Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

Sossoe, Kwami; Lebacque, Jean-Patrick

doi:10.1007/978-3-319-48944-5_17

Cited by 10 publications

(12 citation statements)

References 10 publications

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“…Sossoe and Lebacque [45] develop an RDUE model for bi-directional traffic flow based on the traffic flow model proposed in Saumtally et al [43] and Sossoe et al [46]. The urban network is decomposed into zones, where each zone is meshed into quadrangular cells, as shown in Fig.…”

Section: Discrete-space Modelsmentioning

confidence: 99%

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Aghamohammadi

Laval

2020

Transportation Research Part B: Methodological

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Traditional DTA models of large cities suffer from prohibitive computation times and calibration/validation can become major challenges faced by practitioners. The empirical evidence in 2008 in support of the existence of a Macroscopic Fundamental Diagram (MFD) on urban networks led to the formulation of discrete-space models, where the city is divided into a collection of reservoirs. Prior to 2008, a large body of DTA models based on pedestrian flow models had been formulated in continuum space as 2-dimensional conservation laws where the speed-density relationship can now be interpreted as the MFD. Perhaps surprisingly, we found that this continuum-space literature has been mostly unaware of MFD theory, and no attempts exist to verify the assumptions of MFD theory. This has the potential to create significant inconsistencies, and research is needed to analyze their extent and ways to resolve them. We also find that further research is needed to (i) incorporate departure time choice, (ii) improve existing numerical methods, possibly extending recent advances on the one-dimensional kinematic wave (LWR) model, (iii) study the properties of system optimum solutions, (iv) examine the real-time applicability of current continuum-space models compared to traditional DTA methods, and (v) formulate anisotropic models for the interaction of intersecting flows.

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Section: Discrete-space Modelsmentioning

confidence: 99%

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Aghamohammadi

Laval

2020

Transportation Research Part B: Methodological

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“…The splitting method, or method of fractional steps, was considered first by [Godunov, 1959] and then properly introduced by [Strang, 1968]. The principle of dimensional splitting is to compute separately the different term of the equation for each discrete interval of time.…”

Section: Model Discretizationmentioning

confidence: 99%

“…The direction of the drift vector is fixed in some area and is determined by the shape of the network. In [Saumtally, 2012] and [Sossoe and Lebacque, 2016], the authors investigate the representation of intersection and how it could be interpreted in a 2D model. Following this idea, they take inspiration of junction models in one dimension like [Lebacque and Khoshyaran, 2004] and build extensions to 2D models.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional macroscopic model for large scale traffic networks

Mollier

Monache

Canudas‐de‐Wit

et al. 2019

Transportation Research Part B: Methodological

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In this article we introduce a new traffic flow model for a dense urban area. We consider a two-dimensional conservation law in which the velocity magnitude is given by the fundamental diagram and the velocity direction is constructed following the network geometry. We validate the model using synthetic data from Aimsun and propose a reconstruction technique to recover the 2D density from the data of individual vehicles. A comparison between the model and the data is shown.

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“…While the relevant literature contains no efforts to achieve a consistent formulation both in discrete and continuum space, the Eulerian components of our solution method are closely related to the framework proposed in Sossoe and Lebacque (2017), Hanseler et al (2014Hanseler et al ( , 2017. Sossoe and Lebacque (2017) proposes a multi-reservoir reactive DTA model where the flows between reservoirs are obtained with a network junction model (see e.g., Jin, 2012, Jin andZhang, 2003, andreferences therein). This model considers only two possible paths in each cell for the route choice based on a logit model, where the cost of each path is assumed to be the instantaneous travel time.…”

Section: Introductionmentioning

confidence: 99%

A Continuum Model for Cities Based on the Macroscopic Fundamental Diagram: a Semi-Lagrangian Solution Method

Aghamohammadi

Laval

2019

Transportation Research Procedia

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This paper presents a formulation of the reactive dynamic user equilibrium problem in continuum form using a network-level Macroscopic Fundamental Diagram (MFD). Compared to existing continuum models for cities -all based in Hughes' pedestrian model in 2002 -the proposed formulation (i) is consistent with reservoir-type models of the MFD literature, shedding some light into the connection between these two modeling approaches, (ii) can have destinations continuously distributed on the region, and (iii) can incorporate multi-commodity flows without additional numerical error. The proposed multi-reservoir numerical solution method treats the multi-commodity component of the model in Lagrangian coordinates, which is the natural representation to propagate origin-destination information (and any vehicle-specific characteristic) through the traffic stream. Fluxes between reservoir boundaries are computed in the Eulerian representation, and are used to calculate the speed of vehicles crossing the boundary. Simple examples are included that show the convergence of the model and its agreements with the available analytical solutions. We find that (i) when origins and destinations are uniformly distributed in a region, the distribution of the travel times can be approximated analytically, (ii) the magnitude of the detours from the optimal free-flow route due to congestion increase linearly with the inflow and decreases with the square of the speed, and (iii) the total delay of vehicles in the network converges to the analytical approximation when the size of reservoirs tends to zero.

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Reactive Dynamic Assignment for a Bi-dimensional Traffic Flow Model

Cited by 10 publications

References 10 publications

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models

Two-dimensional macroscopic model for large scale traffic networks

A Continuum Model for Cities Based on the Macroscopic Fundamental Diagram: a Semi-Lagrangian Solution Method

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