Metastable States in Cellular Automata for Traffic Flow

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.Comment: 15 pages, 8 ps-figures included; accepted for publication in EPJ

A simple Monte Carlo model for crowd dynamics

In this paper we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of non-equilibrium hard-disk fluids and discuss general implications of our model.Comment: to be published in Physical Review

Quantum Fields in Nonstatic background: A Histories Perspective

For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This fact suggests a description in terms of time - dependent Hilbert spaces, a concept that fits naturally in a (consistent) histories framework. Our primary tool for the construction of the quantum theory in a continuous -time histories format is the recently developed formalism based on the notion of the history group . This we employ to study a model system involving a 1+1 scalar field in a cavity with moving boundaries. The instantaneous (smeared) Hamiltonian and a decoherence functional are then rigorously defined so that finite values for the time - averaged particle creation rate are obtainable through the study of energy histories. We also construct the Schwinger - Keldysh closed- time - path generating functional as a ``Fourier transform'' of the decoherence functional and evaluate the corresponding n - point functions.Comment: 27 pages, LATEX; minor changes and corrections; version to appear in JM

On- and Off-ramps Generating 1/f Noise in Traffic Flow

A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called ”plateau” in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/fα fluctuations in the global traffic flow of a chosen main road of the simulated system.A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called ”plateau” in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/fα fluctuations in the global traffic flow of a chosen main road of the simulated system

Economics-Based Optimization of Unstable Flows

As an example for the optimization of unstable flows, we present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. It exploits the naturally occuring fluctuations of traffic flow and is flexible enough to adapt in real time to the transient flow characteristics of road traffic. Simulations based on realistic parameter values show that this strategy is feasible for naturally occurring traffic, and that even far from optimality, injection policies can improve traffic flow. Moreover, the same method can be applied to the optimization of flows of gases and granular media.Comment: Revised version of ``Optimizing Traffic Flow'' (cond-mat/9809397). For related work see http://www.parc.xerox.com/dynamics/ and http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Commuters 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

Volatile Decision Dynamics: Experiments, Stochastic Description, Intermittency Control, and Traffic Optimization

The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified ways of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems, and for information service providers. One of the promising fields of application is traffic optimization.Comment: For related work see http://www.helbing.or

On the Stability of the Mean-Field Glass Broken Phase under Non-Hamiltonian Perturbations

We study the dynamics of the SK model modified by a small non-hamiltonian perturbation. We study aging, and we find that on the time scales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a large one). If we assume we are observing a transient behavior the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discuss the slow power law decay of observable quantities to equilibrium, and we show that for small perturbations power like decay is preserved. We also discuss the asymptotically large time region on small lattices.Comment: 34 page

Deterministic approach to microscopic three-phase traffic theory

Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow, or synchronized flow, or else wide moving jam traffic phase. In a speed adaptation model (SA-model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD- and SA-models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD- and SA-models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD- and SA-models are studied. A comparison of the ATD- and SA-models with stochastic models in the context of three phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.Comment: 40 pages, 14 figure