Parallel Implementations of Cellular Automata for Traffic Models

The Biham-Middleton-Levine (BML) traffic model is a simple two-dimensional, discrete Cellular Automaton (CA) that has been used to study self-organization and phase transitions arising in traffic flows. From the computational point of view, the BML model exhibits the usual features of discrete CA, where the state of the automaton are updated according to simple rules that depend on the state of each cell and its neighbors. In this paper we study the impact of various optimizations for speeding up CA computations by using the BML model as a case study. In particular, we describe and analyze the impact of several parallel implementations that rely on CPU features, such as multiple cores or SIMD instructions, and on GPUs. Experimental evaluation provides quantitative measures of the payoff of each technique in terms of speedup with respect to a plain serial implementation. Our findings show that the performance gap between CPU and GPU implementations of the BML traffic model can be reduced by clever exploitation of all CPU features

Non-concave fundamental diagrams and phase transitions in a stochastic traffic cellular automaton

Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions between these phases, allows us to establish a rigorous classification based on their tempo-spatial behavioral characteristics. As a result from the system's complex dynamics, its flow-density relation exhibits a non-concave region in which forward propagating density waves are encountered. All four phases furthermore share the common property that moving vehicles can never increase their speed once the system has settled into an equilibrium

Energy Dissipation Burst on the Traffic Congestion

We introduce an energy dissipation model for traffic flow based on the optimal velocity model (OV model). In this model, vehicles are defined as moving under the rule of the OV model, and energy dissipation rate is defined as the product of the velocity of a vehicle and resistant force which works to it.Comment: 15 pages, 19 Postscript figures. Reason for replacing: This is the submitted for

Performance Evaluation of Road Traffic Control Using a Fuzzy Cellular Model

In this paper a method is proposed for performance evaluation of road traffic control systems. The method is designed to be implemented in an on-line simulation environment, which enables optimisation of adaptive traffic control strategies. Performance measures are computed using a fuzzy cellular traffic model, formulated as a hybrid system combining cellular automata and fuzzy calculus. Experimental results show that the introduced method allows the performance to be evaluated using imprecise traffic measurements. Moreover, the fuzzy definitions of performance measures are convenient for uncertainty determination in traffic control decisions.Comment: The final publication is available at http://www.springerlink.co

Spring-block model for a single-lane highway traffic

A simple one-dimensional spring-block chain with asymmetric interactions is considered to model an idealized single-lane highway traffic. The main elements of the system are blocks (modeling cars), springs with unidirectional interactions (modeling distance keeping interactions between neighbors), static and kinetic friction (modeling inertia of drivers and cars) and spatiotemporal disorder in the values of these friction forces (modeling differences in the driving attitudes). The traveling chain of cars correspond to the dragged spring-block system. Our statistical analysis for the spring-block chain predicts a non-trivial and rich complex behavior. As a function of the disorder level in the system a dynamic phase-transition is observed. For low disorder levels uncorrelated slidings of blocks are revealed while for high disorder levels correlated avalanches dominates.Comment: 6 pages, 7 figure

Urban traffic from the perspective of dual graph

In this paper, urban traffic is modeled using dual graph representation of urban transportation network where roads are mapped to nodes and intersections are mapped to links. The proposed model considers both the navigation of vehicles on the network and the motion of vehicles along roads. The road's capacity and the vehicle-turning ability at intersections are naturally incorporated in the model. The overall capacity of the system can be quantified by a phase transition from free flow to congestion. Simulation results show that the system's capacity depends greatly on the topology of transportation networks. In general, a well-planned grid can hold more vehicles and its overall capacity is much larger than that of a growing scale-free network.Comment: 7 pages, 10 figure

Metric properties of discrete time exclusion type processes in continuum

A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to the particle density (the so called Fundamental Diagram) is analyzed rigorously. The main technical tool is a "dynamical" coupling applied in a nonstandard fashion: we do not prove the existence of the successful coupling (which even might not hold) but instead use its presence/absence as an important diagnostic tool. Despite that this approach cannot be applied to lattice systems directly, it allows to obtain new results for the lattice systems embedding them to the systems in continuum. Applications to the traffic flows modelling are discussed as well.Comment: 27 pages, 4 figures; minor errors corrected; details added to proofs of Theorems 4.1 and 5.

Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation

[EN] The phenomenon of chaos has been exhibited in mathematical nonlinear models that describe traffic flows, see, for instance (Li and Gao in Modern Phys Lett B 18(26-27):1395-1402, 2004; Li in Phys. D Nonlinear Phenom 207(1-2):41-51, 2005). At microscopic level, Devaney chaos and distributional chaos have been exhibited for some car-following models, such as the quick-thinking-driver model and the forward and backward control model (Barrachina et al. in 2015; Conejero et al. in Semigroup Forum, 2015). We present here the existence of chaos for the macroscopic model given by the Lighthill Whitham Richards equation.The authors are supported by MEC Project MTM2013-47093-P. The second and third authors are supported by GVA, Project PROMETEOII/2013/013Conejero, JA.; Martínez Jiménez, F.; Peris Manguillot, A.; Ródenas Escribá, FDA. (2016). Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation. 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