{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:02:35Z","timestamp":1760101355826},"reference-count":22,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\mathbf{L^{\\infty}} $\\end{document}<\/tex-math><\/inline-formula> and <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\mathbf{BV} $\\end{document}<\/tex-math><\/inline-formula> estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.<\/p><\/jats:p>","DOI":"10.3934\/nhm.2022003","type":"journal-article","created":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T09:33:36Z","timestamp":1645522416000},"page":"203","source":"Crossref","is-referenced-by-count":4,"title":["Nonlocal reaction traffic flow model with on-off ramps"],"prefix":"10.3934","volume":"17","author":[{"given":"Felisia Angela","family":"Chiarello","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences \"G. L. Lagrange\", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy"}]},{"given":"Harold Deivi","family":"Contreras","sequence":"additional","affiliation":[{"name":"GIMNAP-Departamento de Matem\u00e1ticas, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n, Chile"}]},{"given":"Luis Miguel","family":"Villada","sequence":"additional","affiliation":[{"name":"GIMNAP-Departamento de Matem\u00e1ticas, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n, Chile, and CI2<\/sup>MA, Universidad de Concepci\u00f3n, Casilla 160-C, Concepci\u00f3n, Chile"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2022003-1","doi-asserted-by":"publisher","unstructured":"P. Amorim, R. M. Colombo, A. Teixeira.On the numerical integration of scalar nonlocal conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis<\/i>, 49<\/b> (2015), 19-37.","DOI":"10.1051\/m2an\/2014023"},{"key":"key-10.3934\/nhm.2022003-2","unstructured":"A. Bayen, A. Keimer, L. Pflug and T. Veeravalli, Modeling multi-lane traffic with moving obstacles by nonlocal balance laws, Preprint, (2020)."},{"key":"key-10.3934\/nhm.2022003-3","doi-asserted-by":"publisher","unstructured":"S. Blandin, P. Goatin.Well-posedness of a conservation law with non-local flux arising in traffic flow modeling, Numerische Mathematik<\/i>, 132<\/b> (2016), 217-241.","DOI":"10.1007\/s00211-015-0717-6"},{"key":"key-10.3934\/nhm.2022003-4","doi-asserted-by":"publisher","unstructured":"F. A. Chiarello, J. Friedrich, P. Goatin, S. G\u00f6ttlich, O. Kolb.A non-local traffic flow model for 1-to-1 junctions, European Journal of Applied Mathematics<\/i>, 31<\/b> (2020), 1029-1049.","DOI":"10.1017\/S095679251900038X"},{"key":"key-10.3934\/nhm.2022003-5","doi-asserted-by":"publisher","unstructured":"F. A. Chiarello, P. Goatin.Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel, ESAIM: Mathematical Modelling and Numerical Analysis<\/i>, 52<\/b> (2018), 163-180.","DOI":"10.1051\/m2an\/2017066"},{"key":"key-10.3934\/nhm.2022003-6","doi-asserted-by":"publisher","unstructured":"F. A. Chiarello, P. Goatin.Non-local multi-class traffic flow models, Networks & Heterogeneous Media<\/i>, 14<\/b> (2019), 371-380.","DOI":"10.3934\/nhm.2019015"},{"key":"key-10.3934\/nhm.2022003-7","doi-asserted-by":"publisher","unstructured":"M. L. Delle Monache, J. Reilly, S. Samaranayake, W. Krichene, P. Goatin, A. M. Bayen.A PDE-ODE model for a junction with ramp buffer, SIAM Journal on Applied Mathematics<\/i>, 74<\/b> (2014), 22-39.","DOI":"10.1137\/130908993"},{"key":"key-10.3934\/nhm.2022003-8","doi-asserted-by":"publisher","unstructured":"J. Friedrich, S. G\u00f6ttlich and E. Rossi, Nonlocal approaches for multilane traffic models, Commun. Math. Sci<\/i>., 19<\/b> (2021), 2291\u20132317, arXiv preprint, arXiv: 2012.05794, (2020).","DOI":"10.4310\/CMS.2021.v19.n8.a10"},{"key":"key-10.3934\/nhm.2022003-9","doi-asserted-by":"publisher","unstructured":"J. Friedrich, O. Kolb, S. G\u00f6ttlich.A godunov type scheme for a class of lwr traffic flow models with non-local flux, Networks & Heterogeneous Media<\/i>, 13<\/b> (2018), 531-547.","DOI":"10.3934\/nhm.2018024"},{"key":"key-10.3934\/nhm.2022003-10","doi-asserted-by":"publisher","unstructured":"P. Goatin, E. Rossi.A multilane macroscopic traffic flow model for simple networks, SIAM Journal on Applied Mathematics<\/i>, 79<\/b> (2019), 1967-1989.","DOI":"10.1137\/19M1254386"},{"key":"key-10.3934\/nhm.2022003-11","doi-asserted-by":"publisher","unstructured":"P. Goatin, S. Scialanga.Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity, Netw. Heterog. Media<\/i>, 11<\/b> (2016), 107-121.","DOI":"10.3934\/nhm.2016.11.107"},{"key":"key-10.3934\/nhm.2022003-12","doi-asserted-by":"publisher","unstructured":"Y. Han, M. Ramezani, A. Hegyi, Y. Yuan, S. Hoogendoorn.Hierarchical ramp metering in freeways: An aggregated modeling and control approach, Transportation Research Part C: Emerging Technologies<\/i>, 110<\/b> (2020), 1-19.","DOI":"10.1016\/j.trc.2019.09.023"},{"key":"key-10.3934\/nhm.2022003-13","doi-asserted-by":"publisher","unstructured":"D. Helbing, A. Hennecke, V. Shvetsov, M. Treiber.Master: Macroscopic traffic simulation based on a gas-kinetic, non-local traffic model, Transportation Research Part B: Methodological<\/i>, 35<\/b> (2001), 183-211.","DOI":"10.1016\/S0191-2615(99)00047-8"},{"key":"key-10.3934\/nhm.2022003-14","doi-asserted-by":"publisher","unstructured":"H. Holden, N. H. Risebro.Models for dense multilane vehicular traffic, SIAM Journal on Mathematical Analysis<\/i>, 51<\/b> (2019), 3694-3713.","DOI":"10.1137\/19M124318X"},{"key":"key-10.3934\/nhm.2022003-15","doi-asserted-by":"publisher","unstructured":"D. Jacquet, C. C. De Wit, D. Koenig.Optimal ramp metering strategy with extended lwr model, analysis and computational methods, IFAC Proceedings Volumes<\/i>, 38<\/b> (2005), 99-104.","DOI":"10.3182\/20050703-6-CZ-1902.00877"},{"key":"key-10.3934\/nhm.2022003-16","unstructured":"G. Lipt\u00e1k, M. Pereira, B. Kulcs\u00e1r, M. Kov\u00e1cs and G. Szederk\u00e9nyi, Traffic reaction model, arXiv preprint, arXiv: 2101.10190, (2021)."},{"key":"key-10.3934\/nhm.2022003-17","doi-asserted-by":"publisher","unstructured":"G. Liu, A. S. Lyrintzis, P. G. Michalopoulos.Modelling of freeway merging and diverging flow dynamics, Applied Mathematical Modelling<\/i>, 20<\/b> (1996), 459-469.","DOI":"10.1016\/0307-904X(95)00165-G"},{"key":"key-10.3934\/nhm.2022003-18","doi-asserted-by":"publisher","unstructured":"A. Sopasakis, M. A. Katsoulakis.Stochastic modeling and simulation of traffic flow: Asymmetric single exclusion process with arrhenius look-ahead dynamics, SIAM Journal on Applied Mathematics<\/i>, 66<\/b> (2006), 921-944.","DOI":"10.1137\/040617790"},{"key":"key-10.3934\/nhm.2022003-19","doi-asserted-by":"publisher","unstructured":"J. Sun, Z. Li, J. Sun.Study on traffic characteristics for a typical expressway on-ramp bottleneck considering various merging behaviors, Physica A: Statistical Mechanics and its Applications<\/i>, 440<\/b> (2015), 57-67.","DOI":"10.1016\/j.physa.2015.08.007"},{"key":"key-10.3934\/nhm.2022003-20","doi-asserted-by":"publisher","unstructured":"T.-Q. Tang, H. J. Huang, H.-Y. Shang.Effects of the number of on-ramps on the ring traffic flow, Chinese Physics B<\/i>, 19<\/b> (2010), 050517.","DOI":"10.1088\/1674-1056\/19\/5\/050517"},{"key":"key-10.3934\/nhm.2022003-21","doi-asserted-by":"publisher","unstructured":"T.-Q. Tang, H. J. Huang, S. C. Wong, Z.-Y. Gao, Y. Zhang.A new macro model for traffic flow on a highway with ramps and numerical tests, Communications in Theoretical Physics<\/i>, 51<\/b> (2009), 71.","DOI":"10.1088\/0253-6102\/51\/1\/15"},{"key":"key-10.3934\/nhm.2022003-22","doi-asserted-by":"publisher","unstructured":"T. Wang, J. Zhang, Z. Gao, W. Zhang, S. Li.Congested traffic patterns of two-lane lattice hydrodynamic model with on-ramp, Nonlinear Dynamics<\/i>, 88<\/b> (2017), 1345-1359.","DOI":"10.1007\/s11071-016-3314-z"}],"container-title":["Networks and Heterogeneous Media"],"original-title":[],"deposited":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T10:56:25Z","timestamp":1649847385000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/nhm.2022003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022]]}},"alternative-id":["1556-1801_2022_2_203"],"URL":"https:\/\/doi.org\/10.3934\/nhm.2022003","relation":{},"ISSN":["1556-1801","1556-181X"],"issn-type":[{"value":"1556-1801","type":"print"},{"value":"1556-181X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]}}}