Second order macroscopic traffic flow models are able to reproduce the so-called capacity drop effect, i.e., the phenomenon that the outflow of a congested region is substantially lower than the maximum achievable flow. Within this work, we propose a first order model for a junction with ramp buffer that is solely modified at the intersection so that the capacity drop is captured. Theoretical investigations motivate the new choice of coupling conditions and illustrate the difference to purely first and second order models. The numerical example considering the optimal control of the onramp merging into a main road highlights that the combined model generates similar results as the second order model.

Keywords: traffic flow, numerical analysis, ramp metering control

Jennifer Weissen ^{1};
Oliver Kolb ^{1};
Simone Göttlich ^{1}

@article{SMAI-JCM_2022__8__349_0, author = {Jennifer Weissen and Oliver Kolb and Simone G\"ottlich}, title = {A combined first and second order model for a junction with ramp buffer}, journal = {The SMAI Journal of computational mathematics}, pages = {349--374}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {8}, year = {2022}, doi = {10.5802/smai-jcm.90}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.90/} }

TY - JOUR AU - Jennifer Weissen AU - Oliver Kolb AU - Simone Göttlich TI - A combined first and second order model for a junction with ramp buffer JO - The SMAI Journal of computational mathematics PY - 2022 SP - 349 EP - 374 VL - 8 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.90/ DO - 10.5802/smai-jcm.90 LA - en ID - SMAI-JCM_2022__8__349_0 ER -

%0 Journal Article %A Jennifer Weissen %A Oliver Kolb %A Simone Göttlich %T A combined first and second order model for a junction with ramp buffer %J The SMAI Journal of computational mathematics %D 2022 %P 349-374 %V 8 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.90/ %R 10.5802/smai-jcm.90 %G en %F SMAI-JCM_2022__8__349_0

Jennifer Weissen; Oliver Kolb; Simone Göttlich. A combined first and second order model for a junction with ramp buffer. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 349-374. doi : 10.5802/smai-jcm.90. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.90/

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