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

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Title: Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness
Authors: Han, K
Piccoli, B
Szeto, WY
Item Type: Journal Article
Abstract: We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traf- fic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton-Jacobi equation and junction models defined via the notions of demand and supply. We show that the proposed LKWM can be formulated as a system of differential algebraic equations (DAEs), which captures shock formation and propagation, as well as queue spillback. The DAE system, as we show in this paper, is the continuous-time counterpart of the link transmission model. In addition, we present a solution existence theory for the continuous-time network model and investigate continuous dependence of the solution on the initial data, a property known as well-posedness. We test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.
Issue Date: 18-Aug-2015
Date of Acceptance: 18-Jun-2015
URI: http://hdl.handle.net/10044/1/62789
DOI: https://dx.doi.org/10.1080/21680566.2015.1064793
ISSN: 2168-0566
Publisher: Taylor & Francis Online
Start Page: 187
End Page: 222
Journal / Book Title: Transportmetrica B-Transport Dynamics
Volume: 4
Issue: 3
Copyright Statement: © 2015 Hong Kong Society for Transportation Studies Limited. This is an Accepted Manuscript of an article published by Taylor & Francis in Transportmetrica B: Transport Dynamics on 5 Oct 2015, available online: https://www.tandfonline.com/doi/full/10.1080/21680566.2015.1064793
Keywords: Science & Technology
Technology
Transportation
Transportation Science & Technology
kinematic wave model
continuous-time traffic flow model
link transmission model
differential algebraic equations
well-posedness
DYNAMIC TRAFFIC ASSIGNMENT
CELL-TRANSMISSION MODEL
DIFFERENTIAL-EQUATION FORMULATION
VICKREYS BOTTLENECK MODEL
USER EQUILIBRIUM
BOUNDARY-CONDITIONS
SYSTEM OPTIMUM
FLOW
NETWORK
HIGHWAY
math.AP
35L65, 35C05, 35B30
Publication Status: Published
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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