DERIVATION OF SECOND ORDER TRAFFIC FLOW MODELS WITH TIME DELAYS

被引：7

作者：

Burger, Michael ^{[1
]}

Goettlich, Simone ^{[2
]}

Jung, Thomas ^{[1
]}

机构：

[1] Fraunhofer Inst ITWM, D-67663 Kaiserslautern, Germany

[2] Univ Mannheim, Dept Math, D-68131 Mannheim, Germany

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2019年 / 14卷 / 02期

关键词：

Traffic flow models; hyperbolic delay partial differential equation; numerical simulations; microscopic to macroscopic; data fitting; SCHEMES;

D O I：

10.3934/nhm.2019011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Starting from microscopic follow-the-leader models, we develop hyperbolic delay partial differential equations to govern the density and velocity of vehicular traffic. The proposed models can be seen as an extension of the classical Aw-Rascle-Zhang model, where the reaction time of drivers appears as an additional term in the velocity equation. We propose numerical methods based on first principles and present a numerical study, where we focus on the impact of time delays in comparison to undelayed models.

引用

页码：265 / 288

页数：24

共 50 条

[1] Resurrection of "second order" models of traffic flow
Aw, A
Rascle, M
SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 60 (03) : 916 - 938
[2] Hybridization of a class of "second order" models of traffic flow
Leclercq, L.
Moutari, S.
SIMULATION MODELLING PRACTICE AND THEORY, 2007, 15 (08) : 918 - 934
[3] SECOND-ORDER TRAFFIC FLOW MODELS ON NETWORKS
Goettlich, Simone
Herty, Michael
Moutari, Salissou
Weissen, Jennifer
SIAM JOURNAL ON APPLIED MATHEMATICS, 2021, 81 (01) : 258 - 281
[4] DERIVATION OF DELAYS BASED ON IMPROVED MACROSCOPIC TRAFFIC MODELS
MICHALOPOULOS, PG
PISHARODY, VB
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 1981, 15 (05) : 299 - 317
[5] Lagrangian generic second order traffic flow models for node
Khelifi, Asma
Haj-Salem, Habib
Lebacque, Jean-Patrick
Nabli, Lotfi
JOURNAL OF TRAFFIC AND TRANSPORTATION ENGINEERING-ENGLISH EDITION, 2018, 5 (01) : 14 - 27
[6] Coupling conditions for a class of second-order models for traffic flow
Herty, M.
Rascle, M.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 38 (02) : 595 - 616
[7] Modelling road traffic accidents using macroscopic second-order models of traffic flow
Moutari, S.
Herty, M.
Klein, A.
Oeser, M.
Steinauer, B.
Schleper, V.
IMA JOURNAL OF APPLIED MATHEMATICS, 2013, 78 (05) : 1087 - 1108
[8] Lagrangian generic second order traffic flow models for nodeOA附视频
Asma Khelifi
Habib HajSalem
JeanPatrick Lebacque
Lotfi Nabli
Journal of Traffic and Transportation Engineering(English Edition), 2018, (01) : 14 - 27
[9] Intersections Modeling with a class of "second-order" models for vehicular traffic flow
Herty, M.
Moutari, S.
Rascle, M.
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS: PROCEEDINGS OF THE 11TH INTERNATIONAL CONFERENCE ON HYPERBOLIC PROBLEMS, 2008, : 755 - 763
[10] Steady-state analysis of second-order traffic models and application to traffic flow control
Sau, J.
Monteil, J.
Billot, R.
El Faouzi, N-E.
TRANSPORTMETRICA B-TRANSPORT DYNAMICS, 2019, 7 (01) : 1444 - 1466

← 1 2 3 4 5 →