Traffic Flow Merging and Bifurcating at Junction on Two-Lane Highway

Affiliation(s)

Department of Mechanical Engineering, Division of Thermal Science, Shizuoka University, Hamamatsu 432-8561, Japan.

Department of Mechanical Engineering, Division of Thermal Science, Shizuoka University, Hamamatsu 432-8561, Japan.

ABSTRACT

In this paper we study the traffic states and jams in vehicular traffic merging and bifurcating at a junction on a two-lane highway. The two-lane traffic model for the vehicular motion at the junction is presented where a jam occurs frequently due to merging, lane changing, and bifurcating. The traffic flow is called the weaving. At the weaving section, vehicles slow down and then move aside on the other lane for changing their direction. We derive the fundamental diagrams (flow-density diagrams) for the weaving traffic flow. The traffic states vary with the density, slowdown speed, and the fraction of vehicles changing the lane. The dynamical phase transitions occur. It is shown that the fundamental diagrams depend highly on the traffic states.

In this paper we study the traffic states and jams in vehicular traffic merging and bifurcating at a junction on a two-lane highway. The two-lane traffic model for the vehicular motion at the junction is presented where a jam occurs frequently due to merging, lane changing, and bifurcating. The traffic flow is called the weaving. At the weaving section, vehicles slow down and then move aside on the other lane for changing their direction. We derive the fundamental diagrams (flow-density diagrams) for the weaving traffic flow. The traffic states vary with the density, slowdown speed, and the fraction of vehicles changing the lane. The dynamical phase transitions occur. It is shown that the fundamental diagrams depend highly on the traffic states.

Cite this paper

nullK. Tobita, Y. Naito and T. Nagatani, "Traffic Flow Merging and Bifurcating at Junction on Two-Lane Highway,"*World Journal of Mechanics*, Vol. 2 No. 4, 2012, pp. 203-215. doi: 10.4236/wjm.2012.24025.

nullK. Tobita, Y. Naito and T. Nagatani, "Traffic Flow Merging and Bifurcating at Junction on Two-Lane Highway,"

References

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[12] H. X. Ge, S. Q. Dai, L. Y. Dong and Y. Xue, “Stabilization Effect of Traffic Flow in an Extended Car-Following Model Based on an Intelligent Transportation System Application,” Physical Review E, Vol. 70, No. 6, 2004, pp. 1-6. doi:10.1103/PhysRevE.70.066134

[13] R. Nagai, T. Nagatani and A. Yamada, “Phase Diagram in Multi-Phase Traffic Model,” Physica A, Vol. 355, No. 2, 2005, pp. 530-550. doi:10.1016/j.physa.2005.04.004

[14] R. Nagai, H. Hanaura, K. Tanaka and T. Nagatani, “Discontinuity at Edge of Traffic Jam Induced by Slowdown,” Physica A, Vol. 364, No. 2, 2006, pp. 464-472. doi:10.1016/j.physa.2005.09.055

[15] M. Bando, K. Hasebe, A. Nakayama and Y. Sugiyama, “Dynamical Model of Traffic Congestion and Numerical Simulation,” Physical Review E, Vol. 51, No. 2, 1995, pp. 1035-1042. doi:10.1103/PhysRevE.51.1035

[16] C.-F. Dong, X. Ma and B.-H. Wang, “Weighted Congestion Coefficient Feedback in Intelligent Transportation Systems,” Physics Letters A, Vol. 374, No. 11, 2010, pp. 1326-1331. doi:10.1016/j.physleta.2010.01.011

[17] R. Jiang, Q. Wu and Z. Zhu, “Full Velocity Difference Model for a Car-Following Theory,” Physical Review E, Vol. 64, No. 1, 2002, pp. 1-4. doi:10.1103/PhysRevE.64.017101

[18] B. A. Toledo, V. Munoz, J. Rogan and C. Tenreino, “Modeling Traffic through a Sequence of Traffic Light,” Physical Review E, Vol. 70, No. 1, 2004, pp. 1-6.

[19] T. Nagatani, “Clustering and Maximal Flow in Vehicular Traffic through a Sequence of Traffic Lights,” Physica A, Vol. 377, No. 2, 2007, pp. 651-660. doi:10.1016/j.physa.2006.11.028

[20] C. Chen, J. Chen and X. Guo, “Influences of Overtaking on Two-Lane Traffic with Signals,” Physica A, Vol. 389, No. 1, 2010, pp. 141-148. doi:10.1016/j.physa.2009.09.007

[21] G. H. Peng, X. H. Cai, B. F. Cao and C. Q. Liu, “NonLane-Based Lattice Hydrodynamic Model of Traffic Flow Considering the Lateral Effects of the Lane Width,” Physics Letters A, Vol. 375, No. 30-31, 2011, pp. 2823-2827. doi:10.1016/j.physleta.2011.06.021

[22] G. H. Peng, X. H. Cai, C. Q. Liu, B. F. Cao and M. X. Tuo, “Optimal Velocity Difference Model for a Car-Following Theory,” Physics Letters A, Vol. 375, No. 45, 2011, pp. 3973-3977. doi:10.1016/j.physleta.2011.09.037

[23] W.-X. Zhu and E.-X. Chi, “Analysis of Generalized Optimal Current Lattice Model for Traffic Flow,” International Journal of Modern Physics C, Vol. 19, No. 5, 2008, pp. 727-739. doi:10.1142/S0129183108012467

[24] Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki and S. Yukawa, “Traffic Jams without Bottlenecks-Experimental Evidence for the Physical Mechanism of the Formation of a Jam,” New Journal of Physics, Vol. 10, No. 3, 2008, pp. 1-7. doi:10.1088/1367-2630/10/3/033001

[25] T. Nagatani, “Instability of a Traffic Jam Induced by Slowing Down,” Journal of Physical Society of Japan, Vol. 66, No. 7, 1997, pp. 1928-1931. doi:10.1143/JPSJ.66.1928

[26] H. Hanaura, T. Nagatani and K. Tanaka, “Jam Formation in Traffic Flow on a Highway with Some Slowdown,” Physica A, Vol. 374, No. 1, 2007, pp. 419-430. doi:10.1016/j.physa.2006.07.032

[27] K. Komada, S. Masukura and T. Nagatani, “Traffic Flow on a Toll Highway with Electronic and Traditional Tollgates,” Physica A, Vol. 388, No. 24, 2009, pp. 4979-4990. doi:10.1016/j.physa.2009.08.019

[28] R. Nishi, H. Miki, A. Tomoeda and K. Nishinari, “Achievement of Alternative Configurations of Vehicles on Multiple Lanes,” Physical Review E, Vol. 79, No. 6, 2009, pp. 1-8. doi:10.1103/PhysRevE.79.066119

[29] H. Kita, “A Merging-giveway Interaction Model of Cars in a Merging Section: a Game Theoretic Analysis,” Transportation Research A, Vol. 33, No. 3, 1999, pp. 305-312. doi:10.1016/S0965-8564(98)00039-1

[30] P. Hidas, “Modeling Vehicle Interactions in Microscopic Simulation of Merging and Weaving,” Transportation Research C, Vol. 13, No. 1, 2005, pp. 37-62. doi:10.1016/j.trc.2004.12.003

[1] T. Nagatani, “The Physics of Traffic Jams,” Reports on Progress Physics, Vol. 65, No. 9, 2002, pp. 1331-1386. doi:10.1088/0034-4885/65/9/203

[2] D. Helbing, “Traffic and Related Self-Driven Many-Particle Systems,” Reviews of Modern Physics, Vol. 73, No. 4, 2001, pp. 1067-1141. doi:10.1103/RevModPhys.73.1067

[3] D. Chowdhury, L. Santen, A. Schadscheider, “Statistical Physics of Vehicular Traffic and Some Related Systems,” Physics Report, Vol. 329, No. 4, 2000, pp. 199-329. doi:10.1016/S0370-1573(99)00117-9

[4] K. Nagel and M. Schreckenberg, “A Cellular Automaton Model for Freeway Traffic,” Journal of Physics I France, Vol. 2, No. 12, 1992, pp. 2221-2229. doi:10.1051/jp1:1992277

[5] M. Treiber, A. Hennecke and D. Helbing, “Congested Traffic States in Empirical Observations and Microscopic Simulations,” Physical Review E, Vol. 62, No. 2, 2000, pp. 1805-1824. doi:10.1103/PhysRevE.62.1805

[6] K. Nishinari, D. Chowdhury and A. Schadschneider, “Cluster Formation and Anomalous Fundamental Diagram in an Ant-Trail Model,” Physical Review E, Vol. 67, No. 3, 2002, pp. 1-11. doi:10.1103/PhysRevE.67.036120

[7] K. Yamamoto, S. Kubo and K. Nishinari, “Simulation for Pedestrian Dynamics by Real-Coded Cellular Automata (RCA),” Physica A, Vol. 379, No. 2, 2007, pp. 654-660. doi:10.1016/j.physa.2007.02.040

[8] T. Nagatani, “Chaotic and Periodic Motions of a Cyclic Bus Induced by Speedup,” Physical Review E, Vol. 66, No. 4, 2002, pp. 1-7. doi:10.1103/PhysRevE.66.046103

[9] E. Brockfeld, R. Barlovic, A. Schadschneider and M. Schreckenberg, “Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic,” Physical Review E, Vol. 64, No. 5, 2001, pp. 1-12. doi:10.1103/PhysRevE.64.056132

[10] S. Kurata and T. Nagatani, “Spatio-Temporal Dynamics of Jams in Two-Lane Traffic Flow with a Blockage,” Physica A, Vol. 318, No. 3, 2003, pp. 537-550. doi:10.1016/S0378-4371(02)01376-6

[11] S. Lammer and D. Helbing, “Self-Control of Traffic Lights and Vehicle Flows in Urban Road Networks,” Journal of Statistical Mechanics: Theory and Experiment, Vol. 2008, No. 4, 2008, pp. 1-36. doi:10.1088/1742-5468/2008/04/P04019

[12] H. X. Ge, S. Q. Dai, L. Y. Dong and Y. Xue, “Stabilization Effect of Traffic Flow in an Extended Car-Following Model Based on an Intelligent Transportation System Application,” Physical Review E, Vol. 70, No. 6, 2004, pp. 1-6. doi:10.1103/PhysRevE.70.066134

[13] R. Nagai, T. Nagatani and A. Yamada, “Phase Diagram in Multi-Phase Traffic Model,” Physica A, Vol. 355, No. 2, 2005, pp. 530-550. doi:10.1016/j.physa.2005.04.004

[14] R. Nagai, H. Hanaura, K. Tanaka and T. Nagatani, “Discontinuity at Edge of Traffic Jam Induced by Slowdown,” Physica A, Vol. 364, No. 2, 2006, pp. 464-472. doi:10.1016/j.physa.2005.09.055

[15] M. Bando, K. Hasebe, A. Nakayama and Y. Sugiyama, “Dynamical Model of Traffic Congestion and Numerical Simulation,” Physical Review E, Vol. 51, No. 2, 1995, pp. 1035-1042. doi:10.1103/PhysRevE.51.1035

[16] C.-F. Dong, X. Ma and B.-H. Wang, “Weighted Congestion Coefficient Feedback in Intelligent Transportation Systems,” Physics Letters A, Vol. 374, No. 11, 2010, pp. 1326-1331. doi:10.1016/j.physleta.2010.01.011

[17] R. Jiang, Q. Wu and Z. Zhu, “Full Velocity Difference Model for a Car-Following Theory,” Physical Review E, Vol. 64, No. 1, 2002, pp. 1-4. doi:10.1103/PhysRevE.64.017101

[18] B. A. Toledo, V. Munoz, J. Rogan and C. Tenreino, “Modeling Traffic through a Sequence of Traffic Light,” Physical Review E, Vol. 70, No. 1, 2004, pp. 1-6.

[19] T. Nagatani, “Clustering and Maximal Flow in Vehicular Traffic through a Sequence of Traffic Lights,” Physica A, Vol. 377, No. 2, 2007, pp. 651-660. doi:10.1016/j.physa.2006.11.028

[20] C. Chen, J. Chen and X. Guo, “Influences of Overtaking on Two-Lane Traffic with Signals,” Physica A, Vol. 389, No. 1, 2010, pp. 141-148. doi:10.1016/j.physa.2009.09.007

[21] G. H. Peng, X. H. Cai, B. F. Cao and C. Q. Liu, “NonLane-Based Lattice Hydrodynamic Model of Traffic Flow Considering the Lateral Effects of the Lane Width,” Physics Letters A, Vol. 375, No. 30-31, 2011, pp. 2823-2827. doi:10.1016/j.physleta.2011.06.021

[22] G. H. Peng, X. H. Cai, C. Q. Liu, B. F. Cao and M. X. Tuo, “Optimal Velocity Difference Model for a Car-Following Theory,” Physics Letters A, Vol. 375, No. 45, 2011, pp. 3973-3977. doi:10.1016/j.physleta.2011.09.037

[23] W.-X. Zhu and E.-X. Chi, “Analysis of Generalized Optimal Current Lattice Model for Traffic Flow,” International Journal of Modern Physics C, Vol. 19, No. 5, 2008, pp. 727-739. doi:10.1142/S0129183108012467

[24] Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki and S. Yukawa, “Traffic Jams without Bottlenecks-Experimental Evidence for the Physical Mechanism of the Formation of a Jam,” New Journal of Physics, Vol. 10, No. 3, 2008, pp. 1-7. doi:10.1088/1367-2630/10/3/033001

[25] T. Nagatani, “Instability of a Traffic Jam Induced by Slowing Down,” Journal of Physical Society of Japan, Vol. 66, No. 7, 1997, pp. 1928-1931. doi:10.1143/JPSJ.66.1928

[26] H. Hanaura, T. Nagatani and K. Tanaka, “Jam Formation in Traffic Flow on a Highway with Some Slowdown,” Physica A, Vol. 374, No. 1, 2007, pp. 419-430. doi:10.1016/j.physa.2006.07.032

[27] K. Komada, S. Masukura and T. Nagatani, “Traffic Flow on a Toll Highway with Electronic and Traditional Tollgates,” Physica A, Vol. 388, No. 24, 2009, pp. 4979-4990. doi:10.1016/j.physa.2009.08.019

[28] R. Nishi, H. Miki, A. Tomoeda and K. Nishinari, “Achievement of Alternative Configurations of Vehicles on Multiple Lanes,” Physical Review E, Vol. 79, No. 6, 2009, pp. 1-8. doi:10.1103/PhysRevE.79.066119

[29] H. Kita, “A Merging-giveway Interaction Model of Cars in a Merging Section: a Game Theoretic Analysis,” Transportation Research A, Vol. 33, No. 3, 1999, pp. 305-312. doi:10.1016/S0965-8564(98)00039-1

[30] P. Hidas, “Modeling Vehicle Interactions in Microscopic Simulation of Merging and Weaving,” Transportation Research C, Vol. 13, No. 1, 2005, pp. 37-62. doi:10.1016/j.trc.2004.12.003