic through conservation laws. As is well known, a source term in the equation for the vehicular density may represent entries or exits. When a second conservation laws is present, suitable source terms may describe various inhomogeneities of the road, such as ascents, descents or fog banks. In each of these cases,...
Summary The aim of this article is to study how the obstruction caused by slow vehicles (like trucks for example) on other ones can be modelled in a two-flow macroscopic model based on the Lighthill-Whitham-Richards (LWR) theory. This will be done by using the results of moving bottleneck models which describe the effect of a single slow vehicle on the rest of the flow.
Summary This contribution re-visits the classical optimal-velocity model of Bando et al [1], describing vehicles on a loop, and explains the different wave types and meta-stable behaviour from the mathematical viewpoint of bifurcation theory. We apply the numerical continuation package AUTO for a rapid derivation of phase diagrams to investigate the relation between coexisting states, flow transitions...
Summary A traffic model based on a cellular automaton (CA) approach with the focus on limited braking capabilities is presented. It is shown that the known empirical features of traffic flow can be reproduced including even the so called pinch effect being the object of actual investigations.
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