Fig. 1

Illustration of gravitational force acting upon vehicles on an uphill and downhill highway"

Table 1

Coefficients $k_i $ of the model"

Table 2

Coefficients $g_i $ of the model"

Fig. 2

Temporal and spatial evolution of density wave under different uphill slopes $\theta $ when $k=0.01$, $t_0 =1$"

Fig. 3

Density profile of different uphill slopes when $k=0.01$, $t_0 =1$, $t=3 000$ s"

Fig. 4

Flux profile of different uphill slopes $\theta $ when $k=0.01$, $t_0 =1$, $t=3 000$ s"

Fig. 5

Hysteresis loop of different uphill slopes $\theta $ when $k=0.01$, $t_0 =1$, $t=3 000$ s"

Fig. 6

Temporal and spatial evolution of density wave under different downhill slope $\theta $ when $k=0.01$, $t_0 =1$"

Fig. 7

Density profile of different downhill slopes $\theta$ when $k=0.01$, $t_0 =1$, $t=3 000$ s"

Fig. 8

Flux profile of different downhill slopes $\theta$ when $k=0.01$, $t_0 =1$, $t=3 000$ s"

Fig. 9

Hysteresis loop of different downhill slopes $\theta $ when $k=0.01$, $t_0 =1$, $t=3 000$ s"

Fig. 10

Temporal and spatial evolution of density wave under different $k$ when $\theta =2^{\circ}$, $t_0 =1$"

Fig. 11

Density profile of different $k$ when $\theta =2^{\circ}$, $t_0 =1$, $t=3 000$ s"

Fig. 12

Flux profile of different $k$ when $\theta =2^{\circ}$, $t_0 =1$, $t=3 000$ s"

Fig. 13

Tysteresis loop of different $k$ when $\theta =2^{\circ}$, $t_0 =1$, $t=3 000$ s"