Stochastic Modeling and Simulation of Traffic Flow: Asymmetric Single Exclusion Process with Arrhenius look-ahead dynamics

Sopasakis, Alexandros; Katsoulakis, Markos A.

doi:10.1137/040617790

Cited by 110 publications

(117 citation statements)

References 48 publications

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“…We propose here a different type of potential which due to its one-sided anisotropy attributes advective affects in the stochastic dynamics. This potential originated from modeling applications in traffic flow [21,22] where look-ahead mechansisms have direct connection to the physics of the application.…”

Section: Asep With Look-ahead Potentialmentioning

confidence: 99%

“…The dynamics in this section allow for spin-exchange interactions using a non-symmetric, lookahead, potential. An equivalent look-ahead stochastic mechanism for microscopic spin-exchange dynamics related to traffic flow has been proposed in [21] and [22]. The corresponding coarse grained mechanism is now introduced below.…”

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

confidence: 99%

“…Here l = k + 1 due to the look-ahead potential. Performing simple clean-up operations it is easy to see that (22) …”

Section: Spin-exchange 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%

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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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Section: Asep With Look-ahead Potentialmentioning

confidence: 99%

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

confidence: 99%

“…Here l = k + 1 due to the look-ahead potential. Performing simple clean-up operations it is easy to see that (22) …”

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hybrid deterministic stochastic systems with microscopic look-ahead dynamics

Katsoulakis¹,

Majda²,

Sopasakis

2010

Communications in Mathematical Sciences

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“…Traffic models may roughly be classified as "microscopic" (keeping track of each car in a deterministic way, see for example [6,7,12,13,22,24]), of stochastic type (there is much variation here; see [2,28,29]), or variations including both features, such as cellular automata [12,26,27]. The model which leads to Equation (1.1) is of macroscopic type, and earlier versions of macroscopic models and their analysis may be found in [1,8,9,10,11,17,18,23,30].…”

mentioning

confidence: 99%

On a Functional-Differential Equation Arising from a Traffic Flow Model

Illner¹,

McGregor²

2012

SIAM J. Appl. Math.

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An Overview of Non-local Traffic Flow Models

Chiarello

2020

Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models

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Stochastic Modeling and Simulation of Traffic Flow: Asymmetric Single Exclusion Process with Arrhenius look-ahead dynamics

Cited by 110 publications

References 48 publications

Hybrid deterministic stochastic systems with microscopic look-ahead dynamics

Hybrid deterministic stochastic systems with microscopic look-ahead dynamics

On a Functional-Differential Equation Arising from a Traffic Flow Model

An Overview of Non-local Traffic Flow Models

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