A Riemann solver for a system of hyperbolic conservation laws at a general road junction

Jin, Wen-Long

doi:10.48550/arxiv.1204.6727

Cited by 3 publications

(4 citation statements)

References 41 publications

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“…}, x q = 50 m}. The penalty variable associated with each congestion sampling point subjects to the constraints defined in equation (23).…”

Section: Decision Variablesmentioning

confidence: 99%

“…It should be noted that p k relates to q b1 (j) in (23) and minimizing p k implicitly minimizes q b1 (j). The selection of w 2 (j) using conditions (25) should subtract the implicit weight on q b1 (j) induced by penalizing the congested states.…”

Section: Decision Variablesmentioning

confidence: 99%

“…It is well known that conservation of vehicles across the junction, i.e., s∈Sv q s (t, b s ) = r∈Rv q r (t, a r ), is insufficient to uniquely define the flows at the junction. To address this issue, a variety of junction models [10,15,18,19,20,22,23,24,27] have been proposed to define a unique internal boundary flow solution using additional rules governing the distribution or priority of the flows. Compared to the merge junction, for which relatively few models have been proposed, the diverge junctions have led to a number of modeling efforts.…”

mentioning

confidence: 99%

“…Simulation configuration. This subsection briefly describes the experiment setup and the next subsection constructs an optimal on-ramp metering controller using the convex program (19) and the additional constraints (23).…”

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confidence: 99%

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A Convex Formulation of Traffic Dynamics on Transportation Networks

Claudel

Piccoli³

et al. 2017

SIAM J. Appl. Math.

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This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation (PDE), which is an equivalent form of the Lighthill-Whitham-Richards PDE. The main contribution of this article is the construction of a single convex optimization program which computes the traffic flow at a junction over a finite time horizon and decouples the PDEs on connecting links. Compared to discretization schemes which require the computation of all traffic states on a time-space grid, the proposed convex optimization approach computes the boundary flows at the junction using only the initial condition on links and the boundary conditions of the network. The computed boundary flows at the junction specify the boundary condition for the HJ PDE on connecting links, which then can be separately solved using an existing semi-explicit scheme for single link HJ PDE. As demonstrated in a numerical example of ramp metering control, the proposed convex optimization approach also provides a natural framework for optimal traffic control applications.

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“…}, x q = 50 m}. The penalty variable associated with each congestion sampling point subjects to the constraints defined in equation (23).…”

Section: Decision Variablesmentioning

confidence: 99%

Section: Decision Variablesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A Convex Formulation of Traffic Dynamics on Transportation Networks

Claudel

Piccoli³

et al. 2017

SIAM J. Appl. Math.

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A link queue model of network traffic flow

Jin

2012

Preprint

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Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a deterministic queueing model of network traffic flow, in which traffic on each link is considered as a queue.In the link queue model, the demand and supply of a queue are defined based on the link's fundamental diagram, and its in-and out-fluxes are computed from junction flux functions corresponding to macroscopic merging and diverging rules. We demonstrate that the model is well defined and can be considered as a continuous approximation to the kinematic wave model on a road network. From careful analytical and numerical studies, we conclude that the model is physically meaningful, computationally efficient, always stable, and mathematically tractable for network traffic flow. As an addition to the multiscale modeling framework of network traffic flow, the model strikes a balance between mathematical tractability and physical realism and can be used for analyzing traffic dynamics, developing traffic operation strategies, and studying drivers' route choice and other behaviors in large-scale road networks.

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A convex formulation of traffic dynamics on transportation networks

Claudel

Piccoli³

et al. 2017

Preprint

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A Riemann solver for a system of hyperbolic conservation laws at a general road junction

Cited by 3 publications

References 41 publications

A Convex Formulation of Traffic Dynamics on Transportation Networks

A Convex Formulation of Traffic Dynamics on Transportation Networks

A link queue model of network traffic flow

A convex formulation of traffic dynamics on transportation networks

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