# A Reliable Routing Algorithm Based on Path Satisfaction in the Energy Internet
## 3 Network Architecture and System Model
### System Model
#### 3.2.1 Link Model
Additionally, due to the impacts of man-made sabotage and the aging factor, communication links and power lines consequently have a similar failure probability. Obviously, this characteristic differs from other performance evaluation metrics employed in the telecommunication networks, such as traffic volume and bandwidth utilization. The metric of link importance is closely related to the voltage scale of substations in the EI. Generally, the higher voltage of power lines denote a wider transmission range. For instance, the importance of the power line with 500 kV is higher than that of the 220 kV power line. As the power line voltage is a large positive integer, it is necessary to normalize the power line voltage for calculation convenience, as follows:  
\[\mathcal{V}_{e}=\frac{\mathcal{V}_{e}-\mathcal{V}_{\min}}{\mathcal{V}_{\max}- \mathcal{V}_{e}},\forall e\in E,\mathcal{V}_{e}\in V\] (  
The link reliability is used to measure the link transmission ability without failures. The link mean time to repair (MTTR) and the mean time between failures (MTBF) are used to compute the link reliability as follows:  
\[A_{e}=(\mathrm{MTBR}/(\mathrm{MTBR}+\mathrm{MTTR}))^{L} \tag{5}\]  
Here, \(L\) is the length of link \(e\). The substations are often interconnected with different transmission mediums in the EI, such as an all-dielectric self-supporting optic fiber cable (ADSS), an optical fiber composite overhead ground wire (OPGW), and an ordinary optical fiber. Different types of links demonstrate discrepant reliability levels even under the same conditions. Relevant studies demonstrate that the failure probability of the ADSS per kilometer is higher than that of the OPGW in the range of [0.4%, 0.6%] [38]. Generally, the larger the link betweenness centrality, the more important the link. Meanwhile, the link delivered more services easily, resulting in service aggregation. Therefore, to make sure services are uniformly distributed on the links, the link availability should be related to the value of the link betweenness. To avoid service aggregation in the routing with larger link betweenness centrality, the link availability should be inversely proportional to it. In the same way, the link delivers heavier traffic and is assigned a lower availability. Additionally, OPGW has a higher availability than ADSS. Finally, the link availability is computed as follows:  
\[\chi_{e}=\frac{\zeta_{e}\cdot A_{e}}{I_{e}\cdot(\psi_{e}+\varepsilon)} \tag{6}\]  
where \(\zeta_{e}\) denotes the link type, and \(\varepsilon\) is a very small positive constant. * Link spectrum connectivity. In the EONs, lightpaths are frequently established or torn down with the dynamic arrival and departure of service requests. Furthermore, it is necessary to meet the needs of continuity, contiguity, and non-overlapping constraints during resource allocation over EONs [39; 40]. Therefore, it is prone to result in spectrum fragmentation on the links, which will increase the service blocking ratio and worsen network performance. Thus, we incorporated the link spectrum connectivity into the route computation to further improve path effectiveness. This is distinct from other routing algorithms concentrating on the metrics of delay, hops, and so on. Link spectrum connectivity describes the adjacency and availability of spectrum resources on each link. It can be estimated as the following: \[\varphi_{e}=\frac{\sum\limits_{f=1}^{F-1}U_{e}^{f}\cdot U_{e}^{f+1}}{B_{e}} \times\frac{\sum\limits_{f=1}^{F}U_{e}^{f}}{F},\forall e\] (7) \[U_{e}^{f}=\left\{ \begin{array}{ll}0,&\text{if the $f$th }\text{fenqucy slot of the link $e$ is idle}\\ 1,&\text{Otherwise}\end{array} \right.\] (8) where \(U_{e}^{f}\) is a binary variable representing the occupied state of the \(f\)-th frequency slot (FS) on the link \(e\), and \(B_{e}\) and \(F\) are the number of the available spectrum blocks and the total number of FSs on the link \(e\), respectively.