Abstract
We have revealed general physical conditions for the maximization of the network throughput at which free flow conditions are ensured, i.e., traffic breakdown cannot occur in the whole traffic or transportation network. A physical measure of the network – network capacity is introduced that characterizes general features of the network with respect to the maximization of the network throughput. The network capacity allows us also to make a general proof of the deterioration of traffic system occurring when dynamic traffic assignment is performed in a network based on the classical Wardrop’ user equilibrium (UE) and system optimum (SO) equilibrium.
Similar content being viewed by others
References
J.G. Wardrop, Proc. Inst. Civil Eng. II. 1, 325 (1952)
Y. Sheffi, Urban transportation networks: Equilibrium analysis with mathematical programming methods (Prentice-Hall, New Jersey, 1984)
M.G.H. Bell, Y. Iida, Transportation network analysis (John Wiley & Sons, Incorporated, Hoboken, 1997)
S. Peeta, A.K. Ziliaskopoulos, Networks and Spatial Economics 1, 233 (2001)
H.S. Mahmassani, Networks and Spatial Economics 1, 267 (2001)
H. Rakha, A. Tawfik, in Encyclopedia of Complexity and System Science, edited by R.A. Meyers (Springer, Berlin, 2009), pp. 9429–9470
T.L. Friesz, D. Bernstein, Foundations of Network Optimization and Games, in Complex Networks and Dynamic Systems (Springer, New York, Berlin 2016), Vol. 3
C.F. Daganzo, Y. Sheffi, Transp. Sci. 11, 253 (1977)
C.F. Daganzo, Transp. Res. 11, 385 (1977)
C.F. Daganzo, Transp. Res. B 14, 229 (1980)
C.F. Daganzo, Trans. Sci. 32, 3 (1998)
E.J. Gonzales, C.F. Daganzo, Transp. Res. B 46, 1519 (2012)
C.F. Daganzo, Transp. Res. B 55, 98 (2013)
D.K. Merchant, G.L. Nemhauser, Transp. Sci. 12, 187 (1978)
M.G.H. Bell, Transp. Res. B 26, 303 (1992)
M.G.H. Bell, Transp. Sci. 17, 198 (1983)
M.G.H. Bell, Transp. Res. B 25, 13 (1991)
M.G.H. Bell, Transp. Res. B 25, 115 (1991)
M.G.H. Bell, Transp. Res. B 29, 125 (1995)
M.G.H. Bell, Transp. Res. B 29, 287 (1995)
M.G.H. Bell, Ch. Cassir, Transp. Res. B 36, 671 (2002)
M.G.H. Bell, Transp. Res. B 34, 533 (2000)
M.G.H. Bell, C.M. Shielda, F. Busch, G. Kruse, Transp. Res. C 5, 197 (1997)
H. Ceylan, M.G.H. Bell, Transp. Res. B 39, 169 (2005)
H. Yang, M.G.H. Bell, Transp. Res. B 31, 303 (1997)
H. Yang, M.G.H. Bell, Transp. Res. B 32, 539 (1998)
H. Yang, M.G.H. Bell, Q. Menga, Transp. Res. B 34, 255 (2000)
H. Yang, M.G.H. Bell, Transport Rev. 18, 257 (1998)
H.S. Mahmassani, G.L. Chang. Transp. Sci. 21, 89 (1987)
H.S. Mahmassani, R. Herman, Transp. Sci. 18, 362 (1984)
H.S. Mahmassani, S. Peeta, Transp. Res. Rec. 1408, 83 (1993)
S. Peeta, H.S. Mahmassani, Transp. Res. C 3, 83 (1995)
S. Peeta, H.S. Mahmassani, Ann. Oper. Res. 60, 81 (1995)
A. Ziliaskopoulos, D. Kotzinos, H.S. Mahmassani, Transp. Res. C 5, 95 (1997)
K. Abdelghany, D. Valdes, A. Abdelfatah, H.S. Mahmassani, Transp. Res. Rec. 1667, 67 (1999)
Y.-C. Chiu, H.S. Mahmassani, Transp. Res. Rec. 1783, 89 (2002)
N. Huynh, H.S. Mahmassani, H. Tavana, Transp. Res. Rec. 1783, 55 (2002)
X. Zhou, H.S. Mahmassani, K. Zhang, Transp. Res. C 16, 167 (2008)
K. Zhang, H.S. Mahmassani, C.-C. Lu, Transp. Res. Rec. 2085, 86 (2008)
E.D. Miller-Hooks, H.S. Mahmassani, Transp. Sci. 34, 198 (2000)
T.L. Friesz, K. Han, P.A. Neto, A. Meimand, T. Yao, Transp. Res. B 47, 102 (2013)
T.L. Friesz, D. Bernstein, T.E. Smith, R.L. Tobin, B.W. Wie, Oper. Res. 41, 179 (1993)
T.L. Friesz, J. Luque, R.L. Tobin, B.-W. Wie, Oper. Res. 37, 893 (1989)
R.L. Tobin, T.L. Friesz, Transp. Sci. 22, 242 (1988)
Ch. Suwansirikul, T.L. Friesz, R.L. Tobin, Transp. Sci. 21, 254 (1987)
T.L. Friesz, D. Bernstein, T.E. Smith, R.L. Tobin, B.W. Wie, Oper. Res. 41, 179 (1993)
T.L. Friesz, D. Bernstein, N.J. Mehta, R.L. Tobin, S. Ganjalizadeh, Oper. Res. 42, 1120 (1994)
T.L. Friesz, H.-J. Cho, N.J. Mehta, R.L. Tobin, G. Anandalingam, Transp. Sci. 26, 18 (1992)
T.L. Friesz, Transp. Res. A 19, 413 (1985)
T.L. Friesz, R.L. Tobin, T.E. Smith, P.T. Harker, J. Regional Sci. 23, 337 (1983)
B.-W. Wie, T.L. Friesz, R.L. Tobin, Transp. Res. B 24, 431 (1990)
K. Han, T.L. Friesz, T. Yao, Transp. Res. B 53, 17 (2013)
C. Zhang, X. Chen, A. Sumalee, Transp. Res. B 45, 534 (2011)
S.P. Hoogendoorn, V.L. Knoop, H.J. Van Zuylen, J. Adv. Transp. 42, 357 (2008)
Y. Nesterov, A. de Palma, Networks Spatial Econ. 3, 371 (2003)
L. Lu, Y. Xu, C. Antoniou, M. Ben-Akiva, Transport. Res. C 51, 149 (2015)
Y. Jiang, S.C. Wong, H.W. Ho, P. Zhang, R. Liu, A. Sumalee, Transp. Res. B 4, 343 (2011)
J. Yang, G. Jiang, Transp. Res. C 47, 168 (2014)
W. Shen, H.M. Zhang, Transp. Res. B 65, 1 (2014)
M. Carey, P. Humphreys, M. McHugh, R. McIvor, Transp. Res. B 65, 90 (2014)
K. Doan, S.V. Ukkusuri, Transport. Res. C 51, 41 (2015)
X. Xu, A. Chen, S. Kitthamkesorn, H. Yang, H.K. Lo, Transp. Res. B 81, 686 (2015)
S.D. Ahipas, R. Meskarian, T.L. Magnanti, K. Natarajan, Transp. Res. B 81, 333 (2015)
H. Liu, D.Z.W. Wang, Transp. Res. B 72, 20 (2015)
M. Amirgholy, E.J. Gonzales, Transp. Res. B (2016), Doi: 10.1016/j.trb.2015.11.006
Y.E. Ge, B.R. Sun, H.M. Zhang, W.Y. Szeto, Xizhao Zhou, Networks and Spatial Economics 15, 583 (2015)
T. Iryo, Networks and Spatial Economics 15, 599 (2015)
Wen-Long Jin, Networks and Spatial Economics 15, 617 (2015)
Ampol Karoonsoontawong, Dung-Ying Lin, Networks and Spatial Economics 15, 1011 (2015)
Byung Do Chung, Hsun-Jung Cho, Terry L. Friesz, Henh Huang, Tao Yao, Networks and Spatial Economics 14, 183 (2014)
P. Kachroo, S. Sastry, IEEE Trans. ITS 17, 1438 (2016)
J. Wahle, A.L.C. Bazzan, F. Klugl, M. Schreckenberg, Physica A 287, 669 (2000)
L.C. Davis, Physica A 388, 4459 (2009)
L.C. Davis, Physica A 389, 3588 (2010)
Wen-Xu Wang, Bing-Hong Wang, Wen-Chen Zheng, Chuan-Yang Yin, Tao Zhou, Phys. Rev. E 72, 066702 (2005)
R. Claes, T. Holvoet, D. Weyns, IEEE Trans. ITS 12, 364 (2011)
Chuan-Fei Donga, Xu Mab, Bing-Hong Wang, Phys. Lett. A 374, 1326 (2010)
A. Sopasakis, M.A. Katsoulakis, SIAM J. Appl. Math. 66, 921 (2006)
Cory Hauck, Yi Sun, Ilya Timofeyev, Stoch. Dyn. 14, 1350022 (2014)
Yi Sun, Ilya Timofeyev, Phys. Rev. E 89, 052810 (2014)
Transportation and Traffic Theory, edited by J.-B. Lesort (Elsevier Science Ltd, Oxford, 1996)
Transportation and Traffic Theory, edited by A. Ceder (Elsevier Science Ltd, Oxford, 1999)
Transportation and Traffic Theory in the 21st Century, edited by M.A.P. Taylor (Elsevier Science Ltd, Amsterdam, 2002)
Traffic and Transportation Theory, edited by H.S. Mahmassani (Elsevier Science, Amsterdam, 2005)
Transportation and Traffic Theory 2007, edited by R.E. Allsop, M.G.H. Bell, B.G. Heydecker (Elsevier Science Ltd, Amsterdam, 2007)
Transportation and Traffic Theory 2009, edited by W.H.K. Lam, S.C. Wong, H.K. Lo (Springer, Dordrecht, Heidelberg, London, New York, 2009)
Papers selected for the 19th Int. Sym. on Transp. and Traffic Theory, Procedia – Social and Behavioral Sci., edited by M.J. Cassidy, A. Skabardonis (2011), Vol. 17, pp. 1–716
20th International Symposium on Transportation and Traffic Theory (ISTTT 2013) Procedia – Social and Behavioral Sciences, edited by Serge P. Hoogendoorn, V.L. Knoop, H. van Lint (2013), Vol. 80, pp. 1–996
M. Kuwahara, H. Kita, Y. Asakura (Eds.), Transp. Res. Proc. 7, 1 (2015)
B.S. Kerner, Physica A 392, 5261 (2013)
B.S. Kerner, Physica A 450, 700 (2016)
H. Rehborn, S.L. Klenov, in Springer Encyclopedia of Complexity and System Science, edited by R.A. Meyers (Springer, Berlin, 2009)
B.S. Kerner, The Physics of Traffic (Springer, Berlin, 2004)
B.S. Kerner, Introduction to Modern Traffic Flow Theory and Control (Springer, Berlin, 2009)
B.S. Kerner, J. Phys. A 44, 092001 (2011)
B.S. Kerner, Phys. Rev. E 84, 045102(R) (2011)
L. Elefteriadou, An Introduction to Traffic Flow Theory (Springer, Berlin, 2014)
A.D. May, Traffic Flow Fundamentals (Prentice-Hall, Inc., New Jersey, 1990)
D. Helbing, Rev. Mod. Phys. 73, 1067 (2001)
D. Chowdhury, L. Santen, A. Schadschneider, Phys. Rep. 329, 199 (2000)
A. Schadschneider, D. Chowdhury, K. Nishinari, Stochastic Transport in Complex Systems (Elsevier Science Inc., New York, 2011)
M. Treiber, A. Kesting, Traffic Flow Dynamics (Springer, Berlin, 2013)
Highway Capacity Manual 2000, National Research Council, Transportation Research Boad, Washington, D.C., 2000
Highway Capacity Manual 2010, National Research Council, Transportation Research Boad, Washington, D.C., 2010
Traffic Flow Theory, edited by N.H. Gartner, C.J. Messer, A.K. Rathi (Transportation Research Board, Washington, D.C., 2001)
D.C. Gazis, Traffic Theory (Springer, Berlin 2002)
T. Nagatani, Rep. Prog. Phys. 65, 1331 (2002)
K. Nagel, P. Wagner, R. Woesler, Oper. Res. 51, 681 (2003)
B.S. Kerner, Physica A 397, 76 (2014)
B.S. Kerner, S.L. Klenov, J. Phys. A 35, L31 (2002)
B.S. Kerner, S.L. Klenov, Phys. Rev. E 80, 056101 (2009)
K. Hausken, H. Rehborn, in Game Theoretic Analysis of Congestion, Safety and Security, Springer Series in Reliability Engineering (Springer, Berlin, 2015), pp. 113–141
H. Rehborn, S.L. Klenov, J. Palmer, Physica A 390, 4466 (2011)
H. Rehborn, M. Koller, J. Adv. Transp. 48, 1107 (2014)
L.C. Davis, Phys. Rev. E 69, 016108 (2004)
H.K. Lee, R. Barlović, M. Schreckenberg, D. Kim, Phys. Rev. Lett. 92, 238702 (2004)
R. Jiang, Q.-S. Wu, J. Phys. A 37, 8197 (2004)
K. Gao, R. Jiang, S.-X. Hu, B.-H. Wang, Q.-S. Wu, Phys. Rev. E 76, 026105 (2007)
L.C. Davis, Physica A 368, 541 (2006)
L.C. Davis, Physica A 361, 606 (2006)
L.C. Davis, Physica A 387, 6395 (2008)
L.C. Davis, Physica A 391, 1679 (2012)
R. Jiang, M.-B. Hua, R. Wang, Q.-S. Wu, Phys. Lett. A 365, 6 (2007)
R. Jiang, Q.-S. Wu, Phys. Rev. E 72, 067103 (2005)
R. Jiang, Q.-S. Wu, Physica A 377, 633 (2007)
R. Wang, R. Jiang, Q.-S. Wu, M. Liu, Physica A 378, 475 (2007)
A. Pottmeier, C. Thiemann, A. Schadschneider, M. Schreckenberg, in Traffic and Granular Flow’05, edited by A. Schadschneider, T. Pöschel, R. Kühne, M. Schreckenberg, D.E. Wolf (Springer, Berlin, 2007), pp. 503–508
X.G. Li, Z.Y. Gao, K.P. Li, X.M. Zhao, Phys. Rev. E 76, 016110 (2007)
J.J. Wu, H.J. Sun, Z.Y. Gao, Phys. Rev. E 78, 036103 (2008)
J.A. Laval, in Traffic and Granular Flow’05, edited by A. Schadschneider, T. Pöschel, R. Kühne, M. Schreckenberg, D.E. Wolf (Springer, Berlin, 2007), pp. 521–526
S. Hoogendoorn, H. van Lint, V.L. Knoop, Trans. Res. Rec. 2088, 102 (2008)
K. Gao, R. Jiang, B.-H. Wang, Q.-S. Wu, Physica A 388, 3233 (2009)
B. Jia, X.-G. Li, T. Chen, R. Jiang, Z.-Y. Gao, Transportmetrica 7, 127 (2011)
J.-F. Tian, B. Jia, X.-G. Li, R. Jiang, X.-M. Zhao, Z.-Y. Gao, Physica A 388, 4827 (2009)
S. He, W. Guan, L. Song, Physica A 389, 825 (2009)
C.-J. Jin, W. Wang, R. Jiang, K. Gao, J. Stat. Mech. 2010, P03018 (2010)
S.L. Klenov, in Proceedings of Moscow Inst. Phys. Technol., edited by V.V. Kozlov (Moscow Inst. of Phys. and Technology, Moscow, 2010), Vol. 2, pp. 75–90 (in Russian)
A.V. Gasnikov, S.L. Klenov, E.A. Nurminski, Y.A. Kholodov, N.B. Shamray, Introduction to mathematical simulations of traffic flow (MCNMO, Moscow, 2013) (in Russian)
S. Kokubo, J. Tanimoto, A. Hagishima, Physica A 390, 561 (2011)
H.-K. Lee, B.-J. Kim, Physica A 390, 4555 (2011)
C.-J. Jin, W. Wang, Physica A 390, 4184 (2011)
J.P.L. Neto, M.L. Lyra, C.R. da Silva, Physica A 390, 3558 (2011)
P. Zhang, C.-X. Wu, S.C. Wong, Physica A 391, 456 (2012)
W.-H. Lee, S.-S. Tseng, J.-L. Shieh, H.-H. Chen, IEEE Trans. ITS 12, 1047 (2011)
S. Lee, B. Heydecker, Y.H. Kim, E.-Y. Shon, J. Adv. Trans. 45, 143 (2011)
J.-F. Tian, Z.-Z. Yuan, M. Treiber, B. Jia, W.-Y. Zhang, Physica A 391, 3129 (2012)
R. Borsche, M. Kimathi, A. Klar, Comp. Math. Appl. 64, 2939 (2012)
Y. Wang, Y.I. Zhang, J. Hu, L. Li, Int. J. Mod. Phys. C 23, 1250060 (2012)
J.-F. Tian, Z.-Z. Yuan, B. Jia, H.-Q. Fan, T. Wang, Phys. Lett. A 376, 2781 (2012)
Y. Qiu, J. Non-Newtonian Fluid Mechanics 197, 1 (2013)
H. Yang, J. Lu, X. Hu, J. Jiang, Physica A 392, 4009 (2013)
F. Knorr, M. Schreckenberg, J. Stat. Mech. 2013, P07002 (2013)
Xiang Zheng-Tao, Li Yu-Jin, Chen Yu-Feng, Xiong Li, Physica A 392, 5399 (2013)
A.R. Mendez, R.M. Velasco, J. Phys. A 46, 462001 (2013)
R. Jiang, M.-B. Hu, H.M. Zhang, Z.-Y. Gao, B. Jia, Q.-S. Wu, B. Wang, M. Yang, Plos One 9, e94351 (2014)
J.F. Tian, M. Treiber, B. Jia, S.F. Ma, B. Jia, W.Y. Zhang, Transp. Res. B 71, 138 (2015)
J.F. Tian, B. Jia, S.F. Ma, C.Q. Zhu, R. Jiang, Y.X. Ding, arXiv:1503.05986 (2015)
J.F. Tian, R. Jiang, B. Jia, G. Li, M. Treiber, N. Jia, S.F. Ma, arXiv:1507.04054 (2015)
R. Jiang, M.B. Hu, H.M. Zhang, Z.Y. Gao, B. Jia, Q.S. Wu, Transp. Res. B 80, 338 (2015)
C.-J. Jin, W. Wanga, R. Jiang, H.M. Zhang, H. Wanga, M.-B. Hud, Transp. Res. C 60, 324 (2015)
Ch. Xu, P. Liu, W. Wang, Zh. Li, Acc. Anal. Prevent. 85, 45 (2015)
L.C. Davis, Physica A 451, 320 (2016)
B. Yang, Ch. Monterola, Phys. Rev. E 92, 042802 (2015)
P. Hemmerle, M. Koller, H. Rehborn, B.S. Kerner, M. Schreckenberg, IET Intell. Transp. Syst. 10, 122 (2015)
S. Krauß, P. Wagner, C. Gawron, Phys. Rev. E 55, 5597 (1997)
P.G. Gipps, Trans. Res. B 15, 105 (1981)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kerner, B. The maximization of the network throughput ensuring free flow conditions in traffic and transportation networks: Breakdown minimization (BM) principle versus Wardrop’s equilibria. Eur. Phys. J. B 89, 199 (2016). https://doi.org/10.1140/epjb/e2016-70395-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2016-70395-8