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Fundamental diagrams for kinetic equations of traffic flow
The LWR traffic model at a junction with multibuffers
1. | Dipartimento di Matematica e Applicazioni, Via R. Cozzi 55, 20125 Milano, Italy |
References:
[1] |
A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow,, SIAM J. Appl. Math., 60 (2000), 916.
doi: 10.1137/S0036139997332099. |
[2] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks,, Netw. Heterog. Media, 1 (2006), 41.
doi: 10.3934/nhm.2006.1.41. |
[3] |
S. Blandin, D. Work, P. Goatin, B. Piccoli and A. Bayen, A general phase transition model for vehicular traffic,, SIAM J. Appl. Math., 71 (2011), 107.
doi: 10.1137/090754467. |
[4] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem,, Oxford Lecture Series in Mathematics and its Applications, (2000).
|
[5] |
G. M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network,, SIAM J. Math. Anal., 36 (2005), 1862.
doi: 10.1137/S0036141004402683. |
[6] |
R. M. Colombo, Hyperbolic phase transitions in traffic flow,, SIAM J. Appl. Math., 63 (2002), 708.
doi: 10.1137/S0036139901393184. |
[7] |
R. M. Colombo, P. Goatin and B. Piccoli, Road networks with phase transitions,, J. Hyperbolic Differ. Equ., 7 (2010), 85.
doi: 10.1142/S0219891610002025. |
[8] |
R. M. Colombo, F. Marcellini and M. Rascle, A 2-phase traffic model based on a speed bound,, SIAM J. Appl. Math., 70 (2010), 2652.
doi: 10.1137/090752468. |
[9] |
C. D'apice, R. Manzo and B. Piccoli, Packet flow on telecommunication networks,, SIAM J. Math. Anal., 38 (2006), 717.
doi: 10.1137/050631628. |
[10] |
M. Garavello and P. Goatin, The Cauchy problem at a node with buffer,, Discrete Contin. Dyn. Syst., 32 (2012), 1915.
doi: 10.3934/dcds.2012.32.1915. |
[11] |
M. Garavello and B. Piccoli, Traffic flow on a road network using the Aw-Rascle model,, Comm. Partial Differential Equations, 31 (2006), 243.
doi: 10.1080/03605300500358053. |
[12] |
M. Garavello and B. Piccoli, Traffic Flow on Networks. Conservation Laws Models,, AIMS Series on Applied Mathematics, (2006).
|
[13] |
M. Garavello and B. Piccoli, Conservation laws on complex networks,, Ann. H. Poincaré, 26 (2009), 1925.
doi: 10.1016/j.anihpc.2009.04.001. |
[14] |
M. Garavello and B. Piccoli, A multibuffer model for lwr road networks,, in Advances in Dynamic Network Modeling in Complex Transportation Systems, (2013), 143.
doi: 10.1007/978-1-4614-6243-9_6. |
[15] |
P. Goatin, The Aw-Rascle vehicular traffic flow model with phase transitions,, Math. Comput. Modelling, 44 (2006), 287.
doi: 10.1016/j.mcm.2006.01.016. |
[16] |
S. Göttlich, M. Herty and A. Klar, Modelling and optimization of supply chains on complex networks,, Commun. Math. Sci., 4 (2006), 315.
doi: 10.4310/CMS.2006.v4.n2.a3. |
[17] |
M. Herty, A. Klar and B. Piccoli, Existence of solutions for supply chain models based on partial differential equations,, SIAM J. Math. Anal., 39 (2007), 160.
doi: 10.1137/060659478. |
[18] |
M. Herty, J.-P. Lebacque and S. Moutari, A novel model for intersections of vehicular traffic flow,, Netw. Heterog. Media, 4 (2009), 813.
doi: 10.3934/nhm.2009.4.813. |
[19] |
M. Herty, S. Moutari and M. Rascle, Optimization criteria for modelling intersections of vehicular traffic flow,, Netw. Heterog. Media, 1 (2006), 275.
doi: 10.3934/nhm.2006.1.275. |
[20] |
M. Herty and M. Rascle, Coupling conditions for a class of second-order models for traffic flow,, SIAM J. Math. Anal., 38 (2006), 595.
doi: 10.1137/05062617X. |
[21] |
H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Vonservation Laws,, Applied Mathematical Sciences, (2002).
doi: 10.1007/978-3-642-56139-9. |
[22] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317.
doi: 10.1098/rspa.1955.0089. |
[23] |
A. Marigo and B. Piccoli, A fluid dynamic model for $T$-junctions,, SIAM J. Math. Anal., 39 (2008), 2016.
doi: 10.1137/060673060. |
[24] |
P. I. Richards, Shock waves on the highway,, Operations Res., 4 (1956), 42.
doi: 10.1287/opre.4.1.42. |
[25] |
D. Sun, I. S. Strub and A. M. Bayen, Comparison of the performance of four Eulerian network flow models for strategic air traffic management,, Netw. Heterog. Media, 2 (2007), 569.
doi: 10.3934/nhm.2007.2.569. |
[26] |
H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior,, Transportation Research Part B, 236 (2002), 275.
doi: 10.1016/S0191-2615(00)00050-3. |
show all references
References:
[1] |
A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow,, SIAM J. Appl. Math., 60 (2000), 916.
doi: 10.1137/S0036139997332099. |
[2] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks,, Netw. Heterog. Media, 1 (2006), 41.
doi: 10.3934/nhm.2006.1.41. |
[3] |
S. Blandin, D. Work, P. Goatin, B. Piccoli and A. Bayen, A general phase transition model for vehicular traffic,, SIAM J. Appl. Math., 71 (2011), 107.
doi: 10.1137/090754467. |
[4] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem,, Oxford Lecture Series in Mathematics and its Applications, (2000).
|
[5] |
G. M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network,, SIAM J. Math. Anal., 36 (2005), 1862.
doi: 10.1137/S0036141004402683. |
[6] |
R. M. Colombo, Hyperbolic phase transitions in traffic flow,, SIAM J. Appl. Math., 63 (2002), 708.
doi: 10.1137/S0036139901393184. |
[7] |
R. M. Colombo, P. Goatin and B. Piccoli, Road networks with phase transitions,, J. Hyperbolic Differ. Equ., 7 (2010), 85.
doi: 10.1142/S0219891610002025. |
[8] |
R. M. Colombo, F. Marcellini and M. Rascle, A 2-phase traffic model based on a speed bound,, SIAM J. Appl. Math., 70 (2010), 2652.
doi: 10.1137/090752468. |
[9] |
C. D'apice, R. Manzo and B. Piccoli, Packet flow on telecommunication networks,, SIAM J. Math. Anal., 38 (2006), 717.
doi: 10.1137/050631628. |
[10] |
M. Garavello and P. Goatin, The Cauchy problem at a node with buffer,, Discrete Contin. Dyn. Syst., 32 (2012), 1915.
doi: 10.3934/dcds.2012.32.1915. |
[11] |
M. Garavello and B. Piccoli, Traffic flow on a road network using the Aw-Rascle model,, Comm. Partial Differential Equations, 31 (2006), 243.
doi: 10.1080/03605300500358053. |
[12] |
M. Garavello and B. Piccoli, Traffic Flow on Networks. Conservation Laws Models,, AIMS Series on Applied Mathematics, (2006).
|
[13] |
M. Garavello and B. Piccoli, Conservation laws on complex networks,, Ann. H. Poincaré, 26 (2009), 1925.
doi: 10.1016/j.anihpc.2009.04.001. |
[14] |
M. Garavello and B. Piccoli, A multibuffer model for lwr road networks,, in Advances in Dynamic Network Modeling in Complex Transportation Systems, (2013), 143.
doi: 10.1007/978-1-4614-6243-9_6. |
[15] |
P. Goatin, The Aw-Rascle vehicular traffic flow model with phase transitions,, Math. Comput. Modelling, 44 (2006), 287.
doi: 10.1016/j.mcm.2006.01.016. |
[16] |
S. Göttlich, M. Herty and A. Klar, Modelling and optimization of supply chains on complex networks,, Commun. Math. Sci., 4 (2006), 315.
doi: 10.4310/CMS.2006.v4.n2.a3. |
[17] |
M. Herty, A. Klar and B. Piccoli, Existence of solutions for supply chain models based on partial differential equations,, SIAM J. Math. Anal., 39 (2007), 160.
doi: 10.1137/060659478. |
[18] |
M. Herty, J.-P. Lebacque and S. Moutari, A novel model for intersections of vehicular traffic flow,, Netw. Heterog. Media, 4 (2009), 813.
doi: 10.3934/nhm.2009.4.813. |
[19] |
M. Herty, S. Moutari and M. Rascle, Optimization criteria for modelling intersections of vehicular traffic flow,, Netw. Heterog. Media, 1 (2006), 275.
doi: 10.3934/nhm.2006.1.275. |
[20] |
M. Herty and M. Rascle, Coupling conditions for a class of second-order models for traffic flow,, SIAM J. Math. Anal., 38 (2006), 595.
doi: 10.1137/05062617X. |
[21] |
H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Vonservation Laws,, Applied Mathematical Sciences, (2002).
doi: 10.1007/978-3-642-56139-9. |
[22] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317.
doi: 10.1098/rspa.1955.0089. |
[23] |
A. Marigo and B. Piccoli, A fluid dynamic model for $T$-junctions,, SIAM J. Math. Anal., 39 (2008), 2016.
doi: 10.1137/060673060. |
[24] |
P. I. Richards, Shock waves on the highway,, Operations Res., 4 (1956), 42.
doi: 10.1287/opre.4.1.42. |
[25] |
D. Sun, I. S. Strub and A. M. Bayen, Comparison of the performance of four Eulerian network flow models for strategic air traffic management,, Netw. Heterog. Media, 2 (2007), 569.
doi: 10.3934/nhm.2007.2.569. |
[26] |
H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior,, Transportation Research Part B, 236 (2002), 275.
doi: 10.1016/S0191-2615(00)00050-3. |
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