A new fundamental diagram theory with the individual difference of the driver's perception ability

Based on the driver's individual difference of the driver's perception ability, we in this paper develop a new fundamental diagram with the driver's perceived error and speed deviation difference. The analytical and numerical results show that the speed-density and flow-density data are divided into three prominent regions. In the first region, the speed-density and flow-density data are scattered around the equilibrium speed-density and flow-density curves of the classical fundamental diagram theory, where the widths of these scattered data are very narrow and slightly increase with the real density (i.e., the scattered data appear as two thicker lines); the running speed is approximately equal to the free flow speed and the real flow approximately linearly increases with the real density. In the second region, the speed-density and flow-density data are scattered widely in a two-dimensional region, but the shapes of these widely scattered data are related to the properties of the driver's perceived error and speed deviation difference. In the third region, the scattered speed-density and flow-density data appear but these scattered data will quickly degenerate into the equilibrium speed-density and flow-density curves with the increase of the real density. Finally, the numerical results illustrate that the new fundamental diagram theory also produces the F-line, U-line, and L-line. The shapes of the scattered data, F-line, U-line, and L-line are relevant to the properties of the driver's perceived error and speed deviation difference. These results are qualitatively accordant with the real traffic, which shows that the new fundamental diagram theory can better describe some complex traffic phenomena in the real traffic system. In addition, the above results can help us to further explain why the widely scattered speed-density and flow-density data appear in the real traffic system and better understand the effects of the driver's individual difference on traffic flow.