中文

Journal of Shanghai University >

2020 , Vol. 26 >Issue 3: 367 - 381

DOI: https://doi.org/10.12066/j.issn.1007-2861.2209

Transportation Science and Computation

Predicted effect of average flux difference in a lattice hydrodynamic model with gradients

Expand
  • 1. College of International Economics and Trade, Ningbo University of Finance and Economics, Ningbo 315175, Zhejiang, China
    2. Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, Zhejiang, China

Received date: 2020-02-10

  Online published: 2020-07-07

Fold

Abstract

By studying the predicted effect of average flux difference, a new lattice hydrodynamic model was proposed for a gradient highway. The control theory was employed using linear analysis, and the stability condition for this new model was analyzed. To depict the evolution of traffic density waves in the traffic system, the mKdV equation near the critical point was derived by nonlinear analysis. Additionally, numerical simulation was performed to directly describe the evolution of traffic, which verified the results of the theoretical analysis. The results revealed that the predicted effect of average flux difference can stabilize the traffic flow.

Key words： average flux difference; predicted effect; control signal; gradients; lattice hydrodynamic model

Cite this article

WEI Qi, CHANG Yinyin, GE Hongxia, CHENG Rongjun . Predicted effect of average flux difference in a lattice hydrodynamic model with gradients[J]. Journal of Shanghai University, 2020 , 26(3) : 367 -381 . DOI: 10.12066/j.issn.1007-2861.2209

References

[1] Bando M, Hasebe K, Nakayama A. Dynamical model of traffic congestion and numerical simulation[J]. Physical Review E, 1995,51:1035-1042.
[2] Wang J F, Sun F X, Ge H X. Effect of the driver's desire for smooth driving on the car-following model[J]. Physica A, 2018,512:96-108.
[3] Xue Y, Dong L Y, Dai S Q. An improved one-dimensional cellular automaton model of traffic flow and the effect of deceleration probability[J]. Acta Physics Sinica, 2001,50:445-449.
[4] Gao K, Jiang R, Hu S X, et al. Cellular-automaton model with velocity adaptation in the framework of Kerner's three-phase traffic theory[J]. Physical Review E, 2007,76:026105.
[5] Guptaa K, Sharma S, Redhu P, Analyses of lattice traffic flow model on a gradient highway[J]. Communications in Theoretical Physica, 2014,62:393-404.
[6] Kaur R, Sharma S. Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles[J]. Physics Letters A, 2018,382:1449-1455.
[7] Treiber M, Hennecke A, Helbing D. Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model[J]. Physical Review E, 1999,59:239-253.
[8] Helbing D, Treiber M. Gas-Kinetic-Based traffic model explaining observed hysteretic phase transition[J]. Physical Review Letters, 1998,81:3042-3045.
[9] Nagatani T. Modified KdV equation for jamming transition in the continuum models of traffic[J]. Physica A, 1998,261:599-607.
[10] Komada K, Masukura S, Nagatani T. Effect of gravitational force upon traffic flow with gradients[J]. Physica A, 2009,388:2880-2894.
[11] Ge H X, Cheng R J, Lo S M. A lattice model for bidirectional pedestrian flow on gradient road[J]. Communications in Theoretical Physica, 2014,62:259-264.
[12] Gupta A K, Sharma S, Redhu P. Analyses of lattice traffic flow model on a gradient highway[J]. Communications in Theoretical Physica, 2014,62:393-404.
[13] Cao J L, Shi Z K. Analysis of a novel two-lane lattice model on a gradient road with the consideration of relative current[J]. Communications in Nonlinear Science and Numerical Simulation, 2016,33:1-18.
[14] Kaur R, Sharma S. Modeling and simulation of driver's anticipation effect in a two-lane system on curved road with slope[J]. Physica A, 2018,499:110-120.
[15] Jiang C T, Cheng R J, Ge H X. Mean-field flow difference model with consideration of on-ramp and off-ramp[J]. Physica A, 2019,513:465-476.
Options
Outlines

/

〈 〉