First-order Macroscopic Traffic Flow Models

Lebacque, Jean-Patrick; Khoshyaran, Megan M.

doi:10.1016/b978-008044680-6/50021-0

Cited by 82 publications

(49 citation statements)

References 8 publications

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“…A "merge model" takes as input the demands from each upstream link and the available supply from the downstream link, and produces the flow rates out of each upstream link into the downstream link. Several merge models have been proposed in the literature (Daganzo 1995;Lebacque 1996;Jin and Zhang 2003).…”

Section: A Symmetric Monotone Merge Modelmentioning

confidence: 99%

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A fresh look at symmetric traffic assignment and algorithm convergence

Patil¹

2023

Preprint

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Extensions of the static traffic assignment problem with link interactions were studied extensively in the past. Much of the network modeling community has since shifted to dynamic traffic assignment incorporating these interactions. We believe there are several reasons to re-examine static assignment with link interactions. First, if link interactions can be captured in a symmetric, monotone manner, equilibrium always exists and is unique, and provably-correct algorithms exist. We show that several of the most efficient algorithms for the separable traffic assignment problem can be readily applied with symmetric interactions. We discuss how the (asymmetric) Daganzo merge model can be approximated by symmetric linear cost functions. Second, we present computational evidence suggesting that convergence to equilibrium is faster when symmetric, monotone link interactions are present. This is true even when interactions are asymmetric, despite the lack of a provable convergence result. Lastly, we present convergence behavior analysis for commonly used network and link metrics. For these reasons, we think static assignment with link interactions deserves additional attention in research and practice.

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Section: A Symmetric Monotone Merge Modelmentioning

confidence: 99%

“…This is an approximation to the actual dynamic model, since if a queue forms, the demand will increase to the saturation flow u. Indeed, one critique of the Jin-Zhang model is that it is unstable with respect to this transition, a violation of the "invariance principle," cf Lebacque and Khoshyaran (2005)…”

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confidence: 99%

A fresh look at symmetric traffic assignment and algorithm convergence

Patil¹

2023

Preprint

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“…T (x, t) def = IT T (x, b; t) is instantaneous travel time from x to b estimated at time t, labeled backward in [7]. This formula is valid in non-interrupted traffic flow, particularly when velocity is always bound by a strictly positive lower speed.…”

Section: Instantaneous Travel Timementioning

confidence: 99%

“…The authors of [7] have give clear computational definition of the IT T in interrupted traffic. The cell exit speed defined as V c,i,max is the maximal exit speed of vehicles in the cell (c) and in the direction (i).…”

Section: Instantaneous Travel Timementioning

confidence: 99%

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Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

Sossoe

Lebacque²

2016

Advances in Intelligent Systems and Computing

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Abstract. This paper develops a graph-theoretic framework for large scale bi-dimensional transport networks and provides new insight into the dynamic traffic assignment. Reactive dynamic assignment are deployed to handle the traffic contingencies, traffic uncertainties and traffic congestion. New shortest paths problem in large networks is defined and routes cost calculation is provided. Since mathematical modelling of traffic flow is a keystone in the theory of traffic flow management, and then in the traffic assignment, it is convenient to elaborate a good model of assignment for large scale networks relying on an appropriate model of flow related to very large networks. That is the zone-based optimization of traffic flow model on networks developed by [8], completed and improved by [9].

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Data‐driven models for traffic flow at junctions

Herty,

Kolbe

2024

Math Methods in App Sciences

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The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws, there exist nowadays many ad‐hoc models describing this behavior. Based on real‐world car trajectory data we propose a new class of data‐driven models with the requirements of being consistent to networked hyperbolic traffic flow models. To this end, the new models combine artificial neural networks with a parametrization of the solution space to the half‐Riemann problem at the junction. A method for deriving density and flux corresponding to the traffic close to the junction for data‐driven models is presented. The model parameters are fitted to obtain suitable boundary conditions for macroscopic first‐ and second‐order traffic flow models. The prediction of various models are compared considering also existing coupling rules at the junction. Numerical results imposing the data‐fitted coupling models on a traffic network are presented exhibiting accurate predictions of the new models.

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First-order Macroscopic Traffic Flow Models

Cited by 82 publications

References 8 publications

A fresh look at symmetric traffic assignment and algorithm convergence

A fresh look at symmetric traffic assignment and algorithm convergence

Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

Data‐driven models for traffic flow at junctions

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