Towers, John D. An explicit finite volume algorithm for vanishing viscosity solutions on a network. (English) Zbl 1487.90206 Netw. Heterog. Media 17, No. 1, 1-13 (2022). MSC: 90B10 90B20 35L65 PDFBibTeX XMLCite \textit{J. D. Towers}, Netw. Heterog. Media 17, No. 1, 1--13 (2022; Zbl 1487.90206) Full Text: DOI
Bertaglia, Giulia; Pareschi, Lorenzo Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of COVID-19 in Italy. (English) Zbl 1478.92178 Math. Models Methods Appl. Sci. 31, No. 12, 2495-2531 (2021). MSC: 92D30 92-10 65M08 65L04 35K57 82C40 PDFBibTeX XMLCite \textit{G. Bertaglia} and \textit{L. Pareschi}, Math. Models Methods Appl. Sci. 31, No. 12, 2495--2531 (2021; Zbl 1478.92178) Full Text: DOI arXiv
Bertaglia, Giulia; Pareschi, Lorenzo Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods. (English) Zbl 1472.65105 ESAIM, Math. Model. Numer. Anal. 55, No. 2, 381-407 (2021). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65L04 65L06 35L50 35K57 82C40 92D30 PDFBibTeX XMLCite \textit{G. Bertaglia} and \textit{L. Pareschi}, ESAIM, Math. Model. Numer. Anal. 55, No. 2, 381--407 (2021; Zbl 1472.65105) Full Text: DOI arXiv
Ancona, Fabio; Cesaroni, Annalisa; Coclite, Giuseppe M.; Garavello, Mauro On optimization of traffic flow performance for conservation laws on networks. (English) Zbl 1470.35229 Minimax Theory Appl. 6, No. 2, 205-226 (2021). MSC: 35L65 35D30 35L45 35Q93 35R02 76A30 PDFBibTeX XMLCite \textit{F. Ancona} et al., Minimax Theory Appl. 6, No. 2, 205--226 (2021; Zbl 1470.35229) Full Text: Link
Tang, Tie-Qiao; Shi, Wei-Fang; Huang, Hai-Jun; Wu, Wen-Xiang; Song, Ziqi A route-based traffic flow model accounting for interruption factors. (English) Zbl 07562414 Physica A 514, 767-785 (2019). MSC: 82-XX PDFBibTeX XMLCite \textit{T.-Q. Tang} et al., Physica A 514, 767--785 (2019; Zbl 07562414) Full Text: DOI
Bretti, Gabriella; Cristiani, Emiliano; Lattanzio, Corrado; Maurizi, Amelio; Piccoli, Benedetto Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road. (English) Zbl 1435.35244 Math. Eng. (Springfield) 1, No. 1, 55-83 (2019). MSC: 35L65 90B20 PDFBibTeX XMLCite \textit{G. Bretti} et al., Math. Eng. (Springfield) 1, No. 1, 55--83 (2019; Zbl 1435.35244) Full Text: DOI arXiv
Bayen, Alexandre; Keimer, Alexander; Porter, Emily; Spinola, Michele Time-continuous instantaneous and past memory routing on traffic networks: a mathematical analysis on the basis of the link-delay model. (English) Zbl 1432.34107 SIAM J. Appl. Dyn. Syst. 18, No. 4, 2143-2180 (2019). MSC: 34K60 90B20 92B20 PDFBibTeX XMLCite \textit{A. Bayen} et al., SIAM J. Appl. Dyn. Syst. 18, No. 4, 2143--2180 (2019; Zbl 1432.34107) Full Text: DOI
Sun, Ye; Work, Daniel B. Error bounds for Kalman filters on traffic networks. (English) Zbl 1405.93218 Netw. Heterog. Media 13, No. 2, 261-295 (2018). MSC: 93E11 93E10 93C20 90B20 PDFBibTeX XMLCite \textit{Y. Sun} and \textit{D. B. Work}, Netw. Heterog. Media 13, No. 2, 261--295 (2018; Zbl 1405.93218) Full Text: DOI
Towers, John D. Convergence via OSLC of the Godunov scheme for a scalar conservation law with time and space flux discontinuities. (English) Zbl 1395.65042 Numer. Math. 139, No. 4, 939-969 (2018). MSC: 65M08 65M12 35L65 PDFBibTeX XMLCite \textit{J. D. Towers}, Numer. Math. 139, No. 4, 939--969 (2018; Zbl 1395.65042) Full Text: DOI
Towers, John D. Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. (English) Zbl 1406.35190 J. Hyperbolic Differ. Equ. 15, No. 2, 175-190 (2018). MSC: 35L65 65M06 65M08 65M12 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Hyperbolic Differ. Equ. 15, No. 2, 175--190 (2018; Zbl 1406.35190) Full Text: DOI
Li, Yanning; Claudel, Christian G.; Piccoli, Benedetto; Work, Daniel B. A convex formulation of traffic dynamics on transportation networks. (English) Zbl 1378.90036 SIAM J. Appl. Math. 77, No. 4, 1493-1515 (2017). MSC: 90B20 90C25 PDFBibTeX XMLCite \textit{Y. Li} et al., SIAM J. Appl. Math. 77, No. 4, 1493--1515 (2017; Zbl 1378.90036) Full Text: DOI arXiv
Banda, Mapundi K.; Häck, Axel-Stefan; Herty, Michael Numerical discretization of coupling conditions by high-order schemes. (English) Zbl 1348.35287 J. Sci. Comput. 69, No. 1, 122-145 (2016). MSC: 35R02 35Q35 35F30 PDFBibTeX XMLCite \textit{M. K. Banda} et al., J. Sci. Comput. 69, No. 1, 122--145 (2016; Zbl 1348.35287) Full Text: DOI Link
Briani, Maya; Piccoli, Benedetto; Qiu, Jing-Mei Notes on RKDG methods for shallow-water equations in canal networks. (English) Zbl 1437.76020 J. Sci. Comput. 68, No. 3, 1101-1123 (2016). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{M. Briani} et al., J. Sci. Comput. 68, No. 3, 1101--1123 (2016; Zbl 1437.76020) Full Text: DOI
Shi, YuFeng; Guo, Yan A maximum-principle-satisfying finite volume compact-WENO scheme for traffic flow model on networks. (English) Zbl 1346.65043 Appl. Numer. Math. 108, 21-36 (2016). MSC: 65M08 35L05 90B20 35B50 PDFBibTeX XMLCite \textit{Y. Shi} and \textit{Y. Guo}, Appl. Numer. Math. 108, 21--36 (2016; Zbl 1346.65043) Full Text: DOI
Göttlich, Simone; Herty, Michael; Ziegler, Ute Modeling and optimizing traffic light settings in road networks. (English) Zbl 1348.90186 Comput. Oper. Res. 55, 36-51 (2015). MSC: 90B20 90B10 90C11 PDFBibTeX XMLCite \textit{S. Göttlich} et al., Comput. Oper. Res. 55, 36--51 (2015; Zbl 1348.90186) Full Text: DOI
Canic, Suncica; Piccoli, Benedetto; Qiu, Jing-Mei; Ren, Tan Runge-Kutta discontinuous Galerkin method for traffic flow model on networks. (English) Zbl 1321.90034 J. Sci. Comput. 63, No. 1, 233-255 (2015). MSC: 90B20 90B06 90B15 68U20 PDFBibTeX XMLCite \textit{S. Canic} et al., J. Sci. Comput. 63, No. 1, 233--255 (2015; Zbl 1321.90034) Full Text: DOI arXiv
Pfaff, Sebastian; Ulbrich, Stefan; Leugering, Günter Optimal control of nonlinear hyperbolic conservation laws with switching. (English) Zbl 1327.49014 Leugering, Günter (ed.) et al., Trends in PDE constrained optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-05082-9/hbk; 978-3-319-05083-6/ebook). ISNM. International Series of Numerical Mathematics 165, 109-131 (2014). MSC: 49J20 PDFBibTeX XMLCite \textit{S. Pfaff} et al., ISNM, Int. Ser. Numer. Math. 165, 109--131 (2014; Zbl 1327.49014) Full Text: DOI
Göttlich, Simone; Ziegler, Ute Traffic light control: a case study. (English) Zbl 1292.90080 Discrete Contin. Dyn. Syst., Ser. S 7, No. 3, 483-501 (2014). MSC: 90B20 35L50 90B90 90C06 PDFBibTeX XMLCite \textit{S. Göttlich} and \textit{U. Ziegler}, Discrete Contin. Dyn. Syst., Ser. S 7, No. 3, 483--501 (2014; Zbl 1292.90080) Full Text: DOI
Costeseque, Guillaume; Lebacque, Jean-Patrick Discussion about traffic junction modelling: conservation laws vs Hamilton-Jacobi equations. (English) Zbl 1292.65088 Discrete Contin. Dyn. Syst., Ser. S 7, No. 3, 411-433 (2014). MSC: 65M06 35F21 90B20 PDFBibTeX XMLCite \textit{G. Costeseque} and \textit{J.-P. Lebacque}, Discrete Contin. Dyn. Syst., Ser. S 7, No. 3, 411--433 (2014; Zbl 1292.65088) Full Text: DOI
Farjoun, Yossi; Seibold, Benjamin A characteristic particle method for traffic flow simulations on highway networks. (English) Zbl 1311.65121 Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations VI. Selected papers of the sixth international workshop, Bonn, Germany, October 4–6, 2011. Berlin: Springer (ISBN 978-3-642-32978-4/hbk; 978-3-642-32979-1/ebook). Lecture Notes in Computational Science and Engineering 89, 199-219 (2013). MSC: 65M25 35L65 65M75 90B20 76M28 PDFBibTeX XMLCite \textit{Y. Farjoun} and \textit{B. Seibold}, Lect. Notes Comput. Sci. Eng. 89, 199--219 (2013; Zbl 1311.65121) Full Text: DOI arXiv
Berrone, Stefano; De Santi, Francesca; Pieraccini, Sandra; Marro, Massimo Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies. (English) Zbl 1268.90011 Comput. Math. Appl. 64, No. 6, 1975-1991 (2012). MSC: 90B20 91B76 PDFBibTeX XMLCite \textit{S. Berrone} et al., Comput. Math. Appl. 64, No. 6, 1975--1991 (2012; Zbl 1268.90011) Full Text: DOI
Manzo, R.; Piccoli, B.; Rarità, L. Optimal distribution of traffic flows in emergency cases. (English) Zbl 1460.90064 Eur. J. Appl. Math. 23, No. 4, 515-535 (2012). MSC: 90B20 49N90 PDFBibTeX XMLCite \textit{R. Manzo} et al., Eur. J. Appl. Math. 23, No. 4, 515--535 (2012; Zbl 1460.90064) Full Text: DOI
Cutolo, Alfredo; D’Apice, Ciro; Manzo, Rosanna Traffic optimization at junctions to improve vehicular flows. (English) Zbl 1243.90041 ISRN Appl. Math. 2011, Article ID 679056, 19 p. (2011). MSC: 90B20 90C90 PDFBibTeX XMLCite \textit{A. Cutolo} et al., ISRN Appl. Math. 2011, Article ID 679056, 19 p. (2011; Zbl 1243.90041) Full Text: DOI
Caramia, Massimiliano; D’apice, Ciro; Piccoli, Benedetto; Sgalambro, Antonino Fluidsim: a car traffic simulation prototype based on fluiddynamic. (English) Zbl 1461.90033 Algorithms (Basel) 3, No. 3, 294-310 (2010). MSC: 90B20 35L65 35Q35 65Y15 PDFBibTeX XMLCite \textit{M. Caramia} et al., Algorithms (Basel) 3, No. 3, 294--310 (2010; Zbl 1461.90033) Full Text: DOI
Rarità, Luigi; D’Apice, Ciro; Piccoli, Benedetto; Helbing, Dirk Sensitivity analysis of permeability parameters for flows on Barcelona networks. (English) Zbl 1203.90050 J. Differ. Equations 249, No. 12, 3110-3131 (2010). MSC: 90B20 90B10 PDFBibTeX XMLCite \textit{L. Rarità} et al., J. Differ. Equations 249, No. 12, 3110--3131 (2010; Zbl 1203.90050) Full Text: DOI
Blandin, S.; Bretti, G.; Cutolo, A.; Piccoli, B. Numerical simulations of traffic data via fluid dynamic approach. (English) Zbl 1180.90175 Appl. Math. Comput. 210, No. 2, 441-454 (2009). MSC: 90B90 90B20 76M12 PDFBibTeX XMLCite \textit{S. Blandin} et al., Appl. Math. Comput. 210, No. 2, 441--454 (2009; Zbl 1180.90175) Full Text: DOI
Bretti, G.; Natalini, R.; Piccoli, B. Numerical algorithms for simulations of a traffic model on road networks. (English) Zbl 1146.90365 J. Comput. Appl. Math. 210, No. 1-2, 71-77 (2007). MSC: 90B20 90B10 65M06 35L65 34B45 PDFBibTeX XMLCite \textit{G. Bretti} et al., J. Comput. Appl. Math. 210, No. 1--2, 71--77 (2007; Zbl 1146.90365) Full Text: DOI
Bretti, Gabriella; Natalini, Roberto; Piccoli, Benedetto A fluid-dynamic traffic model on road networks. (English) Zbl 1127.76004 Arch. Comput. Methods Eng. 14, No. 2, 139-172 (2007). MSC: 76M12 90B20 90B10 76-02 PDFBibTeX XMLCite \textit{G. Bretti} et al., Arch. Comput. Methods Eng. 14, No. 2, 139--172 (2007; Zbl 1127.76004) Full Text: DOI