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This paper investigates the congestion and efficiency in complex traffic and transportation networks. Effects of different distributions of capacity and origin-destination traffic demand on the degree of congestion and efficiency are explored in different network topologies including scale-free networks, random networks and small-world networks. According to the increase of average traffic demand, the transition from free flow state to congested state is analyzed. For easy comparison, we discuss the reciprocal of the congestion degree, which is defined as the network unobstructedness. A linear relation between the degree of unobstructedness and efficiency in different networks is uncovered, and the linear proportional coefficients are different in scale-free networks, random networks and small-world networks. These coefficients can also be used to describe the different transport performance in different networks.
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Keywords:
- complex networks /
- congestion /
- efficiency
[1] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[2] Watts D J, Strogatz S H 1998 Nature 393 440
[3] Barabási A L, Albert R 1999 Science 286 509
[4] Latora V, Marchiori M 2002 Physica A 314 109
[5] Wu J J, Gao Z Y, Sun H J, Huang H J 2004 Mod. Phys. Lett. B 18 1043
[6] Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. 97 11149
[7] Chi L P, Wang R, Su H, Xu X P, Zhao J S, Li W, Cai X 2003 Chin. Phys. Lett. 20 1393
[8] Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 56 106]
[9] Hu Y, Zhu D 2009 Physica A 388 2061
[10] Echenique P, Gomez-Gardenes J, Moreno Y 2004 Phys. Rev. E 70 056105
[11] Wang W X, Wang B H, Yin C Y, Xie Y B, Zhou T 2006 Phys. Rev. E 73 026111
[12] Yan G, Zhou T, Hu B, Fu Z Q, Wan B H 2006 Phys. Rev. E 73 046108
[13] Wang D, Yu H, Jing Y W, Jiang N, Zhang S Y 2009 Acta Phys. Sin. 58 6802 (in Chinese) [王丹, 于灏, 井元伟, 姜囡, 张嗣瀛 2009 58 6802]
[14] Wu J J, Gao Z Y, Sun H J, Huang H J 2006 Europhys. Lett. 74 560
[15] Wu J J, Gao Z Y, Sun H J 2008 Physica A 387 1025
[16] Wu J J, Gao Z Y, Sun H J 2008 Journal of Transportation Systems Engineering and Information Technology 4 69 (in Chinese) [吴建军, 高自友, 孙会君 2008 交通运输系统工程与信息 4 69]
[17] Zhao X M, Gao Z Y 2007 Phys. lett. 24 283
[18] O’Kelly M E, Bryan D L 1998 Transp. Res. B 32 605
[19] Alumur S A, Kara B Y 2008 Euro. J. Oper. Res. 190 1
[20] Sheffi Y 1985 Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Prentice Hall, Englewood Cliffs, New Jersey)
[21] Wardrop J G 1952 Proceedings of the Institute of Civil Engineers Part II 1 325
[22] Beckmann M, Mcguire C B, Winsten C B 1956 Studies in the Economics of Transportation (New Haven: Yale University Press) p325
[23] Kim T J 1990 Advanced Transport and Spatial Systems Model (New York: Springer Verlag)
[24] Latora V, Marchiori M 2001 Phys. Rev. Lett. 87 198701
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[1] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[2] Watts D J, Strogatz S H 1998 Nature 393 440
[3] Barabási A L, Albert R 1999 Science 286 509
[4] Latora V, Marchiori M 2002 Physica A 314 109
[5] Wu J J, Gao Z Y, Sun H J, Huang H J 2004 Mod. Phys. Lett. B 18 1043
[6] Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. 97 11149
[7] Chi L P, Wang R, Su H, Xu X P, Zhao J S, Li W, Cai X 2003 Chin. Phys. Lett. 20 1393
[8] Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 56 106]
[9] Hu Y, Zhu D 2009 Physica A 388 2061
[10] Echenique P, Gomez-Gardenes J, Moreno Y 2004 Phys. Rev. E 70 056105
[11] Wang W X, Wang B H, Yin C Y, Xie Y B, Zhou T 2006 Phys. Rev. E 73 026111
[12] Yan G, Zhou T, Hu B, Fu Z Q, Wan B H 2006 Phys. Rev. E 73 046108
[13] Wang D, Yu H, Jing Y W, Jiang N, Zhang S Y 2009 Acta Phys. Sin. 58 6802 (in Chinese) [王丹, 于灏, 井元伟, 姜囡, 张嗣瀛 2009 58 6802]
[14] Wu J J, Gao Z Y, Sun H J, Huang H J 2006 Europhys. Lett. 74 560
[15] Wu J J, Gao Z Y, Sun H J 2008 Physica A 387 1025
[16] Wu J J, Gao Z Y, Sun H J 2008 Journal of Transportation Systems Engineering and Information Technology 4 69 (in Chinese) [吴建军, 高自友, 孙会君 2008 交通运输系统工程与信息 4 69]
[17] Zhao X M, Gao Z Y 2007 Phys. lett. 24 283
[18] O’Kelly M E, Bryan D L 1998 Transp. Res. B 32 605
[19] Alumur S A, Kara B Y 2008 Euro. J. Oper. Res. 190 1
[20] Sheffi Y 1985 Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Prentice Hall, Englewood Cliffs, New Jersey)
[21] Wardrop J G 1952 Proceedings of the Institute of Civil Engineers Part II 1 325
[22] Beckmann M, Mcguire C B, Winsten C B 1956 Studies in the Economics of Transportation (New Haven: Yale University Press) p325
[23] Kim T J 1990 Advanced Transport and Spatial Systems Model (New York: Springer Verlag)
[24] Latora V, Marchiori M 2001 Phys. Rev. Lett. 87 198701
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