# Robot Delay-Tolerant Sensor Network for Overhead Transmission Line Monitoring
## 3 RDTSN Model and Data Delivery Strategy
### Discrete-Time Multi-Path Routing Algorithm  
This section describes a discrete time multi-path routing algorithm (DTMA), which is similar to the prophet algorithm. The prophet algorithm predicts the probability of message delivery, depending on the historical data of the encountered nodes. The shorter the encounter time interval of the nodes, the more the encounter times, and the higher the probability of predicting delivery. However, the inspection movement of the robot is different from the common random motion. After the robot meets a node, the probability of the return movement is low. The return movement is carried out only when the robot is inspecting. In particular, in the BPRW and BMI movement model, the robot cannot have a reverse motion. Furthermore, the layout of SNs and WCNs is sparse along the long-distance transmission line. The historical data that the robot meets with other nodes change too slowly. Therefore, it is impossible to accurately describe the relationship between the network change and the message delivery probability by calculating the historical data of the encountered nodes. The method of the prophet algorithm is no longer applicable in this situation. DTMA is similar to the prophet algorithm, and it is based on the nodes' social and historical information. Furthermore, it is combined with the discrete time DTSN mathematical model. In DTMA, the prediction of message delivery rate depends on the exact calculation of link availability. The availability of links between nodes is determined by the signal strength of nodes in the wireless networks [8]. When the signal strength reaches a certain threshold \(Sr\), the wireless link is connected. In addition, the link availability probability between node \(i\) and \(j\) equals 1, as shown in Equation (9). Each node records the intensity of the signal between itself and the neighbors at different time. If the current signal strength \(S_{ij}(t)\) is lower than the threshold value \(S_{r}\), the value \(a_{ij}(t)\) can be calculated by discrete-time weighted average of the signal strength \(S_{ij}(t)\), as shown in Equation (10). This value not only reflects the nodal motion in the front stage, but also highlights the influence of the node's current position. For example, as the node is away from the others, the value of \(a_{ij}(t)\) can be much smaller. If node \(i\) hovers around node \(j\) for a period, the value of \(a_{ij}(t)\) will become larger. This means that the message will more probably be transmitted to node \(j\). If node i is always away from node \(j\), the value of \(a_{ij}(t)\) will be very small. In addition, the discrete time variable \(\delta_{t}(t)\) has a strong negative relationship with the value of \(a_{ij}(t)\). \[a_{ij}(t)=1,\,S_{i}(t)\geq S_{r} \tag{9}\]  
\[a_{ij}(t)=\frac{\sum tS_{ij}(t)}{\sum tS_{r}+\delta_{t}(t)S_{r}},\,S_{i}(t)<S_ {r} \tag{10}\]  
In addition, this paper combines the DTMA with the discrete time DTSN mathematical model. Each node can obtain a better transmission path based on its own information, as shown in Figure 3. The message is transmitted from one node to the appropriate neighbor node, when the condition is allowed. Or messages will be stored in the local buffer, until the transmission conditions are satisfied. The process of message delivery is as follows. * Firstly, the node calculates the availability probability according to the social and historical information. * Secondly, the message delivery ratio and the node survivability are calculated according to the graph information in the mathematical model. * Thirdly, for determining the weight function \(w_{ij}(t)\) of each edge, the message delivery ratio and the node survivability need to be adjusted. * Finally, the node determines the message forwarding process based on the objective function and the constraint conditions. In RDTSN, a special scene is identified, as described in Figure 8. A number of WSNs are deployed in the network, leading to the formation of many homogeneity wireless destinations.