Effect of damaged vehicle evacuation on traffic flow with open boundaries

The effects of the damaged car evacuation $\left(P_{exit}\right)$ and the collision $\left(P_{col}\right)$ probabilities on the traffic flow behavior of a car accident are investigated in the one-dimensional cellular automaton Nagel-Schreckenberg model, with injecting $\left(\alpha \right)$ and extracting $\left(\beta \right)$ rates in parallel dynamics. In this study, we suppose that the car involved in collision is evacuated from the road, with an exit probability $P_{exit}$. It is found that the behaviors of density, current, and $\left(\alpha ,\beta \right)$ phase diagram topology depend strongly on the values of $P_{exit}$ and $P_{col}$. Indeed, the high-density region shrinks when increasing $P_{exit}$. Moreover, the critical value ${\alpha }_c\left(\beta \right)$, at which the low-density–high-density transition occurs, increases when increasing $P_{col}$ and/or $P_{exit}$. Furthermore, the critical value at which the transition high-density–low-density occurs decreases when increasing $\beta$ and increases with $\alpha$.

Figure 1

Variation of density $\rho$ as a function of injecting rate $\alpha$ for $P_{col}={10}^{-3}$. (a) $P_{exit}=0.1$ and for different values of extracting rate $\beta$. (b) $\beta =0.5$ and for three values of $P_{exit}$.

Figure 2

Variation of current $⟨J⟩$ vs the injection rate $\alpha$ for $P_{col}={10}^{-3}$. (a) $P_{exit}=0.1$ and for different values of extracting rate $\beta$ and (b) for $\beta =0.5$ in three following cases: (1) without removing cars, (2) $P_{exit}=0.5$, and (3) $P_{exit}=1$.

Figure 3

Phase diagram $\left(\alpha ,\beta \right)$ planes for (a) $P_{col}={10}^{-3}$ and (b) $P_{col}=2\times {10}^{-3}$. (1) $P_{exit}=0$, (2) $P_{exit}=0.5$, and (3) $P_{exit}=1$.

Figure 4

Variation of density $\rho$ as a function of removing rate $P_{exit}$ for $P_{col}=0.1$ and $\alpha =0.8$ and for several values of $\beta$.

Figure 5

Average density behavior as a function of $P_{col}$ in the case where $P_{exit}=0.5$ (a) for $\alpha =0.8$ and for several values of $\beta$ and (b) for $\beta =0.1$ and for different values of $\alpha$.

Figure 6

Phase diagram $\left(P_{col},\beta \right)$ plane for $P_{exit}=0.5$ and $\alpha =0.8$.

Figure 7

Space-time structure for $\alpha =0.8$, $P_{exit}=0.5$, and $P_{col}={10}^{-2}$ in two following cases: (a) $\beta =0.1$ and (b) $\beta =0.8$. Each horizontal row of full triangles represents the instantaneous position of cars moving right, while the successive rows indicate the position of the same cars at successive time steps.