## 3 Access Control Policy Combination Method for Data Fusion in Railway Traffic Systems
### Subject Trust  
The trust in an access control model refers to the rating given by the participating entities in the current request or session. The more frequent and positive the interaction between the requesting subject and the target object during the authorization process, the higher the trust value between them. Trust consists of direct trust and recommendation trust.  
Although the performance of the accessing subject is evaluated based on different standards in different environments specifically, the general criteria include security attributes, reliability attributes, and performance attributes. Security attributes refer to the average number of illegal connections, the average number of scans on important ports, the average number of unauthorized attempts, the average number of virus carriers, and the average number of attacks. Reliability attributes consist of the average user error rate, the average user packet loss rate, the average connection establishment failure rate, and the average service success rate. Performance attributes include the average user IP packet response time, the average throughput, the average IP packet transmission delay, and the average storage resource occupancy rate [16]. For a given attribute index \(B_{k}\in[0,1]\) and the corresponding weight coefficient \(t_{k}\), where \(t_{k}\in[0,1]\) and \(\sum\)\(t_{k}=1\), the trust between \(i\) and \(j\) is \(D_{ij}=\sum\)\(t_{k}B_{k}\), ranging from 0 to 1.  
Direct trust refers to the rating given by a target object. For requesting subject \(i\) and object \(j\), direct trust of the \(k\)-\(th\) participation is evaluated based on their direct interaction or session, denoted as \(DT^{k}{}_{ij}\). To reflect the behavior of \(i\) in real time, time decay is taken into account, thus \(DT^{k}{}_{ij}\) can be represented in a recursive form as:  
\[DT_{ij}=\tau DT_{ij}^{k-1}+\sigma(1-\tau)DT_{ij}^{k},k\geq 1 \tag{6}\]  
where \(DT_{ij}^{0}\) represents the initial value, and is set to 0.5, indicating a moderate level of trust. The time decay factor \(\tau\in[0,\,1]\) describes the influence of previous interactions on the current trust value. A larger \(\alpha\) indicates a higher weight of historical trust in the calculation, and \(\tau=0\) indicates that the previous trust value is not considered. The success rate of historical interactions is represented by \(\sigma=\sqrt{N_{ij}/(M_{ij}+1)}\), where \(N_{ij}\) represents the number of successful interactions and \(M_{ij}\) represents the total number of historical interactions. The index \(\sigma\) aims to incentivize entities to maintain a high trust level gained before, preventing dishonest or malicious behavior by the subject.  
Recommendation trust.  
Recommendation trust \(RT^{k}{}_{ij}\) refers to the trust between two entities \(i\) and \(j\), obtained through recommendations from a third entity \(k\) with whom both \(i\) and \(j\) have interacted. To prevent malicious entities from exaggerating or defaming behaviors during the evaluation process, as well as to avoid external interference on the accessing entity, the trust of entity \(k\) towards entity \(i\) is used as the recommendation trust coefficient. So \(RT^{k}{}_{ij}\) is represented as:  
\[RT_{ij}=\frac{\sum\limits_{k}DT_{kj}DT_{ik}(x_{i},x_{k})N_{ik}}{\sum\limits_{ k\in K_{i}}N_{ik}} \tag{7}\]  
The trust \(T_{ij}\) of the accessing subject is mainly calculated based on the relevant direct trust and recommendation trust in the policy:  
\[T_{ij}=\beta DT_{ij}+(1-\beta)RT_{ij} \tag{8}\]  
where \(\beta\in[0,\,1]\) represents the influence of direct trust on the total trust. When \(\beta=1\), it indicates that the entity is newly added to the access control system, so the recommendation trust is not considered. If the accessing subject receives feedback information due to previous malicious behavior, its trust will be decreased. When the trust of the subject decreases to a certain level, it indicates that the entity is a malicious node and its trust cannot be recovered for a long period of time.