Abstract
This paper attempts to reproduce the empirical phenomena of congested traffic flow with an on-ramp through a microscopic traffic model. First, an improved two-lane lattice hydrodynamic traffic flow model is proposed, which is capable of avoiding vehicles backward moving in original lattice hydrodynamic model. Then, the deterministic and stochastic on-ramps are designed and mapped into the new lattice model to reproduce the empirical phenomena. For the stochastic case, many empirical congested patterns are reproduced, such as moving localized cluster, triggered stop-and-go traffic (TSG), pinned localized cluster (PLC), oscillating congested traffic (OCT) and homogeneous congested traffic. For the deterministic case, a number of combination patterns of HST, PLC, TSG and OCT are found. Taken together, these results suggest that the present model is able to predict the congested traffic patterns.
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References
Kerner, B.S., Rehborn, H.: Experimental properties of phase transitions in traffic flow. Phys. Rev. Lett. 79(20), 4030–4033 (1997)
Helbing, D., Treiber, M.: Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Phys. Rev. Lett. 81(14), 3042–3045 (1998)
Helbing, D., Hennecke, A., Treiber, M.: Phase diagram of traffic states in the presence of inhomogeneities. Phys. Rev. Lett. 82(21), 4360–4363 (1999)
Lee, H.Y., Lee, H.W., Kim, D.: Dynamic states of a continuum traffic equation with on-ramp. Phys. Rev. E 59(5), 5101–5111 (1999)
Gupta, A.K., Katiyar, V.K.: Phase transition of traffic states with on-ramp. Phys. A 371, 674–682 (2006)
Tang, C.F., Jiang, R., Wu, Q.S.: Phase diagram of speed gradient model with an on-ramp. Phys. A 377, 641–650 (2007)
Tang, T.Q., Huang, H.J., Wong, S.C., Gao, Z.Y., Zhang, Y.: A new macro model for traffic flow on a highway with ramps and numerical tests. Commun. Theor. Phys. 51, 71–78 (2009)
Helbing, D., Treber, M., Kesting, A., Schonhof, M.: Theoretical vs. empirical classification and prediction of congested traffic states. Eur. Phys. J. B 69, 583–598 (2009)
Berg, P., Woods, A.: On-ramp simulations and solitary waves of a car-following model. Phys. Rev. E 64, 035602(R) (2001)
Jiang, R., Wu, Q.S., Wang, B.H.: Cellular automata model simulating traffic interactions between on-ramp and main road. Phys. Rev. E 66, 036104 (2002)
Treiber, M., Kesting, A.: Traffic Flow Dynamics: Data, Models and Simulation. Springer, Heidelberg (2013)
Nagatani, T.: Modified KdV equation for jamming transition in the continuum models of traffic. Phys. A 261, 599–607 (1998)
Nagatani, T.: TDGL and MKdV equations for jamming transition in the lattice models of traffic. Phys. A 264, 581–592 (1999)
Nagatani, T.: Jamming transitions and the modified Korteweg–de Vries equation in a two-lane traffic flow. Phys. A 265, 297–310 (1999)
Kang, Y.R., Sun, D.H.: Lattice hydrodynamic traffic flow model with explicit drivers physical delay. Nonlinear Dyn. 71(3), 531–537 (2012)
Ge, H.X., Zheng, P.J., Lo, S.M., Cheng, R.J.: TDGL equation in lattice hydrodynamic model considering drivers physical delay. Nonlinear Dyn. 76(1), 441–445 (2014)
Gupta, A.K., Redhu, P.: Analyses of the drivers anticipation effect in a new lattice hydrodynamic traffic flow model with passing. Nonlinear Dyn. 76(2), 1001–1011 (2014)
Gupta, A.K., Sharma, S., Redhu, P.: Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing. Nonlinear Dyn. 76(3), 1091–1108 (2015)
Redhu, P., Gupta, A.K.: Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing. Phys. A 421, 249–260 (2015)
Sharma, S.: Modeling and analyses of driver’s characteristics in a traffic system with passing. Nonlinear Dyn. 86(3), 2093–2104 (2016)
Sharma, S.: Effect of driver’s anticipation in a new two-lane lattice model with the consideration of optimal current difference. Nonlinear Dyn. 81, 991–1003 (2015)
Gupta, A.K., Redhu, P.: Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system. Phys. A 392, 5622–5632 (2013)
Redhu, P., Gupta, A.K.: Phase transition in a two-dimensional triangular flow with consideration of optimal current difference effect. Nonlinear Dyn. 78, 957–968 (2014)
Gupta, A.K., Redhu, P.: Jamming transition of a two-dimensionaL traffic dynamics with consideration of optimal current difference. Phys. Lett. A 377, 2027–2033 (2014)
Sharma, S.: Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior. Phys. A 421, 401–411 (2015)
Ge, H.X., Cui, Y., Zhu, K.Q., Cheng, R.J.: The control method for the lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 22(1–3), 903–908 (2015)
Redhu, P., Gupta, A.K.: Delayed-feedback control in a Lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 27(1–3), 263–270 (2015)
Gupta, A.K., Redhu, P.: Analyses of a modified two-lane lattice model by considering the density difference effect. Commun. Nonlinear Sci. Numer. Simul. 19(5), 1600–1610 (2014)
Tian, J.F., Jia, B., Li, X.G., Gao, Z.Y.: Flow difference effect in the lattice hydrodynamic model. Chin. Phys. B 19(4), 040303 (2010)
Tian, J.F., Yuan, Z.Z., Jia, B., Li, M.H., Jiang, G.J.: The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow. Phys. A 391(19), 4476–4482 (2012)
Wang, T., Gao, Z.Y., Zhang, J., Zhao, X.M.: A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect. Nonlinear Dyn. 75(1), 27–34 (2014)
Peng, G.H., Cai, X.H., Liu, C.Q., Tuo, M.X.: A new lattice model of traffic flow with the anticipation effect of potential lane changing. Phys. Lett. A 376, 447–451 (2011)
Peng, G.H., Nie, Y.F., Cao, B.F., Liu, C.Q.: A driver’s memory lattice model of traffic flow and its numerical simulation. Nonlinear Dyn. 67(3), 1811–1815 (2012)
Gupta, A.K., Dhiman, I.: Phase diagram of a continuum traffic flow model with a static bottleneck. Nonlinear Dyn. 79(1), 663–671 (2014)
Redhu, P., Gupta, A.K.: Effect of forward looking sites on a multi-phase lattice hydrodynamic model. Phys. A 445, 150–160 (2016)
Gupta, A.K., Sharma, S., Redhu, P.: Analyses of lattice traffic flow model on a gradient highway. Commun. Theor. Phys. 62, 393–404 (2014)
Acknowledgements
This research is supported in part by the National Natural Science Foundation of China (Grant Nos. 71571109, 71621001, 71471104, 71601015, 61472195), the Taishan Scholar Project Fund of Shandong Province of China, the Natural Science Foundation of Shandong Province (Grant No. ZR2013GQ001), the Fundamental Research Funds for the Central Universities (No. 2015JBM060).
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Wang, T., Zhang, J., Gao, Z. et al. Congested traffic patterns of two-lane lattice hydrodynamic model with on-ramp. Nonlinear Dyn 88, 1345–1359 (2017). https://doi.org/10.1007/s11071-016-3314-z
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DOI: https://doi.org/10.1007/s11071-016-3314-z