Dynamic system‐optimal traffic assignment for a city using the continuum modeling approach

Tao, Yizhou; Jiang, Yan; Du, Jian; Wong, S. C.; Zhang, P.; Xia, Yun‐Jie; Choi, Keechoo

doi:10.1002/atr.1227

Cited by 9 publications

(10 citation statements)

References 42 publications

(43 reference statements)

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“…Only two papers, Tao et al [47] in continuum space and Yildirimoglu et al [54] in discrete space, has tried to establish DSO conditions, but the proposed solution methods are numerical. Since it is hard to extract insights from numerical solution methods, future research should focus on analytical Decomposes the urban network into zones, which are meshed into cells, and computes the turning proportion in each cell using logit solutions, possibly of simplified systems.…”

Section: System Optimummentioning

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: System Optimummentioning

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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“…There are two DUO assignment patterns (Tong and Wong 2000): the reactive dynamic user-optimal (RDUO) assignment, in which a user chooses a route that minimizes his/her instantaneous travel time/cost based on instantaneous travel time/cost information gained through broadcasting (Wie et al 1990, Lam and Huang 1995, Boyce et al 1995, Li et al 2000, Huang et al 2009, Jiang et al 2009, Friesz et al 2010, and the predictive dynamic user-optimal (PDUO) assignment, in which an individual chooses a route that minimizes his/her actual travel time/cost based on predictive travel time/cost information gained through experience (Tong and Wong 2000, Hoogendoorn and Bovy 2004, Du et al 2013. In DSO models, each user is assigned the route that minimizes the total travel time/cost of the system (Ghali and Smith 1995, Ziliaskopoulos 2000, Clarka et al 2009, Carey and Watling 2012, Tao et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City

Jiang

Wong²,

Zhang

et al. 2017

Transportation Science

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This paper presents the development of a macroscopic dynamic traffic assignment (DTA) model for continuum transportation systems with elastic demand. A reactive dynamic user equilibrium model is extended to simulate network equilibrium problems for an urban area with multiple central business districts (CBDs). Each copy of traffic flow makes route choice decisions in a reactive manner to minimize the total travel cost from origin to destination, based on instantaneous traffic information from a radio broadcasting service or route guidance system. The elastic demand function for each copy of flow is associated with its total instantaneous travel cost. The model is solved by a cell-centered finite volume method for conservation law equations and a fast sweeping method for Eikonal-type equations on unstructured grids. Numerical experiments for an urban traffic network with two CBDs are presented to verify the rationality of the model and the validity of the numerical method. The numerical results indicate that the model captures some macroscopic characteristics of two copies of flow interacting in time-varying urban transportation systems, e.g., the spatial distributions of the flow density and flux and the path choice behavior in response to elastic demand, and can describe traffic equilibrium phenomena, such as self-organization and traffic congestion build-up and dissipation.

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“…This extension added realism because congestion externalities and demand elasticity exist in practice. More recently, the continuum model has also been applied to solve multiclass equilibrium problems (Ho et al, 2003(Ho et al, , 2004(Ho et al, , 2006, cordon-based congestion-pricing problems (Ho et al, , 2013, dynamic paradigm problems (Jiang et al, 2011;Du et al, 2013;Tao et al, 2014), environmental problems (Yin et al, 2012(Yin et al, , 2013, airport problems (Loo et al, 2005), and housing problems Wong, 2005, 2007).…”

Section: Introductionmentioning

confidence: 99%

A multi-commodity discrete/continuum model for a traffic equilibrium system

Wong

Sun

2016

Transportmetrica A: Transport Science

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We consider a city with several highly compact central business districts (CBDs). The commuters' origins are continuously dispersed. The travel demand to each CBD, which is considered to be a distinct commodity of traffic movements, is dependent on the total travel cost to that CBD. The transportation system is divided into two layers: major freeways and a dense network of surface streets. Whereas the major freeway network is modeled according to the conventional discrete network approach, the dense surface streets are approximated as a continuum. Travelers to each CBD can either travel within the continuum (surface streets) and then transfer to the discrete network (freeways) at an interchange (ramp) before moving to the CBD on the discrete network, or they can travel directly to the CBD within the continuum. Specific travel cost-flow relationships for the two layers of transportation facilities are considered. We develop a traffic equilibrium model for this discrete/continuum transportation system in which, for each origin-destination pair, no traveler can reduce his or her individual travel cost by unilaterally changing routes. The problem is formulated as a simultaneous optimization program with two sub-problems. One sub-problem is a traffic 2 assignment problem from the interchanges to the CBD in the discrete network, and the other is a traffic assignment problem within a continuum system with multiple centers (i.e., the interchange points and the CBDs). A Newtonian algorithm based on sensitivity analyses of the two sub-problems is proposed to solve the resultant simultaneous optimization program. A numerical example is given to demonstrate the effectiveness of the proposed method.

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Dynamic system‐optimal traffic assignment for a city using the continuum modeling approach

Cited by 9 publications

References 42 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

Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City

A multi-commodity discrete/continuum model for a traffic equilibrium system

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