Density Fluctuations and Phase Transition in the Nagel-Schreckenberg Traffic Flow Model

We consider the transition of the Nagel-Schreckenberg traffic flow model from the free flow regime to the jammed regime. We examine the inhomogeneous character of the system by introducing a new method of analysis which is based on the local density distribution. We investigated the characteristic fluctuations in the steady state and present the phase diagram of the system.Comment: 4 pages, 7 figures, accepted for publication in Phys. Rev.

Density fluctuations and phase separation in a traffic flow model

Within the Nagel-Schreckenberg traffic flow model we consider the transition from the free flow regime to the jammed regime. We introduce a method of analyzing the data which is based on the local density distribution. This analyzes allows us to determine the phase diagram and to examine the separation of the system into a coexisting free flow phase and a jammed phase above the transition. The investigation of the steady state structure factor yields that the decomposition in this phase coexistence regime is driven by density fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M. Schreckenberg, Springer, Singapore (1998

Continuous Time and Consistent Histories

We discuss the use of histories labelled by a continuous time in the approach to consistent-histories quantum theory in which propositions about the history of the system are represented by projection operators on a Hilbert space. This extends earlier work by two of us \cite{IL95} where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time average of the energy. We also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.Comment: Typeset in RevTe

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

Car-oriented mean-field theory for traffic flow models

We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with $v_{max}=1$ the exact solution is reproduced. For $v_{max}=2$ the fundamental diagram shows a good agreement with results from simulations.Comment: LaTex, 10 pages, 2 postscript figure

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.Comment: to be published in Physica A, 19 pages, 9 out of 13 postscript figures, 24kB in format .tar.gz., 33kB in format .tar.gz.uu, for a full version including all figures see http://studguppy.tsasa.lanl.gov/research_team/papers

A Simplified Cellular Automaton Model for City Traffic

We systematically investigate the effect of blockage sites in a cellular automaton model for traffic flow. Different scheduling schemes for the blockage sites are considered. None of them returns a linear relationship between the fraction of ``green'' time and the throughput. We use this information for a fast implementation of traffic in Dallas.Comment: 12 pages, 18 figures. submitted to Phys Rev

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.Comment: 7 pages, 7 figure

Two-dimensional Burgers Cellular Automaton

A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA, such as shock wave solutions, are studied in detail.Comment: Latex2.09, 17 pages including 7 figure

The Effect of absorbing sites on the one-dimensional cellular automaton traffic flow with open boundaries

The effect of the absorbing sites with an absorbing rate $\beta_{0}$, in both one absorbing site (one way out) and two absorbing sites (two ways out) in a road, on the traffic flow phase transition is investigated using numerical simulations in the one-dimensional cellular automaton traffic flow model with open boundaries using parallel dynamics.In the case of one way out, there exist a critical position of the way out $i_{c1}$ below which the current is constant for $\beta_{0}$$<$$\beta_{0c2}$ and decreases when increasing $\beta_{0}$ for $\beta_{0}$$>$$\beta_{0c2}$. When the way out is located at a position greater than $i_{c2}$, the current increases with $\beta_{0}$ for $\beta_{0}$$<$$\beta_{0c1}$ and becomes constant for any value of $\beta_{0}$ greater than $\beta_{0c1}$. While, when the way out is located at any position between $i_{c1}$ and $i_{c2}$ ($i_{c1}$$<$$i_{c2}$), the current increases, for $\beta_{0}$$<$$\beta_{0c1}$, with $\beta_{0}$ and becomes constant for $\beta_{0c1}$$<$$\beta_{0}$$<$$\beta_{0c2}$ and decreases with $\beta_{0}$ for $\beta_{0}$$>$$\beta_{0c2}$. In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at $\beta_{0}$$=$$\beta_{0c1}$ and from intermediate density to the low one at $\beta_{0}$$=$$\beta_{0c2}$. In the case of two ways out located respectively at the positions $i_{1}$ and $i_{2}$, the two successive transitions occur only when the distance $i_{2}$-$i_{1}$ separating the two ways is smaller than a critical distance $d_{c}$. Phase diagrams in the ($\alpha,\beta_{0}$), ($\beta,\beta_{0}$) and ($i_{1},\beta_{0}$) planes are established. It is found that the transitions between Free traffic, Congested traffic and maximal current phase are first order