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In this paper, using the Nagel-Schreckenberg model, we numerically investigate the probability $P_{\mathrm{\text{ac}}}$ of entering/circulating car accidents to occur at single-lane roundabout under the expanded open boundary. The roundabout consists of N on-ramps (respectively, off-ramps). The boundary is controlled by the injecting rates ${\alpha }_1,{\alpha }_2$ and the extracting rate $\beta$. The simulation results show that, depending on the injecting rates, the car accidents are more likely to happen when the capacity of the rotary is set to its maximum. Moreover, we found that the large values of rotary size L and the probability of preferential $P_{\mathrm{\text{exit}}}$ are reliable to improve safety and reduce accidents. However, the usage of indicator, the increase of $\beta$ and/or N provokes an increase of car accident probability.

In this paper, we propose a stochastic cellular automata model to study the traffic behavior at a single-lane roundabout. Vehicles can enter the interior lane or exit from it via $N$ intersecting lane, the boundary conditions are stochastic. The traffic is controlled by a self-organized scheme. It has turned out that depending on the rules of insertion to the roundabout, five distinct traffic phases can appear, namely, free flow, congestion, maximum current, jammed and gridlock. The transition between the free flow and the gridlock is forbidden. The density profiles are used to study the traffic pattern at the interior lane of the roundabout. In order to quantify the interactions between vehicles in the interior lane of the roundabout, the velocity correlation coefficient (VCC) is also studied. Besides, the spatiotemporal diagrams corresponding to the entry/exit lanes are derived numerically. Furthermore, we have investigated the effect of displaying signal ($P_{\mathrm{\text{In}}})$, as the $P_{\mathrm{\text{In}}}$ decreases, the maximum current increases at the expense of the free flow and the jamming phase. Finally, we have investigated the effect of the braking probability $P$ on the interior lane of the roundabout. We have found that the increase of $P$ raises the spontaneous jam formation on the ring. Thus, enlarges the maximum current and the jamming phase while the free flow phase decreases.

In this paper, we examine the impact of vehicles executing a full turn or U-turn in a single-lane roundabout system using a cellular automaton model. We investigate how increasing the number of these U-turning vehicles affects traffic flow characteristics and energy dissipation. Our findings reveal that as the prevalence of U-turning vehicles rises, the phase diagram undergoes significant changes; the maximum current phase expands, detrimentally impacting the free flow and congestion phases, while giving rise to a jamming phase. This shift results in a gradual increase in capacity at circulating lanes and a steady decline at entry/exit lanes. We also explore the role of aimless vehicles — those circulating without a fixed destination. As the proportion of such vehicles augments, it fosters an enlargement of the maximum current phase at the expense of the free flow and congestion phases. Furthermore, these vehicles influence energy dissipation across the three lanes of a roundabout. Significantly, we elucidate that variations in the percentage of these specific vehicular groups critically affect CO₂ emissions. Our research unravels vital insights into optimizing roundabout management to enhance traffic flow and reduce environmental impact.

In this paper, we propose a cellular automata model to study the energy dissipation in the roundabout system. The energy dissipation and the phase diagram of the system in the space ($\alpha ,\beta$) are constructed. The energy dissipation profile (SE${}_d$(i)), and the effect of the rate $\gamma$ (i.e., the rate of vehicles with no aimed exit point) and the probability P${}_{\mathrm{\text{exit}}}$ of choosing the next exit point to leave the circulating lane on the energy dissipation are shown. The simulation results show that the energy dissipation explains the nature of the phases, the quasi-free-flow (Q-FF) phase take place on the free flow phase because some vehicles decelerate at the entry point. Likewise, the results also indicate that the energy dissipation takes small values with the increases of the two probability $\gamma$ and P${}_{\mathrm{\text{exit}}}$ which enhance the environmental statutes of the roundabout system.