Stochastic Description of Traffic Flow

Alperovich, Timur; Sopasakis, Alexandros

doi:10.1007/s10955-008-9652-6

Cited by 32 publications

(26 citation statements)

References 34 publications

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“…The model describes a single class of cars that move in one direction along a single-lane highway. Possible multi-lane and multi-class extensions are considered in [1,7]. The modeled is defined over a one-dimensional lattice L = {1, .…”

Section: Cellular Automata Modelmentioning

confidence: 99%

On cellular automata models of traffic flow with look-ahead potential

2014

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We study the statistical properties of a cellular automata model of traffic flow with the lookahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions needed for the derivation of the coarse-grained model and demonstrate that it is possible to relax some of them to obtain an improved coarsegrained ODE model. We also demonstrate that spatial correlations play a crucial role in the presence of the look-ahead potential and propose a simple empirical correction to account for the spatial dependence between neighboring cells.

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Section: Cellular Automata Modelmentioning

confidence: 99%

On cellular automata models of traffic flow with look-ahead potential

2014

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“…Microscopic spin-flip dynamics with look-ahead interactions have recently been explored in [3] and [1] in the context of traffic flow modeling. The coarse grained spin-flip mechanism with look-ahead interactions is now presented below.…”

Section: Spin-flip Coarse Grained Dynamics With Look-aheadmentioning

confidence: 99%

“…We further enhance the stochastic dynamics and introduce a new type of stochastic, look-ahead, interactions with direct links to physical applications [21,22,1]. As a result the hybrid system under the influence of directional fluctuations from the stochastic piece may cooperate or conflict against advective trends arising from the PDE.…”

Section: Introductionmentioning

confidence: 99%

Hybrid deterministic stochastic systems with microscopic look-ahead dynamics

Katsoulakis¹,

Majda²,

Sopasakis

2010

Communications in Mathematical Sciences

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Hybrid deterministic stochastic systems with microscopic look-ahead dynamics. Communications in Mathematical Sciences AbstractWe study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection diffusion reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type inter-particle interactions. Furthermore, we consider a new, asymmetric, single exclusion process, studied elsewhere in the context of traffic flow modeling, with an one-sided interaction potential which imposes advective trends on the stochastic. This is our look-ahead stochastic mechanism which is responsible for rich nonlinear behavior in solutions.Our approach relies heavily on first deriving approximate differential mesoscopic equations. These approximations become exact either in the long range, Kac interaction partial differential equation case, or, given sufficient time separation conditions, between the partial differential equation and the stochastic model giving rise to a stochastic averaging partial differential equation. Although these approximations can in some cases be crude, they can still give a first indication, via linearized stability analysis, of the interesting regimes for the stochastic model.Motivated by this linearized stability analysis we choose particular regimes where interacting nonlinear stochastic waves are responsible for phenomena, such as random switching, convective instability and metastability, all driven by stochastisity. Numerical kinetic Monte Carlo simulations of the coarse grained hybrid system are implemented to assist in producing solutions and understanding their behavior.

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“…Alperovich and Sopasakis [7] categorize the models describing traffic behaviour. According to the categories, deterministic type models (without random effects) have no descriptive capabilities especially to capture transient behaviour.…”

Section: Introductionmentioning

confidence: 99%