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

Hauck, Cory D.; Sun, Yu; Timofeyev, Ilya

doi:10.1142/s0219493713500226

Cited by 18 publications

(13 citation statements)

References 20 publications

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“…For instance, the floor-field velocity can depend on the look-ahead potential. However, if this dependence is strong, then correlations in the system may become considerable [24], thereby making the derivation of macroscopic PDEs more challenging. Nevertheless, weak dependence of the floor-field velocity on the look-ahead potential can be incorporated into the model with relative ease.…”

Section: Discussionmentioning

confidence: 99%

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Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Ott

Timofeyev

Weber

2020

Physica D: Nonlinear Phenomena

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We study the evolution of interacting groups of agents in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules. From this microscopic model we derive an analytically-tractable system of conservation laws that governs the evolution of the macroscopic densities. Numerical simulations show good agreement between the system of conservation laws and the microscopic model, though the latter is slightly more diffusive. We conclude by deriving second-order corrections to the system of conservation laws.

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Section: Discussionmentioning

confidence: 99%

“…In order to derive dynamical equations for the densities, we proceed in a manner similar to the approach outlined in [14,24,40]. In particular, the process σ t = {σ A t , σ B t } constitutes a continuoustime Markov chain, so we consider the generator L of the stochastic process σ t given by…”

Section: Mesoscopic Deterministic Modelmentioning

confidence: 99%

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Ott

Timofeyev

Weber

2020

Physica D: Nonlinear Phenomena

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“…The coarse-grained macroscopic dynamics corresponding to the two CA models above are LWR model (1) and SK model (2), respectively. The formal derivation for the latter case can be found, for instance, in [16,46].…”

Section: Cellular Automata Models With Look-ahead Rulesmentioning

confidence: 99%

“…Followed from [16,46], we define σ(τ ) = {σ i (τ )} M i=1 be a continuous-in-time stochastic process with a generator…”

Section: 1mentioning

confidence: 99%

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On a class of new nonlocal traffic flow models with look-ahead rules

Sun

Tan

2020

Preprint

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This paper presents a new class of one-dimensional (1D) traffic models with look-ahead rules that take into account of two effects: nonlocal slow-down effect and rightskewed non-concave asymmetry in the fundamental diagram. The proposed 1D cellular automata models with the Arrhenius type look-ahead interactions implement stochastic rules for cars' movement following the configuration of the traffic ahead of each car. In particular, we take two different look-ahead rules: one is based on the distance from the car under consideration to the car in front of it; the other one depends on the car density ahead. Both rules feature a novel idea of multiple moves, which plays a key role in recovering the nonconcave flux in the macroscopic dynamics. Through a semi-discrete mesoscopic stochastic process, we derive the coarse-grained macroscopic dynamics of the CA model. We also design a numerical scheme to simulate the proposed CA models with an efficient list-based kinetic Monte Carlo (KMC) algorithm. Our results show that the fluxes of the KMC simulations agree with the coarse-grained macroscopic averaged fluxes for the different look-ahead rules under various parameter settings.

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Renormalization Group Approach to Cellular Automata-Based Multi-scale Modeling of Traffic Flow

Yang

Haeri

Jerath

2021

Unifying Themes in Complex Systems X

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Traffic flow modeling is typically performed at one of three different scales (microscopic, mesoscopic, or macroscopic), each with distinct modeling approaches. Recent works that attempt to merge models at different scales have yielded some success, but there still exists a need for a single modeling framework that can seamlessly model traffic flow across several spatiotemporal scales. The presented work utilizes a renormalization group (RG) theoretic approach, building upon our prior research on statistical mechanics-inspired traffic flow modeling. Specifically, we use an Ising model-inspired cellular automata model to represent traffic flow dynamics. RG transformations are applied to this model to obtain coarse-grained parameters (interaction and field coefficients) to simulate traffic at coarser spatiotemporal scales and different vehicular densities. We measure the accuracy of the coarse-grained traffic flow simulation using a pixel-based image correlation metric and find good correlation between the dynamics at different scales. Importantly, emergent traffic dynamics such as backward moving congestion waves are retained at coarser scales with this approach. The presented work has the potential to spur the development of a unified traffic flow modeling framework for transportation analysis across varied spatiotemporal scales, while retaining an analytical relationship between the model parameters at these scales.

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

Cited by 18 publications

References 20 publications

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

On a class of new nonlocal traffic flow models with look-ahead rules

Renormalization Group Approach to Cellular Automata-Based Multi-scale Modeling of Traffic Flow

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