# Energy-Efficient Opportunistic Routing Algorithm for Post-Disaster Mine Internet of Things Networks
## 3 System Model and Problem Description  
### Network Architecture  
In the accident rescue communication scenario of planar areas such as fully mechanized coal mining working faces, we consider a network architecture for post-disaster Mine Internet of Things (MIoT) opportunity routing, as shown in Figure 2. The post-disaster MIoT network consists of two types of available nodes, i.e., multiple surviving sensor nodes and one sink node. All surviving nodes with the ability to sense and transmit information are randomly distributed in the accident tunnel. After the disaster, these sensor nodes are responsible for periodically collecting environmental and equipment information from the accident field. In addition, the sink node is deployed at the entrance of the accident mine and can adopt a wired power supply after the disaster, so the power is considered infinite. Before the post-disaster data transmission, the sink node will broadcast a detection message containing its own location information to the entire affected area with maximum transmit power. Then, source nodes in the network perform directional routing based on the sink's location information, aiming to send data information to the destination node. As the gateway node of the post-disaster network, the sink is responsible for collecting various information collected by sensor nodes. In the post-disaster MIoT, each node can directly or multi-hop forward data packets to the sink node.  
In the data transmission process of the post-disaster network shown in Figure 2, the source node \(n_{i}\) that currently carries the data packet first constructs the CFS within its one-hop communication range for packet forwarding and sends the data packet to all neighbor nodes in the CFS to improve the success rate for packet forwarding. Then, a candidate node \(n_{j}\) is selected as a relay node for \(n_{i}\) through the node collaboration in the CFS. When the node \(n_{j}\) successfully sends the packet to the next hop routing node, other candidate nodes in the CFS will drop the packet copies. According to this data transmission method, the sender carrying the data packet can select the appropriate relay node to forward the packet until the data information of the source node \(n_{i}\) is sent to the sink. Next, the information is transmitted to the underground base station in the mine's normal region through the sink. Finally, the information is sent to the ground control center through mining switches and Ethernet ring networks. Consequently, the post-disaster MIoT enables effective monitoring of the entire accident area through the proposed data transmission scheme.  
We assume that all surviving nodes are homogeneous and stationary. Each node knows its geographical location through any re-localization scheme of drift nodes after mine disasters (e.g., the scheme studied in [32; 33]), and the location of the sink is public. The post-disaster network is formed from a set of a finite number of surviving nodes,  
Figure 2: Opportunistic routing network model for post-disaster MIoT.  
denoted by \(N=\left\{n_{1},n_{2},\ldots,n_{|N|}\right\}\). Any node \(n_{i}\in N\) is located at \((x_{i},y_{i})\), and has a limited communication range r and initial battery power \(e_{\text{ini}}\). For node \(n_{i}\), its neighbor node set is denoted as \(N_{i}=\left\{n_{j}|n_{j}\in N\ \&\ d_{i,j}\leq r\right\}\), where \(N_{i}\subseteq N\) and \(d_{i,j}\) denotes the Euclidean distance from \(n_{i}\) to \(n_{j}\). The length of the neighbor set is denoted by \(m_{i}=|N_{i}|\). All nodes know their neighbors using any neighbor discovery strategy (e.g., the strategy studied in [34; 35]), thereby calculating the distribution density of surviving nodes in the current accident area. In this paper, we define the data forwarding direction toward the sink in the underground accident region as an upward routing path, i.e., the forwarder is closer to the sink than the current sender. The notations used frequently in this paper are listed in Table 2.