A stochastic model of traffic flow: Gaussian approximation and estimation

Jabari, Saif Eddin; Liu, Henry

doi:10.1016/j.trb.2012.09.004

Cited by 78 publications

(52 citation statements)

References 35 publications

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“…Proof of (19). First, it can be easily demonstrated that V m (s, ω) is Lipschitz continuous (in s); let 0 ≤ K < ∞ denote its Lipschitz constant: K is the smallest constant such that for all m = 1, · · · , M and any s 1 ,…”

Section: Mean Dynamicsmentioning

confidence: 99%

“…In general, there still remain issues related to the physical accuracy of the sample paths of existing stochastic traffic models, particularly those developed for purposes of traffic state estimation (see [36,39] for recent reviews). The main culprit is the dominance of time-stochasticity (or noise) in the stochastic models, mostly developed in Eulerian coordinates [15,38,28,16,40,2,41,43,10,37,1,19], but also in Lagrangian coordinates [46,45,3]. This results in sample paths prone to aggressive oscillation in the time dimension.…”

Section: Introductionmentioning

confidence: 99%

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Traffic state estimation using stochastic Lagrangian dynamics

Zheng

Jabari

Liu

et al. 2018

Transportation Research Part B: Methodological

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This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty. It also results in smooth vehicle trajectories in a stochastic context, which is in agreement with real-world traffic dynamics and, thereby, overcoming issues with aggressive oscillation typically observed in sample paths of stochastic traffic flow models. We utilize ensemble filtering techniques for data assimilation (traffic state estimation), but derive the mean and covariance dynamics as the ensemble sizes go to infinity, thereby bypassing the need to sample from the parameter distributions while estimating the traffic states. As a result, the estimation algorithm is just a standard Kalman-Bucy algorithm, which renders the proposed approach amenable to real-time applications using recursive data. Data assimilation examples are performed and our results indicate good agreement with out-of-sample data.

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Section: Mean Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Traffic state estimation using stochastic Lagrangian dynamics

Zheng

Jabari

Liu

et al. 2018

Transportation Research Part B: Methodological

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“…Macroscopic traffic flow models based on hyperbolic conservation laws have been intensively investigated during the last decades, see [13,14] for an overview. The various research directions include theoretical and numerical investigations such for instance well-posedness [4], coupled models [6], network extensions [14,19], optimal control [16], or more recently, data-driven approaches [10] while stochastic traffic models have been less considered [20,30].…”

Section: Introductionmentioning

confidence: 99%

Modeling random traffic accidents by conservation laws

Göttlich

Knapp

2020

Mathematical Biosciences and Engineering

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We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with space-dependent flux function. Using a Lax-Friedrichs discretization, we show that the total variation is bounded in finite time and provide a theoretical framework to embed the stochastic process. Additionally, a solution algorithm is introduced to also investigate the model numerically.

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“…2 Many scholars have proposed a large number of traffic models to study the complex phenomena of transport system. [3][4][5][6][7][8][9][10][11][12][13][14][15] The cellular automaton model has been progressively used to model a great variety of dynamical systems in different application domains. The first typical cellular automaton model is the Nagel-Schreckenberg (NaSch) model presented by Nagel and Schreckenberg in 1992, on the basis of which a large number of improvements have been developed by the latecomers.…”

Section: Introductionmentioning

confidence: 99%

Dynamic simulation of energy consumption in mixed traffic flow considering highway toll station

et al. 2015

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An improved model of energy consumption including toll station is presented in this paper. Using the model, we study the influences of mixed ratio, the idling energy consumption of vehicle, vehicle peak velocity, dwell time and random deceleration probability on energy consumption of Electronic Toll Collection or Manual Toll Collection mixed traffic flow on single lane under periodic condition. Simulating results indicate that the above five parameters are all increasing functions of total energy consumption, in which the idling energy consumption represents the major amounts with the increase of mixed ratio and occupancy rate. Thus, the existence of toll station has significant effect on the energy consumption of mixed traffic flow.

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A stochastic model of traffic flow: Gaussian approximation and estimation

Cited by 78 publications

References 35 publications

Traffic state estimation using stochastic Lagrangian dynamics

Traffic state estimation using stochastic Lagrangian dynamics

Modeling random traffic accidents by conservation laws

Dynamic simulation of energy consumption in mixed traffic flow considering highway toll station

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