Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness

Han, Ke; Piccoli, Benedetto; Szeto, W.Y.

doi:10.1080/21680566.2015.1064793

Cited by 35 publications

(38 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the superscripts 'up' and 'dn' represent the upstream and downstream boundaries of the link, respectively. Han et al (2016b) derive explicit formulae for the link demand and supply based on a variational formulation known as the Lax-Hopf formula (Aubin et al, 2008;Claudel and Bayen, 2010), as follows:…”

Section: The Variational Representation Of Link Dynamicsmentioning

confidence: 99%

Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

2019

Self Cite

View full text Add to dashboard Cite

Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment, in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational theory of DUE with numerical implementation encapsulated in a MATLAB software package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixedpoint algorithm is employed to solve the DUE problems on several large-scale networks. We make openly available the MATLAB package, which can be used to solve DUE problems on user-defined networks, aiming to not only help DTA modelers with benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. Updates of the package and computational examples are available at https://github.com/DrKeHan/DTA.

show abstract

Section: The Variational Representation Of Link Dynamicsmentioning

confidence: 99%

Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…The constraints used are highly dependent on the underlying DNL model, such as point queue models (Ban et al, 2008(Ban et al, , 2012Long et al, 2015b;Ren et al, 2016), exit flow models (e.g., Nemhauser, 1978a, 1978b;Carey and Srinivasan, 1993;Lam and Huang, 1995;Wie and Tobin, 2002), and advanced exit flow models (e.g., Kuwahara and Akamatsu, 2001;Lo and Szeto, 2002;Yperman, 2007;Nie, 2011;Meng and Khoo, 2012;Long et al, 2013bLong et al, , 2015aLong et al, , 2016Zheng et al, 2015;Han et al, 2015aHan et al, , 2015b. The traffic flow models used in DTA problems should also have certain desirable properties, such as queue spillback (e.g., Daganzo, 1995;Lo and Szeto, 2002;Szeto and Lo, 2004;Ma et al, 2014;Chow et al, 2015;Stewart and Ge, 2015;Han et al, 2016;Jiang et al, 2016), first-in-first-out (FIFO) (e.g., Astarita, 1996;Huang and Lam, 2002;Long and Szeto, 2015), and non-vehicle holding (NVH) (e.g., Ziliaskopoulos, 2000;Shen et al, 2007;Nie, 2011;Zheng and Chiu, 2011;Zhu and Ukkusuri, 2013). Queue spillback occurs when the end of a queue spills backward in the network.…”

Section: Introductionmentioning

confidence: 99%

Link-based system optimum dynamic traffic assignment problems with environmental objectives

Long

Chen

Szeto

et al. 2018

Transportation Research Part D: Transport and Environment

Self Cite

View full text Add to dashboard Cite

a b s t r a c tMaintaining air-quality standards has been a priority for transportation planners and policy makers worldwide. However, most existing system optimum dynamic traffic assignment (SO-DTA) models do not accommodate environmental objectives. In this paper, we use the link transmission model (LTM) to develop SO-DTA models that minimize total system emissions (TSE) in single destination networks. We use step functions to approximate cumulative flow curves for individual links, and to decompose link inflow into sub-flows according to time intervals at which they leave the link. The decomposed link inflows are used to estimate link emissions. Dynamic network constraints, non-vehicle holding constraints and link inflow decomposition constraints are considered, and SO-DTA problems with environmental objectives are formulated as mixed integer linear programming (MILP) problems. Any average speed based emission functions can be used for our models. Finally, numerical examples are provided to demonstrate the performance of the proposed models. IntroductionDynamic traffic assignment (DTA) has long been recognized as a key component of network planning and transport policy evaluation, in addition to real-time traffic operation and management (Szeto and Lo, 2006). System-optimum DTA (SO-DTA), a special case of DTA based on a dynamic extension of Wardrop's (1952) second principle, is used to predict a time-dependent traffic state with optimal network performance, and to provide a benchmark for controlling and managing dynamic traffic networks. For example, SO-DTA models are used in road congestion pricing (e.on whether the modeling period is discretized into many time steps. Both categories of model have advantages and disadvantages. Continuous-time models can provide analytical insights (such as the closed form externality analysis), but cannot be efficiently solved due to their complex structure (Nie, 2011). Discrete-time models are usually formulated as mathematical programming problems, such as linear programming (LP) problems (e.g., Ziliaskopoulos, 2000) and mixed integer linear programming (MILP) problems http://dx.Please cite this article in press as: Long, J., et al. Link-based system optimum dynamic traffic assignment problems with environmental objectives. Transport. Res. Part D (2016), http://dx.doi.org/10.1016/j.trd.2016.06.003 (e.g., Lin and Wang, 2004;Pavlis and Recker, 2009), and can thus be more easily solved than continuous-time SO-DTA models. However, this category of models also compromise computational tractability in large-scale network applications due to the presence of numerous decision variables and constraints.There are three major types of objectives in existing SO-DTA models: minimizing total system travel time (TSTT) (e.minimizing both TSTT and TSE for a whole network in an integrated manner (e.g., Aziz and Ukkusuri, 2012;Ma et al., 2015). Most existing SO-DTA models accommodate only network mobility, and are used to meet the first of the above objectives: to minimize the TSTT spent by t...

show abstract

“…Any DNL must be consistent with the established path departure rates and link delay model, and is usually performed under the first-in-first-out (FIFO) rule. A few link flow models commonly employed for the DNL procedure include the link delay model (Friesz et al, 1993), the point-queue model (Han et al, 2013a,b), the cell transmission model (Daganzo, 1995), and the link transmission model (Yperman et al, 2005;Han et al, 2016b). Studies of the dynamic network loading models date back to the 1990's with a significant number of publications (Friesz et al, 2013;Lo and Szeto, 2002;Szeto, 2003;Szeto and Lo, 2004;Ukkusuri et al, 2012).…”

Section: Dynamic Network Loadingmentioning

confidence: 99%

Statistical metamodeling of dynamic network loading

Song

Han

Wang

2018

Transportation Research Part B: Methodological

Self Cite

View full text Add to dashboard Cite

Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses the dynamics of flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times. It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult problem, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, while possessing closed-form Jacobians. The implications of these desirable properties for DTA research and model applications are discussed in depth.

show abstract

Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness

Cited by 35 publications

References 58 publications

Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

Link-based system optimum dynamic traffic assignment problems with environmental objectives

Statistical metamodeling of dynamic network loading

Contact Info

Product

Resources

About