The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

H.X. Ge, R.J. Cheng and L. Lei

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 14, 2825-2834

Abstract: The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg–de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg–de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.

Keywords: Traffic flow; Lattice hydrodynamic model; KdV equation; mKdV equation; Numerical simulation (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:14:p:2825-2834

DOI: 10.1016/j.physa.2010.03.007

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