## 4 Discussion  
The cumulative distribution of betweenness values is calculated by Equation (9) and is shown in Figure 8. It can be seen from the figure that the P(a) of the hazardous factors obeys the power-law distribution _P(a) \(\sim\)0.4534x\({}^{-0.268}\)_ (\(R^{2}\) = 0.9049). This indicates that a few hazardous factors have high betweenness values, while most hazardous factors have low betweenness values. For example, in Figure 7, the 11 hazardous factors with top betweenness values hold 6.8 percent of the number of hazardous factors, while they take up to 45 percent of the sum of the overall betweenness value. If these hazardous factors are controlled, a large proportion of causal paths leading to hazards will be blocked. Thus, more resources should be allocated to the control of these 11 hazardous factors for eliminating or mitigating hazards. The control of the 11 hazardous factors can be implemented in two steps. The first step is to identify whether the hazardous factors are terminal, middle, or initial type. Based on the type, it can be determined whether the control of a factor should focus on preventing it from being caused or from causing others. Then, in the second step, control measures can be formulated for the corresponding incoming or outgoing edges. Furthermore, the effort or resources for control measures should be invested by the ranking result of edges. Figure 8: The cumulative distribution of betweenness. Figure 7: The betweenness value of UCAs and causal factors. The top 11 high-betweenness hazardous factors can be mainly divided into three kinds, i.e., UCAs, localization-related factors, and misuse-related factors. Due to the limited space, four representative hazardous factors (UCA4, UCA6, CF75, and CF142) of the three kinds are discussed to demonstrate how to develop targeted control strategies. * It can be seen from Figure 6 that UCA4 (the driver does not provide brake actions before the train exceeds the speed limit of the current section) is a terminal hazardous factor. This means that more resources should be allocated to its incoming edges to preventing it from happening. The importance ranking of its incoming edges in Table 3 shows that ECF76-UCA4 is the most important incoming edge of UCA4, followed by ECF73-UCA4, ECF91-UCA4, ECF95-UCA4, ECF128-UCA4, ECF130-UCA4, and ECF135-UCA4. Measures can be taken on these edges to control the hazard. For ECF76-UCA4, measures, for example, \"lower the speed limit when the TIDS loses localization\" can be taken. ECF73-UCA4 can be treated by \"provide an alarm when the localization of the TIDS is inaccurate\". For ECF91-UCA4, \"the driver-machine interface should be designed to highlight this emergent information\" can be taken. ECF95-UCA4 could be dealt with by \"the TIDS should give a reminder to the driver when the terrible environmental situation may affect the brake performance\". ECF128-UCA4 can be treated by \"the TIDS should provide a reminder of the current speed limit and its variation\". For ECF130-UCA4, \"the speed control of the driver should adjust to the operational environment\" could be taken. The control of ECF134-UCA4 can be \"new speed limit information should be updated to the TIDS in time\". ECF135-UCA4 could be treated by \"electronic map in the TIDS should be updated once any infrastructure in it is changed\". The priority of these measures should follow the importance ranking of the corresponding edges. * UCA6 (the driver uses the TIDS out of its designed zone) is also a terminal hazardous factor, as can be seen from Figure 6. This indicates that more resources should be put into incoming edges to prevent it from happening. The ranking of the incoming edges can be found in Table 3, which is ECF139-UCA6, ECF142-UCA6, ECF143-UCA6, ECF138-UCA6, ECF140-UCA6, and ECF141-UCA6. For ECF139-UCA6, measures, for example, \"the TIDS should provide sufficient reminder to ensure the driver has noticed that the TIDS cannot be used in the current zone\" can be taken.