Michael Schreckenberg

Traffic and Granular Flow '13

The Intelligent Driver Model (IDM) is studied and several dr awbacks with respect to driving simulators are defined. We present two mod ifications of the IDM. The first one gives any predefined distance to the leading vehi cle in a steady state. The second modification is a combination of the first one and th e optimal velocity model. It takes into account driver’s reaction time expl icitly and is described by delay differential equation. This model always results in r ealistic vehicles accelerations what allows simulating real traffic collisions. Necessary and sufficient conditions are obtained, that guar antee a non-oscillating solution near the equilibrium for the vehicle platoon. We su ggest the calibrating framework based on a numerical solution of the constrained o ptimization problem. Nonlinear constraints are generated by the numerical integ ra ion scheme. The suggested procedure incorporates the local stability conditi ons obtained and takes into account vehicle dynamics, drivers’ behavior and weather co nditions.Part I: Pedestrian Dynamics and Evacuation Dynamics.- Part II: Highway and Urban Vehicular Traffic.- Part III: Biological Systems and Granular Flow.

Metastable states in cellular automata for traffic flow

Abstract:Measurements on real traffic have revealed the existence of metastable states with very high flow. Such states have not been observed in the Nagel-Schreckenberg (NaSch) model which is the basic cellular automaton for the description of traffic. Here we propose a simple generalization of the NaSch model by introducing a velocity-dependent randomization. We investigate a special case which belongs to the so-called slow-to-start rules. It is shown that this model exhibits metastable states, thus sheding some light on the prerequisites for the occurance of hysteresis effects in the flow-density relation.

Two lane traffic simulations using cellular automata

We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.

Optimizing traffic lights in a cellular automaton model for city traffic.

We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. 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. Starting from a simple synchronized strategy, we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover, we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights, the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model, improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.

Discrete stochastic models for traffic flow.

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.

Towards a realistic microscopic description of highway traffic

Simple cellular automata models are able to reproduce the basic properties of highway traffic. The comparison with empirical data for microscopic quantities requires a more detailed description of the elementary dynamics. Based on existing cellular automata models, we propose an improved discrete model incorporating anticipation effects, reduced acceleration capabilities and an enhanced interaction horizon for braking. The modified model is able to reproduce the three phases (free-flow, synchronized, and stop-and-go) observed in real traffic. Furthermore we find a good agreement with detailed empirical single-vehicle data in all phases.

Experiments and Simulations on Day-to-Day Route Choice-Behaviour

The paper reports laboratory experiments with a two route choice scenario. In each session 18 subjects had to choose between a main road M and a side road S. The capacity of M was larger. Feedback was given in treatment I only on the subjects’ own travel time and in treatment II on travel time for M and S. The main results are as follows: • Mean numbers on M and S are near to pure equilibrium. • Fluctuations persist until the end of the sessions. • The total number of changes is significantly greater in treatment I. • Subjects’ road changes and payoffs are negatively correlated. • A direct response mode results in more changes for bad payoffs whereas a contrary response mode shows opposite reactions. • Simulations of an extended payoff sum learning model fits the main results of the statistical evaluation of the data.

Single-vehicle data of highway traffic: a statistical analysis

In the present paper, single-vehicle data of highway traffic are analyzed in great detail. By using the single-vehicle data directly, empirical time headway distributions and speed-distance relations can be established. Both quantities yield relevant information about the microscopic states. Several fundamental diagrams are also presented, which are based on time-averaged quantities and compared with earlier empirical investigations. In the remaining part, time-series analyses of the averaged as well as the single-vehicle data are carried out. The results will be used in order to propose objective criteria for an identification of the different traffic states, e.g., synchronized traffic.

Decision dynamics in a traffic scenario

Information is a key commodity in many socio-economic systems like stock markets or traffic systems. In this paper the influence of dynamic information on the stability of traffic patterns is investigated using a very simple route choice scenario. The basis of the route decisions is dynamic information generated by traffic flow simulations. A correlation analysis yields that the system can be destabilized by introducing information. It is found that the overall performance of the system is reduced, although the information should help to distribute traffic more efficiently.

Particle hopping models for two-lane traffic with two kinds of vehicles: Effects of lane-changing rules

We develop particle-hopping models of two-lane traffic with two different types of vehicles (characterized by two different values of the maximum allowed speed Vmax) generalizing the Nagel-Schrecknnberg stochastic cellular-automata model for single-lane traffic with a single Vmax. The simplest of the two models is symmetric with respect to the two lanes as well as with respect to the two types of vehicles. In the asymmetric model, different rules govern the changing from the the “fast” lanes to the “slow” one and the reverse process. Moreover, in the asymmetric model, the drivers of fast vehicles can anticipate, often well in advance, the possibility of getting trapped behind a slow vehicle and tend to avoid such possibilities.