# A Reliable Routing Algorithm Based on Path Satisfaction in the Energy Internet
## 3 Network Architecture and System Model
### System Model
#### 3.2.2 Modulation Level  
The transmission distance in the EI is up to 3000 km within a given region and up to 5000 km in cross regions [43]. On one hand, the longer transmission distance not only increases the end-to-end latency but also impacts the selection of the path modulation format. Furthermore, different modulation methods in the communication process may result in different spectral efficiencies. Therefore, the choice of different modulation formats should be considered during routing computations. Different modulation formats are listed in Table 1. Since each symbol represents a small number of bits in the low-level modulation format, it consequently requires a large number of frequency slots under the condition of the same transmission rate. In contrast, higher modulation levels leveraged in short transmission reaches often require few frequency slots, such as 8 Quadrature Amplitude Modulation (8 QAM) and 16 QAM. Low modulation formats are more suitable for long-distance transmission, e.g., Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK). This flexible distance adaptive modulation format in EDNs not only satisfies variable-bandwidth service requests over the WDM but also enhances channel utilization. Figure 2: Schematic diagram of the SRLG. This network topology has seven nodes, and it is a part of backbone power cable network in the Jiangsu Province in China. Next, we firstly processed the above four types of services by normalization according to the dual-route, and QoS requirements. Then, we calculated the service levels utilizing triangle fusion. Furthermore, the high-level services are preferentially routed and allocated spectrum resources in the case of many service arrivals. The service request is expressed as \(r(s,d,t_{a},t_{d},t_{d},\kappa,\eta,B,l)\), where \(s\) and \(d\) indicate the source and destination of each service, respectively, \(t_{a}\), \(t_{dt}\), and \(t_{d}\) denote the arrival time, transmission time, and maximal ending time, respectively, \(\kappa\) is a binary variable, and \(\kappa=1\) indicates that the dual route is necessary for service \(r\), otherwise \(\kappa=0\). In addition, \(\eta\) indicates resource allocation, which is initialized as 0, and if the resource allocation requirement has been satisfied, then \(\eta=1\). Moreover, \(l\) indicates the service superiority, \(N\) indicates the number of frequency slots with the method of BPSK, and the equation is shown in (18) as follows:  
\[N=\left\lceil\frac{C}{\Theta}\right\rceil+n_{gb} \tag{18}\]  
where \(C\) and \(\Theta\) denote the service capacity and subcarrier capacity, respectively, and \(n_{gb}\) is the number of guard-band slots to avoid spectrum impairments. To obtain more reliable routing paths for dedicated services in the EI, on the one hand, we consider link features in the optical layer including available spectrum resources on the link and modulation methods for paths. On the other hand, the metrics of end-to-end latency and the bandwidth for services are involved, which are critical to ensure reliable service transmission in the IP layer. The objective is to maximize path satisfaction with various constraints. Therefore, the reliable routing paths for services are formally described as a constrained optimization problem. \[\text{Objective Function}:\;Max(\vartheta_{p(r)}\;)\;\;\;r\in \mathbb{R},p\in\mathbb{P} \tag{19}\] \[\text{Subject to}:\;\;\;\;\;\;\;\;\;\;t_{a}(\;r)+t_{dt}(\;r)\leq t _{d}(\;r)\] (20) \[\sum_{r\in\mathbb{R}}C(r)\leq B\] (21) \[\sum_{b_{0}}X_{r,p}^{b_{0}}=S_{r},\forall r,p \tag{22}\] \begin{table}
\begin{tabular}{l l l} \hline
**Modulation Formats** &
\begin{tabular}{l} **Capacity of \(t\) Subcarriers** \\ **(Gb/s)** \\ \end{tabular} & **Transmission Distance (km)** \\ \hline BPSK (M = 1) & 12.5 & 4000 \\ QPSK (M = 2) & 25 & 2000 \\
8 QAM (M = 3) & 37.5 & 1000 \\
16 QAM (M = 4) & 50 & 500 \\ \hline \end{tabular}
\end{table} 
Table 1: Modulation format parameters.