First Order Macroscopic Traffic Flow Models for Networks in the Context of Dynamic Assignment

Lebacque, Jean-Patrick; Khoshyaran, Megan M.

doi:10.1007/0-306-48220-7_8

Cited by 53 publications

(34 citation statements)

References 15 publications

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“…Indeed, despite of its intuitive appeal, the IT principle has never been systematically investigated as a method to compute traffic flow in a general intersection. 1 Lebacque and Koshyaran (2002) relate their lane assignment model to the multi-lane model solved by the IT principle, but they turn to different techniques when it comes to node modeling. Laval and Daganzo (2006) deploy a variant of the IT principle when analyzing the effect of lane changing in traffic streams.…”

Section: Incremental Node Modelmentioning

confidence: 99%

Operational macroscopic modeling of complex urban road intersections

Flötteröd

Rohde

2011

Transportation Research Part B: Methodological

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This article describes a new approach to the macroscopic first order modeling and simulation of traffic flow in complex urban road intersections. The framework is theoretically sound, operational, and comprises a large body of models presented so far in the literature.Working within the generic node model class of Tampere et al. (forthcoming), the approach is developed in two steps. First, building on the incremental transfer principle of Daganzo et al. (1997), an incremental node model for general road intersections is developed. A limitation of this model (as of the original incremental transfer principle) is that it does not capture situations where the increase of one flow decreases another flow, e.g., due to conflicts. In a second step, the new model is therefore supplemented with the capability to describe such situations. A fixed-point formulation of the enhanced model is given, solution existence and uniqueness are investigated, and two solution algorithms are developed. The feasibility and realism of the new approach is demonstrated through both a synthetic and a real case study.

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Section: Incremental Node Modelmentioning

confidence: 99%

Operational macroscopic modeling of complex urban road intersections

Flötteröd

Rohde

2011

Transportation Research Part B: Methodological

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“…Traffic networks, air traffic control, data networks, production chains and supply chains can all be interpreted as multicommodity networks, where the aim is usually to let the highest possible volume of particles of the different classes through the network. Models for multicommodity flow networks based on PDEs and the celebrated LWR model have been studied [1], [2], but solutions are usually difficult to obtain even in simple settings. In this paper, we propose and analyze a dynamical ODE-based model for networks with heterogeneous routing.…”

Section: Introductionmentioning

confidence: 99%

On resilience of multicommodity dynamical flow networks

Nilsson

Como

Lovisari³

2014

53rd IEEE Conference on Decision and Control

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Abstract-Dynamical flow networks with heterogeneous routing are analyzed in terms of stability and resilience to perturbations. Particles flow through the network and, at each junction, decide which downstream link to take on the basis of the local state of the network. Differently from singlecommodity scenarios, particles belong to different classes, or commodities, with different origins and destinations, each reacting differently to the observed state of the network. As such, the commodities compete for the shared resource that is the flow capacity of each link of the network. This implies that, in contrast to the single-commodity case, the resulting dynamical system is not monotone, hence harder to analyze. It is shown that, in an acyclic network, when a feasible globally asymptotically stable aggregate equilibrium exists, then each commodity also admits a unique equilibrium. In addition, a sufficient condition for stability is provided. Finally, it is shown that, differently from the single-commodity case, when this condition is not satisfied, the possible unique equilibrium may be arbitrarily fragile to perturbations of the network.

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“…We restrict from now on to junctions with three roads and use the so called NON-FIFO model [26,23] for three roads. The coupling conditions onρ i are stated first as conditions on the fluxes γ i on road e i .…”

Section: The Traffic Modelmentioning

confidence: 99%

“…The classical macroscopic traffic flow model based on scalar continuity equations is described in [37]. Traffic models on networks for this equation can be found among many others in [25,26,9,23,18]. In [27,28,15,10] pedestrian traffic modeling with scalar conservation laws based on the solution of the eikonal equation have been presented and investigated, see again [5] for further developments and historical comments.…”

Section: Introductionmentioning

confidence: 99%

“…We restrict ourselves to coupling scalar macroscopic models. Traffic flow is considered on a network using a Lighthill-Whitham equation and coupling conditions at the nodes of the network as discussed in [26,9]. Pedestrian flow is described using the model in [27,28], where a nonlocal term including a global knowledge of the physical setting described by the eikonal equation is included into the continuity equation.…”

Section: Introductionmentioning

confidence: 99%

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Coupling Traffic Flow Networks to Pedestrian Motion

Borsche

Klar

Kühn

et al. 2013

Math. Models Methods Appl. Sci.

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In the present paper scalar macroscopic models for traffic and pedestrian flows are coupled and the resulting system is investigated numerically. For the traffic flow the classical Lighthill-Whitham model on a network of roads and for the pedestrian flow the Hughes model are used. These models are coupled via terms in the fundamental diagrams modeling an influence of the traffic and pedestrian flow on the maximal velocities of the corresponding models. Several physical situations, where pedestrians and cars interact, are investigated.

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First Order Macroscopic Traffic Flow Models for Networks in the Context of Dynamic Assignment

Cited by 53 publications

References 15 publications

Operational macroscopic modeling of complex urban road intersections

Operational macroscopic modeling of complex urban road intersections

On resilience of multicommodity dynamical flow networks

Coupling Traffic Flow Networks to Pedestrian Motion

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