## 3 Methodology
### Data Collection  
This study uses AIS data obtained from the Benoa VTS, which is designated not only as a harbor VTS but also has a supervised strait area of 48 km from its location. The annual traffic in the Lombok Strait is shown in Table 1.  
Increases in marine traffic were observed from 2021 to 2023, with the total traffic increasing by 12.7% in 2022 and 10.01% in 2023. Passenger and ferry ships show the most substantial growth, increasing from 46.09% of the total traffic in 2021 to 56.21% in 2023, equivalent to 6913 passages, indicating denser crossing traffic each year. Moreover, cargo ships maintained a relatively stable presence, comprising approximately 31-38% of the traffic. In contrast, tankers and other types of ships experienced a slight decline in their share of the total traffic. Additionally, there was a significant increase in the number of Indonesian ships, increasing from 59.2% in 2021 to 66.17% in 2023. Conversely, the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Classification**} & \multirow{2}{*}{**Description**} & \multicolumn{3}{c}{**Year**} \\ \cline{3-6}  & & & **2021** & **2022** & **2023** \\ \hline \multirow{4}{*}{1.} & \multirow{4}{*}{Traffic} & Passing TSS & 14,965 & 15,092 & 15,136 \\  & & Crossing TSS & 14,649 & 18,302 & 21,603 \\  & & Total & 29,614 & 33,394 & 36,739 \\  & & Annual Increase (\%) & - & 12.7 & 10.01 \\ \hline \multirow{4}{*}{2.} & \multirow{4}{*}{Ship Type} & Cargo Ship & 14,838 & 14,770 & 14,966 \\  & & Passenger & 13,649 & 17,255 & 20,652 \\  & & Others & 1127 & 1369 & 1121 \\ \hline \multirow{2}{*}{3.} & \multirow{2}{*}{Flag} & Indonesian & 17,510 & 21,385 & 24,313 \\  & & Foreign & 12,070 & 12,213 & 12,426 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Annual traffic.  
Figure 3: Study area: (**a**) middle part of Indonesia where ASL II is located; (**b**) Lombok Strait, TSS, and PSSA.  
proportion of foreign ships decreased from 40.8% to 33.82%, suggesting an increasing dominance of Indonesian vessels in this region. This increase in local traffic was due to the increasing demand for direct transportation from Java to Lombok [40]. The monthly traffic in 2023 is shown below.  
Figure 4 depicts the monthly trend of marine traffic in the strait throughout the year. The passing traffic is relatively stable, in contrast to the crossing traffic, where a noticeable increase in August to the highest number in October can be seen. Therefore, since it was the densest month of the year, 7 d AIS data in that specific month were utilized in this study.  
The following sections will focus on redesigning the rectangle precautionary area into circular roundabout wherein Section 4 provides comprehensive marine traffic analysis in the study area with AIS data and the determination of ship domains. Finally, the roundabouts are proposed, as shown in steps 1, 2, and 3 in Figure 1. In Section 5, the validation of roundabout conversion is discussed through the implementation and exploration of track diversion, conflict points, and capacity calculation to define the overall performances. Moreover, risk assessment is also performed. Section 6 discusses the findings, and Section 7 concludes the paper.