Visco-elastic traffic flow model - Zhu, Zuojin (2013)
To increase our understanding of the operations of traffic system, a visco-elastic traffic model was proposed in analogy of non-Newtonian fluid mechanics. The traffic model is based on mass and momentum conservations, and includes a constitutive relation similar to that of linear visco-elastic fluids. The further inclusion of the elastic effect allows us to describe a high-order traffic model more comprehensively because the use of relaxation time indicates that vehicle drivers adjust their time headway in a reasonable and safe range. The self-organizing behaviour is described by introducing the effects of pressure and visco-elasticity from the point of view in fluid mechanics. Both the viscosity and elasticity can be determined by using the relaxation time and the traffic sound speed. The sound speed can be approximately represented by the road operational parameters including the free-flow speed, the jam density, and the density of saturation if the jam pressure in traffic flows is identical to the total pressure at the flow saturation point. A linear stability analysis showed that the traffic flow should be absolutely unstable for disturbances with short spatial wavelengths. There are two critical points of regime transition in traffic flows. The first point happens at the density of saturation, and the second point occurs at a density relating on the sound speed and the fundamental diagram of traffic flows. By using a triangular form flow–density relation, a numerical test based on the new model is carried out for congested traffic flows on a loop road without ramp effect. The numerical results are discussed and compared with the result of theoretical analysis and observation data of traffic flows.