1. Introduction

Figure 1. Architecture of MIoT system.

Figure 1. Architecture of MIoT system.

• In order to restore post-disaster data transmission of MIoT in the planar accident area rescue scenarios such as fully mechanized coal face, a post-disaster flat network architecture of MIoT based on multi-hop routing of surviving nodes is established, which consists of a sink node and multiple surviving sensor nodes. This network architecture achieves the purpose of comprehensive perception and effective transmission of environmental information in the planar accident mine after disasters.
• We propose a directional-area-forwarding-based candidate forwarding set construction strategy. In the network initialization phase, according to the deployment density and communication radius of nodes in the accident roadway, a forwarding zone (FZ) is designed for each node to route packets toward the sink. Then, the candidate forwarding set (CFS) is constructed by the nodes within the FZ that satisfy the energy constraint and the neighboring node degree constraint. By restricting the number of duplicated packets in the network, DEOR improves the energy utilization of the nodes.
• We propose a relay nodes selection method based on routing quality evaluation. In the data transmission phase, we take multiple attributes of nodes into account, such as direction angle, transmission distance, and residual energy. Next, nodes in CFS are prioritized based on the routing quality and the forwarding node with the highest priority is selected as the relay node to forward packets. Other nodes in CFS discard packets after listening for a successful transmission message. By utilizing the collaboration between forwarders, DEOR addresses the hot-spot problem and balances the traffic load between nodes.
• We design a recovery mechanism for void nodes. When packets encounter the routing void during forwarding, a recovery mechanism is triggered. By employing the modified routing quality evaluation function, packets can bypass the void routing region and select available relay nodes to continue forwarding. DEOR overcomes the void routing node problem and improves the robustness of the whole network.

2. Related Work

2.1. MIoT Routing Protocols

Here, we briefly present some existing well-known routing protocol for MIoT networks. A comparison of the protocols is listed in Table 1.

Table 1. Comparison of MIoT routing protocols.

Table 1. Comparison of MIoT routing protocols.

Protocol	Scenario	Node Status	Deployment	Routing metric	Features
RPAPC-MN[13]	Normal	Static & mobile	Partition	Area positive clustering	Reduce system energy consumption and extend network lifetime
DESR[14]	Normal	Static	Random	Transmission delay, packet loss rate and energy consumption	Ensure QoS requirements
LBDA[15]	Normal	Static	Uniform	The forwarding data traffic and forwarding nodes	Balancing node energy consumption and maximizing network lifecycle
SEC[16]	Post-disaster	Static	Random	Energy factor and connectivity factor	Extended network stability cycle, and improved network stability
EAUC[17]	Post-disaster	Static	Random	Energy and distance factors	Balancing cluster head energy consumption and improving data transmission
MVBN[18]	Post-disaster	Static	Random	The centrality of intermediate numbers, node compactness, and residual energy	Optimized network remaining energy, number of dominant nodes, and node coverage
NHCRA-O[19]	Post-disaster	Static & mobile	Random	Residual energy factor, node connectivity, and directional medium	Improve node matching efficiency and network coverage efficiency
RIAC[20]	Post-disaster	Static	Random	Residual energy, distance, and trust factor	Reduce inter-cluster transmission energy consumption

On the one hand, several routing protocols (e.g., [13,14,15]) were proposed to enhance the performance of data transmission in normal coal mine tunnels. Yu et al. [13] proposed a Routing Protocol in mine roadways based on Area Positive Clustering and Mobile Nodes (RPAPC-MN). In RPAPC-MN, an area positive clustering mechanism is applied to avoid data reentry. By utilizing nodes equipped with miners and mobile equipment to forward data, RPAPC-MN reduces the energy consumption and extends the network lifetime. You et al. [14] proposed a Differential Evolution routing (DE) protocol of wireless multimedia sensor networks for underground mines. By setting different weights in normalized sub QoS evaluation function of transmission delay, packet loss rate and transmission energy consumption and applies marking method to obtain the transmission path, DE realize differentiated service and guarantee the QoS for multimedia services. Wu et al. [15] proposed an Optimal Forwarding Algorithm (OFA) for coal mine WSNs. When sensor nodes are evenly deployed in narrow and narrow lanes, OFA can dynamically adjust the node’s forwarded data volume and forwarded routing to balance the node energy consumption and maximize the network life cycle. On the other hand, a number of routing protocols (e.g., [16,17,18,19,20]) were proposed to restore reliable data transmission in mine tunnels after disasters. Wu et al. [16] proposed a Self-organized Energy-efficient Clustering (SEC) protocol for post-disaster reconstructed MIoT networks. SEC designs the election probability function based on the energy factor and connectivity factor. In SEC, cluster head (CH) node was replaced by periodically comparing the residual energy and the threshold energy, which reduce the overall energy consumption and improve the stability of reconfiguration networks. On this basis, Zhao et al. [17] proposed an Energy-balanced Adaptive Uneven Clustering (EAUC) to solve the issue of node energy heterogeneity after disasters. EAUC introduces the CH election threshold function according to residual energy, relative distance and distribution density of surviving nodes. The weight function of relay CH was built by considering the current residual energy of relay CH and the CH with the largest weight was selected as the next hop routing node. Hu et al. [18] proposed a post-disaster reconstruction algorithm of wireless ad hoc network in coal mines based on Multi-dimensional Virtual Backbone Network (MVBN). MVBN constructs a comprehensive evaluation index of virtual backbone nodes by considering betweenness centrality, node closeness and residual energy. In MVBN, the node with large evaluation index is elected as dominant nodes, so as to enhance the robustness of virtual backbone network and prolong the network lifetime. Hu et al. [19] proposed a Network Hole Coverage Reconstruction Algorithm with Obstacles (NHCRA-O) for post-disaster MIoT. In NHCRA-O, Delaunay triangulation is used to divide residual nodes and corner points of obstacles in the network. The virtual repair node position is determined through the distance between the centroid and the vertex of the Delaunay triangle. NHCRA-O selects CHs according to the residual energy factor, node connectivity and directional betweenness, which significantly extends the network lifespan. Chen [20] proposed an energy balanced Routing protocol based on Improved Ant Colony algorithm (RIAC) to address the problem of uneven energy consumption between network clusters after disasters. RIAC introduces residual energy, distance and node trust factors based on the traditional ant colony algorithm. By modifying the transition probability formula, pheromone heuristic function, and pheromone update strategy, RIAC realizes the optimal path selection from CH to base station. However, the above routing protocols used for MIoT networks adopt a clustering approach with predefined routing paths, which ignores the intermittent connection problem of wireless communication links after disasters in the routing process. When sparse topology occurs in the network, these existing methods cannot guarantee reliable data transmission for post-disaster MIoT networks.

3. System Model and Problem Description

3.1. 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 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. Besides, the sink node is deployed at the entrance of the accident mine and can adopt wired power supply after the disaster, so the power is considered infinite. 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.

Figure 2. Opportunistic routing network model for post-disaster MIoT.

Figure 2. Opportunistic routing network model for post-disaster MIoT.

In the data transmission process of post-disaster network shown in Figure 2, the source node $n_i$ that currently carries the data packet first constructs CFS within its one-hop communication range for packets forwarding, and sends the data packet to all neighbor nodes in the CFS to improve the success rate of 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 node $n_j$ successfully sends the packet to the next hop routing node, other candidate nodes in CFS will drop the packet copies. According to this data transmission method, the sender carrying data packet can select the appropriate relay node to forwarding packet, until the data information of the source node $n_i$ is sends to the sink. Next, the information is transmitted to the underground base station in the mine normal region through 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 [30,31]) and the location of the sink are public. The post-disaster network is formed from a set of a finite number of surviving nodes, denoted by $N=\{n_1,n_2,\text{…},n_{|N|}\}$. Any node $n_i\in N$ is located at $(x_i,y_i)$, it has a limited communication range r and initial battery power $e_{\mathrm{ini}}$. For node $n_i$, its neighbor node set is denoted as $N_i=\{n_j|n_j\in N\&d_{i,j}\le r\}$, where $N_i\subseteq N$ and $d_{i,j}$ denotes the Euclidean distance from $n_i$ to $n_j$ . The length of neighbors set is denoted by $m_i=|N_i|$. All nodes know its neighbors using any neighbor discovery strategy (e.g., the strategy studied in [32], [33]), 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.

Table 2. Notations.

Table 2. Notations.

Notation	Meaning
$N$	The network. $n_i\in N$ is a sensor node.
$N_i$	The neighbors set pf node $n_i$.
$m_i$	The size of $N_i$, $m_i=|N_i|$.
$n_s$	The source node.
$n_{\mathrm{sink}}$	The sink node.
$e_{ini}$	The initial energy of node.
$d_{i,j}$	The transmission distance from the node $n_i$ to its neighbor $n_j$.
${\theta }_{i,j}$	The direction angle between the node $n_i$ and $n_j$ towards the sink node.
${\epsilon }_{i,j}$	The residual energy of neighbor $n_j$ of $n_i$.
$e$	The Euler’s constant. Approx. 2.71828.
$D$	The network density.
$F_i$	The forwarding zone for the node $n_i$
$w_i$	The width of forwarding zone for the node $n_i$
$A$	The area of the target field.
$r$	The communication range of node.
$Z_i$	The candidate forwarding zone of $n_i$.
$C(i)$	The candidate forwarding set of $n_i$.
${\alpha }_{\theta },{\alpha }_d,{\alpha }_{\epsilon }$	The control parameters of routing metrics.
${\overline{Q}}_{i,j}$	The routing quality of neighbor $n_j$ of $n_i$.

4. Proposed DEOR Algorithm

4.1. Construction of Candidate Forwarding Set

In this section, we mainly provide a detailed presentation to the construction of Candidate Forwarding Set (CFS). OR utilizes multiple neighbors of the sending node to simultaneously receive and forward packets, thus improving the packet forwarding efficiency. Therefore, the construction criterion of CFS is particularly important in opportunity routing design.

In general, the size of the CFS can affect the post-disaster network performance. The larger the CFS, the more packet copies are generated, the higher packet transfer success rate, however, the waiting time of the sender will also be longer, leading to higher energy consumption and end-to-end latency. On the contrary, the smaller the CFS, the sparser the network topology, and the lower packet transfer success rate, resulting in unreliable data transmission after the disaster. To address the above issue, this paper proposes a directional-area-forwarding-based candidate forwarding set construction strategy. Here, we take the packet forwarding process from the source node ni to the sink in the post disaster network as an example to build a schematic diagram of the CFS selection of node ni, as shown in Figure 3.

Figure 3. Schematic diagram of CFS selection.

Figure 3. Schematic diagram of CFS selection.

As shown in Figure 3, it shows the selection of the CFS in proposed DEOR algorithm. It can be seen that when the accident area is certain, the size of CFS is related to the network density $D$. The higher the network density, the greater probability of packets being overheard and duplicated. In addition, the direction of data transmission in the accident mine is upward to the sink. In order to reduce transmission energy consumption, nodes closer to the sink should be selected as much as possible when constructing the CFS. Therefore, to restrict the number of forwarders and reduce the energy consumption, we defined a Forwarding Zone (FZ) for each node $n_i$, denoted by $F_i$, so that the packets will be routed upwards to the sink within the $F_i$. The size of the FZ is determined by the network density $D$, larger network density means smaller FZ and fewer forwarders, and vice versa, such that the number of forwarders can be dynamically adjusted. Here, we denote the network density $D$ as

$$D=\frac{1}{2}\left(\frac{4\pi |N|r^2}{A}+\frac{{\displaystyle {\sum }_{i=0}^{|N|}{m}_i}}{|N|}\right)=\frac{1}{2A|N|}\left(4\pi |N{|}^2{r}^2+A{\displaystyle \sum _{i=0}^{|N|}{m}_i}\right)$$

(3)

where the first term reflects the deployment density in the target field, the second term reflects the degree of connections between sender and other nodes. Note that, $(\pi |N|r^2)$ is the sum area of $|N|$ nodes, $|N|$ is the size of post-disaster network, $r$ is the communication radius of nodes, $A$ is the area of target field, and $m_i$ is the number of neighbors of $n_i$.

In Figure 3, it can be seen that FZ is a rectangular shape with a size of $l_i\times w_i$ defined by four points $(f_1,f_2,f_3,f_4)$, where the length of FZ is the Euclidean distance from the node to the sink, i.e., $l_i=d_{i,\mathrm{sink}}$. Obviously, the width of FZ $w_i$ is related to the communication range $r$ and the network density $D$. The higher the network density, the smaller the width. According to the model studied in [35], the maximum width of FZ satisfies $w_{i,max}\le 4r$. Consequently, the $w_i$ is expressed as

$$w_i=\frac{4r}{\sqrt{D}}=\frac{4r\sqrt{2A|N|}}{\sqrt{4\pi |N{|}^2{r}^2+A{\displaystyle {\sum }_{i=0}^{|N|}{m}_i}}}$$

(4)

The location of the sink denoted by $(x_{\mathrm{sink}},y_{\mathrm{sink}})$. In the network initialization phase, each node ${\mathrm{n}}_i$ computes the location the four points of the $F_i$ using formular 5. These four points $(f_1,f_2,f_3,f_4)$ are attached to the header of packets. Obviously, the number of forwarders can be limited according to FZ.

$$\begin{array}{l}{f}_1=\left(x_{\mathrm{sink}}+\frac{w_i(y_{\mathrm{sink}}-y_i)}{2d_{i,\mathrm{sink}}},y_{\mathrm{sink}}+\frac{w_i(x_i-x_{\mathrm{sink}})}{2d_{i,\mathrm{sink}}}\right)\\ f_2=\left(x_{\mathrm{sink}}-\frac{w_i(y_{\mathrm{sink}}-y_i)}{2d_{i,\mathrm{sink}}},y_{\mathrm{sink}}-\frac{w_i(x_i-x_{\mathrm{sink}})}{2d_{i,\mathrm{sink}}}\right)\\ f_3=\left(x_i+\frac{w_i(y_{\mathrm{sink}}-y_i)}{2d_{i,\mathrm{sink}}},y_i+\frac{w_i(x_i-x_{\mathrm{sink}})}{2d_{i,\mathrm{sink}}}\right)\\ f_4=\left(x_i-\frac{w_i(y_{\mathrm{sink}}-y_i)}{2d_{i,\mathrm{sink}}},y_i-\frac{w_i(x_i-x_{\mathrm{sink}})}{2d_{i,\mathrm{sink}}}\right)\end{array}$$

(5)

We define the neighbor set of $n_i$ within the forwarding zone as $F_i$. In Figure 3, the candidate zone (CZ) of each node $n_i$ is defined as the intersection area between the forwarding zone $F_i$ and the communication range of $n_i$. Furthermore, the set of nodes within CZ is described as

$$Z_i=\{n_j|n_j\in (F_i\cap N_i)\}$$

(6)

In practice, due to the harsh underground mine environment after the disaster, there still exists the problem of nodes failure at any time. Therefore, in order to void encountering void routing during packet forwarding, candidate nodes with more neighbor nodes should be selected, so that the packet transmission success rate can be improved. In addition, candidate nodes with relatively high residual energy should be selected to balance the node load and extend the network lifetime. Consequently, the node $n_j$ in the CFS of node $n_i$ should satisfy the formula 7 and formula 8.

$$N(m_i)=\left\{\{n_j,n_v\}\in N_i|m_j\ge \frac{{\displaystyle {\sum }_v{m}_v}}{m_i}\right\}$$

(7)

$$N({\epsilon }_i)=\left\{\{n_j,n_v\}\in N_i|{\epsilon }_j\ge \frac{1}{2}\frac{{\displaystyle {\sum }_v{\epsilon }_v}}{m_i}\right\}$$

(8)

where $m_j$ and $m_v$ represent the number of neighbor nodes of $n_j$ and $n_v$, respectively, while ${\epsilon }_j$ and ${\epsilon }_v$ represent the residual energy of $n_j$ and $n_v$, respectively.

As a result, the nodes satisfying formula 6, formula 7, and formular 8 constitute the candidate forwarding set $C_{up}(i)$ of $n_i$ as

$$C_{up}(i)=Z_i\cap N(m_i)\cap N({\epsilon }_i)$$

(9)

In this article, the constructed candidate forwarding set $C_{up}(i)$ restricts the number of forwarders, which contributes to reduce the waiting time of the sender. Moreover, the nodes in $C_{up}(i)$ have the characteristics of high energy and more neighboring nodes, which is conductive to improving the network lifetime and data transmission reliability of post-disaster MIoT. The pseudocode of the selection of candidate forwarding set is shown in Algorithm 1.

Algorithm 1: Construct the Candidate Forwarding Set

Input: $C_{up}(i)=\varnothing$ Output: The candidate forwarding set $C_{up}(i)$ 1: for each node $n_i\in N$ do 2:    Define the Forwarding Zone $F_i$ using Eq. (5) 3:    Get the subset $Z_i$ using Eq. (6) 4: end for 5: for each node $n_j\in N_i$ do 6:    Get the subset $N(m_i)$ using Eq. (7) 7:    Get the subset $N({\epsilon }_i)$ using Eq. (8) 8:  if $n_j\in Z_i$&&&&$n_j\in N({\epsilon }_i)$ 9:    then add $n_v\to C_{up}(i)$ 10:   end if 11: end for 12: if $C_{up}(i)!=\varnothing$ 13:    then $C(i)=C_{up}(i)$ 14:    switch to Algorithm 3 15: else 16:    switch to Algorithm 2 17: end if

4.2. Selection of Relay Node

In this section, the proposed relay nodes selection method based on routing quality based on is described in detail. In opportunistic routing, the relay node is the ultimate node responsible for packets forwarding, so the selection of relay nodes will directly affect the performance of data transmission in the post-disaster MIoT. After the candidate forwarding set is determined, we need to further optimize the forwarding strategy with the goal of selecting the optimal forwarder as the next-hop relay node. Based on the system model shown in Figure 2, aiming to reduce the energy consumption for data transmission in the post-disaster MIoT, an energy-efficient routing path should be selected from the source to the sink [36]. Here, we design a routing quality evaluation function in DEOR for forwarders that considers three factors, including direction angle, transmission distance, and residual energy of nodes. The smaller the directional angle attribute value of the current forwarder, the closer the forwarder is to the sink, and the lower the transmission energy consumption of sensor nodes. The larger the relative distance attribute value between the sender and forwarder, the farther the transmission distance of the current forwarder is within the same communication range, which shortens the total routing path for packets forwarding, and thus reducing the transmission energy consumption of the post-disaster network. In this article, the schematic diagram of the directional angle and transmission distance between sender $n_i$ and forwarder $n_j$ is shown in Figure 4. Then, nodes in CFS are prioritized based on the routing quality value. After the forwarder’s coordination, the node with the highest priority is selected as the relay to forward packets and other nodes in CFS will drop packets after listening for a successful transmission message.

Figure 4. (a) The direction angle ${\theta }_{i,j}$ from $n_i$ to $n_j$ with respect to the location of the sink. (b) The transmission distance $d_{i,j}$ from $n_i$ to $n_j$.

Figure 4. (a) The direction angle ${\theta }_{i,j}$ from $n_i$ to $n_j$ with respect to the location of the sink. (b) The transmission distance $d_{i,j}$ from $n_i$ to $n_j$.

As shown in Figure 4 (a), the directional angle attribute of the node is considered in this paper to give higher priority to forwarders closer to the sink. The direction angle ${\theta }_{i,j}$ between the sender $n_i$ and the neighbor $n_j$ towards the sink is expressed by formular 10, where $\overrightarrow{a}=(x_j-x_i,y_j-y_i)$ and $\overrightarrow{c}=(x_{\mathrm{sink}}-x_i,y_{\mathrm{sink}}-y_i)$. Figure 4(a) shows that smaller the direction angle ${\theta }_{i,j}$ between the sender $n_i$ and its neighbor $n_j$, closer the neighbor $n_j$ is to the sink and can provide lower energy consumption for packets forwarding. To avoid the situation when ${\theta }_{i,j}=0$, the ${\theta }_{i,j}$ is normalized into ${\overline{\theta }}_{i,j}$ by formular 11, where $1\le {\overline{\theta }}_{i,j}\le 2$. Then, the distribution of the direction angle ${\tilde{\theta }}_{i,j}$ is obtained by using the mass function expressed as formular 12.

$${\theta }_{i,j}=arccos\frac{\overrightarrow{a}\cdot \overrightarrow{c}}{||\overrightarrow{a}||\cdot ||\overrightarrow{c}||}$$

(10)

$${\overline{\theta }}_{i,j}=\frac{3-{\theta }_{i,j}}{2}$$

(11)

$${\tilde{\theta }}_{i,j}=\frac{e^{-{({\overline{\theta }}_{i,j})}^{{\alpha }_{\theta }}}}{{\displaystyle {\sum }_{k=0}^{c_i}{e}^{-{({\overline{\theta }}_{i,k})}^{{\alpha }_{\theta }}}}}$$

(12)

where $c_i$ is the number of nodes in $C(i)$, $\{n_j,n_k\}\in C(i)$, ${\alpha }_{\theta }({\alpha }_{\theta }\ge 0)$ is the control parameter of the direction angle factor. Note that, the larger ${\alpha }_{\theta }$ indicates the greater probability distribution of forwarder, which are closer to the sink being selected as relay nodes.

As shown in Figure 4 (b), the transmission distance attribute of nodes is considered in our work to give higher priority to forwarders that are further away from the sender. This is because when the communication radius $r$ of nodes is fixed, larger the distance between the sender $n_i$ and its neighbor $n_j$ means the shorter the routing path toward to the sink, thereby reducing the energy consumption for routing packets. The transmission distance $d_{i,j}$ between $n_i$ and $n_j$ is represented by formular 13. The variable $d_{i,j}$ is normalized to ${\overline{d}}_{i,j}$ by formular 14, where ${\overline{d}}_{i,j}\in [1,2]$. Then, the distribution of transmission distance ${\tilde{d}}_{i,j}$ is obtained by using the mass function expressed as formular 15.

$$d_{i,j}=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}$$

(13)

$${\overline{d}}_{i,j}=\frac{d_{i,j}+r}{r}$$

(14)

$${\tilde{d}}_{i,j}=\frac{e^{{({\overline{d}}_{i,j})}^{{\alpha }_d}}}{{\displaystyle {\sum }_{k=0}^{c_i}{e}^{{({\overline{d}}_{i,k})}^{{\alpha }_d}}}}$$

(15)

where ${\alpha }_d({\alpha }_d\ge 0)$ is the control parameter of the transmission distance factor. Note that, the larger ${\alpha }_d$ indicates the greater probability distribution of forwarder, which are closer to the sink being selected as relay nodes.

Furthermore, some network nodes can deplete energy earlier than others nodes due to undertaking more packet forwarding in data transmission. In order to balance the load of network nodes, the energy attribute of nodes is also considered in our work to give higher priority to forwarders with greater residual energy. For a forwarder $n_j$ of the sender $n_i$, the residual energy ${\epsilon }_{i,j}$ is normalized to ${\overline{\epsilon }}_{i,j}$ by formular 16. Then, the distribution of remaining energy ${\tilde{\epsilon }}_{i,j}$ is obtained by using the mass function expressed as formular 17.

$${\overline{\epsilon }}_{i,j}=\frac{{\epsilon }_{i,j}+e_{ini}}{e_{ini}}$$

(16)

$${\tilde{\epsilon }}_{i,j}=\frac{e^{{({\overline{\epsilon }}_{i,j})}^{{\alpha }_{\epsilon }}}}{{\displaystyle {\sum }_{k=0}^{c_i}{e}^{{({\overline{\epsilon }}_{i,k})}^{{\alpha }_{\epsilon }}}}}$$

(17)

where $e_{ini}$ is the initial energy of $n_j$, ${\alpha }_{\epsilon }({\alpha }_{\epsilon }\ge 0)$ is the control parameter of the energy factor. Note that, the larger ${\alpha }_{\epsilon }$ indicates the greater probability distribution of forwarders, which have greater remaining energy being selected as relay nodes.

Based on the above analysis, we define the routing quality of $n_i$’s forwarder $n_j$ as the product of the directional angle factor ${\tilde{\theta }}_{i,j}$, the transmission distance factor ${\tilde{d}}_{i,j}$ and the residual energy factor ${\tilde{\epsilon }}_{i,j}$, which expressed as ${\tilde{Q}}_{i,j}$ by formular 18. Then, it is normalized to ${\overline{Q}}_{i,j}$ by formular 19.

$${\tilde{Q}}_{i,j}={\tilde{\theta }}_{i,j}\times {\tilde{d}}_{i,j}\times {\tilde{\epsilon }}_{i,j}$$

(18)

$${\overline{Q}}_{i,j}=\frac{{\tilde{Q}}_{i,j}}{{\displaystyle {\sum }_{k=0}^{c_i}{\tilde{Q}}_{i,k}}}=\frac{e^{\left({({\overline{\epsilon }}_{i,j})}^{{\alpha }_{\epsilon }}-{({\overline{\theta }}_{i,j})}^{{\alpha }_{\theta }}+{({\overline{d}}_{i,j})}^{{\alpha }_d}\right)}}{{\displaystyle {\sum }_{k=0}^{c_i}{e}^{\left({({\overline{\epsilon }}_{i,k})}^{{\alpha }_{\epsilon }}-{({\overline{\theta }}_{i,k})}^{{\alpha }_{\theta }}+{({\overline{d}}_{i,k})}^{{\alpha }_d}\right)}}}$$

(19)

According to formular 19, we can deduce that the forwarder with higher routing quality ${\overline{Q}}_{i,j}$ has a higher chance of being selected as a relay node. Note that, these three factors are controlled by three control parameters ${\alpha }_{\theta }$, ${\alpha }_d$ and ${\alpha }_{\epsilon }$, respectively, so that increasing the value of any control parameter will enhance the impact of the corresponding indicator. Normally, the control parameters are set to ${\alpha }_{\theta }={\alpha }_d={\alpha }_{\epsilon }=1$.

Once the CFS of the sender is determined, the number of packet replicas needs to be limited by the collaboration of candidate forwarders, ensuring that only one forwarder is selected as relay node to forward packets. In this article, the proposed relay node selection method based on routing quality evaluation determines the optimal relay node for packets forwarding, so that an energy-efficient routing path between the sender and the sink will be achieved. By utilizing the local metrics of forwarders to make routing decisions, DEOR reduces routing overhead and extends network lifetime. The schematic diagram of relay node selection is shown as Figure 5.

Figure 5. Schematic diagram of relay node selection.

Figure 5. Schematic diagram of relay node selection.

According to the routing quality ${\overline{Q}}_{i,j}$ value, we sort the forwarders of $n_1$ in descending order, denoted as $C({\overline{Q}}_i)$. As we can see in Figure 5, for the current sender $n_1$ carrying packets, $C_{up}(1)$ is the candidate forwarding sets of $n_1$. When $n_1$ needs to find the next hop, it will send a request message to all neighbors. Based on the directional angle, transmission distance and residual energy of nodes, they calculate their ${\overline{Q}}_{i,j}$ value using formular 19. The sender $n_1$ selects the candidate with the largest ${\overline{Q}}_{i,j}$ value as the next hop. The best relay node $n_4$ forwards the packets, and if the transmission is successful, other nodes $n_2$ and $n_3$ discard packets copies. Since $n_4$ is not the destination node, it becomes the new sender and continues to select the next hop through the above process until the packet is forwarded to the sink. Finally, a complete routing path is formed in the network, denoted as $(n_1,n_4,n_6,n_9,Sink)$ in Figure 5. The pseudocode of the selection of relay nodes is shown in Algorithm 2.

Algorithm 2: Select the Best Relay Nodes

Input: ${\overline{Q}}_{i,j}=（{\overline{Q}}_{i,1},{\overline{Q}}_{i,2},\dots ,{\overline{Q}}_{i,c_i})$ Output: The ID of the best relay nodes 1: for each node $n_j\in C(i)$ do 2:  node $n_j$ receives the packets sent by node $n_i$ 3:  Get the ${\tilde{\theta }}_{i,j}$ using Eq. (12) 4:  Get the ${\tilde{d}}_{i,j}$ using Eq. (15) 5:  Get the ${\tilde{\epsilon }}_{i,j}$ using Eq. (17) 6:  Calculate ${\overline{Q}}_{i.j}$ using Eq. (19) 7:  sort $（{\overline{Q}}_{i,1},{\overline{Q}}_{i,2},\dots ,{\overline{Q}}_{i,c_i})$ in descending order to $C({\overline{Q}}_i)$ 8: end for 9: select the node $n_j$ from the highest -$C({\overline{Q}}_i)$ 10: if $n_j$ forwards the packet successfully 11:  then other nodes in $C(i)$ drop the packet 12: else 13:  set the node $n_j$=$n_v$ where $n_j$ has lower -$C({\overline{Q}}_i)$ 14: end if 15: until the timer expired 16: if packet is not delivered to Sink 17:  then $n_{sender}=n_j$ 18:  switch to Algorithm 1 19: end if

4.3. Recovery Mechanism

In this section, we describe in detail of a recovery mechanism in the proposed DEOR. The collapse of loose coal in mines after disasters and the depletion of node energy are common phenomena, which can increase the probability of void nodes being selected as relay nodes [37]. However, although the above methods reduce the probability of selecting void nodes, it cannot completely avoid the problem of void routing. According to the Figure 2, we assume that the routing node $n_j$ of the current sender $n_i$ is an invalid node, the routing recovery process of void nodes in the post-disaster MIoT network is shown in Figure 6. By adopting the proposed recovery mechanism, the current void node $n_j$ can quickly find the optimal relay recovery node $n_k$ on the reverse routing path towards the sink, thereby bypassing the void area and improving the packet delivery rate of post-disaster network data transmission.

Figure 6. Schematic diagram of recovery mechanism.

Figure 6. Schematic diagram of recovery mechanism.

In Figure 6, if relay node $n_j$ of sender $n_i$ is a void node, no neighbors in upward path to sink can forward packets, i.e., the candidate forwarders set $C_{up}(j)$ obtained according to Algorithm 1 is empty. Here, we denote the set of neighbor nodes of the void node $n_j$ as $N_j$, its subset of neighbors $N(d_j)$ in downward path can be defined as

$$N(d_j)=\{n_k\in N_j\subseteq N|d_{k,\mathrm{sink}}-d_{j,\mathrm{sink}}\ge 0\}$$

(20)

where $n_k$ is the neighbor of void node $n_j$, $d_{j,\mathrm{sink}}=\sqrt{{(x_j-x_{\mathrm{sink}})}^2+{(y_j-y_{\mathrm{sink}})}^2}$ represents the Euclidean distance from $n_j$ to the sink.

Similar to formular 8, in order to ensure load balancing and energy conservation in the post-disaster network, nodes with higher residual energy should be selected. Hence, the subset $N({\epsilon }_j)$ of n_j’s neighbors that satisfy energy constraints is denoted as

$$N({\epsilon }_j)=\left\{\{n_k,n_l\}\in N_j\subseteq N|{\epsilon }_k\ge \frac{1}{2}\frac{{\displaystyle {\sum }_l{\epsilon }_l}}{m_j)}\right\}$$

(21)

Combining formular 20 and formular 21, the candidate recovery node set $C_{down}(j)$ of void node $n_j$ can be defined as

$$C_{down}(j)=N(d_j)\cap N({\epsilon }_j)$$

(22)

Unlike the routing method described in Section 4.2, when an invalid node $n_j$ selects a recovery relay node in downward path to the sink, it will consume more energy to forward packets to nodes at greater distances. Therefore, the neighbor node with a smaller transmission distance difference from the void node should be selected as the recovery relay node. Consequently, in the recovery mechanism, formula 15 and formular 19 should be rewritten as

$${\tilde{d}}_{j,k}=\frac{e^{-{({\overline{d}}_{j,k})}^{{\alpha }_d}}}{{\displaystyle {\sum }_{k=0}^{c_j}{e}^{-{({\overline{d}}_{j,k})}^{{\alpha }_d}}}}$$

(23)

$${\overline{Q}}_{j,k}=\frac{{\tilde{Q}}_{j,k}}{{\displaystyle {\sum }_{l=0}^{c_j}{\tilde{Q}}_{j,l}}}=\frac{e^{\left({({\overline{\epsilon }}_{j,k})}^{{\alpha }_{\epsilon }}-{({\overline{\theta }}_{j,k})}^{{\alpha }_{\theta }}-{({\overline{d}}_{j,k})}^{{\alpha }_d}\right)}}{{\displaystyle {\sum }_{k=0}^{c_j}{e}^{\left({({\overline{\epsilon }}_{j,l})}^{{\alpha }_{\epsilon }}-{({\overline{\theta }}_{j,l})}^{{\alpha }_{\theta }}-{({\overline{d}}_{j,l})}^{{\alpha }_d}\right)}}}$$

(24)

where $c_j$ is the number of candidate forwarders of void node $n_j$.

Once the void node forwards packets to a normal routing node, it exits the recovery mechanism and continues to route packets to the sink, as described in Section 4.1 and Section 4.2. In the recovery mechanism, nodes will record the ID of the previous hop node, and these nodes will not be repeatedly selected when selecting the recovery relay node, thus avoiding routing loops. By utilizing the updated routing quality assessment, void nodes can select appropriate recovery relay nodes downward in the planar accident mine, thereby effectively restoring the transmission path. The pseudocode of the recovery mechanism is shown in Algorithm 3.

Algorithm 3: Recovery Mechanism of Void Nodes

Input: $N_i$ Output: The candidate recovery forwarding set $C_{down}(i)$ 1: for each node $n_j\in N_i$ do 2:    Get the subset $N(d_j)$ using Eq. (20) 3:    Get the subset $N({\epsilon }_j)$ using Eq. (21) 4:    if $n_j\in N(d_j)\&\&n_j\in N({\epsilon }_j)$ 5:     then add $n_j\to C_{down}(i)$ 6:   $C(i)=C_{down}(i)$ 7:    end if 8: end for 9: switch to Algorithm 2

4.4. Analysis and Flowchart of DEOR

According to the pseudocode of the three sub-algorithms, the DEOR algorithm mainly consists of a cycle in the calculation process, so the computational complexity of the proposed DEOR in this paper is $O(N)$, where $N$ is the number of nodes in the network. The energy consumption in DEOR entirely depends on how many nodes in the sender’s forwarding zone. For the post-disaster MIoT network, this complexity is usually within the computing capacity of nodes, and the proposed DEOR is an energy-saving routing strategy. Therefore, the surviving nodes have the ability to execute the DEOR algorithm, which restricts the number of duplicate packets generated in the network and avoids routing void problem during data transmission.

The proposed DEOR is an opportunistic routing algorithm that considers both global and local information of the network. Nodes make routing decisions based on network density and multiple attributes of neighboring nodes. The flowchart of DEOR is shown as Figure 7. Firstly, during the network initialization phase, each node defines a forwarding area based on the current network density. Then, the sender constructs a candidate forwarding set (CFS) according to the candidate region constraint, energy constraint, and neighboring node degree constraint. If the CFS is empty, the recovery mechanism is activated. Next, the nodes within the CFS calculate their routing quality ${\overline{Q}}_{i,j}$ values, and be sorted in descending order to $C({\overline{Q}}_{i,j})$. The nodes in $C({\overline{Q}}_{i,j})$ are selected in sequence as relay nodes to forward the packets before the timer expires, otherwise the data transmission fails. Finally, if any node in CFS successfully forwards the packet, the other nodes will discard the packet copies and loop the above process until the packet is routed to the sink.

Figure 7. Flowchart of the proposed DEOR.

Figure 7. Flowchart of the proposed DEOR.

5. Performance Evaluation

5.1. Simulation Settings

Considering the actual post-disaster MIoT environment, we deploy all nodes randomly in a sensing area of $300\mathrm{m}\times 50\mathrm{m}$ in the simulation. This deployment approach ensures that the simulation results in different scenarios are independent of each other. Suppose a sink node with unlimited energy is fixed at the edge of the sensing area and act as a gateway for wireless communication with sensor nodes. Similar to most wireless network routing protocols, we use the Carrier Sense Multiple Access (CSMA) protocol as the underlying MAC protocol. If the channel is idle, the forwarding node can broadcast the data packet. Otherwise, it backs off and the packet will be dropped after backing off for the maximum retransmission times. The maximum retransmission times of each node is set to 4, and the maximum error ratio of each link is set to 0.2. We assume that the network generates a data packet from a random sensor node to the sink in each 0.1s. The size of the data packet is set to 1024bits. The parameter settings required for the simulation are shown in Table 3.

Table 3. Simulation Parameters.

Table 3. Simulation Parameters.

Parameters	Valus
Network topology	Random
Deployment area	$300\mathrm{m}\times 50\mathrm{m}$
Generate rate	1packet/0.1s
Number of nodes Sink	200-300 1 static sink (edge)
Transmission rate	1Mbps
Communication range	40m
Simulation time	2000s
RF channels	2.4GHz
Packet size Initial energy Sleep power	1020bits 0.5J 0.78mW
$E_{\mathrm{elec}}$ ${\epsilon }_{\mathrm{amp}}$ ${\epsilon }_{\mathrm{fs}}$	$50\mathrm{nJ}/\mathrm{bit}$ $0.0013\mathrm{pJ}/\mathrm{bit}/{\mathrm{m}}^4$ $10\mathrm{pJ}/\mathrm{bit}/{\mathrm{m}}^2$

The following routing metrics are used to evaluate the performance of routing algorithms: 1) Energy Consumption (EC): EC is defined as the total energy consumption required to deliver data packets from source nodes to the sink. 2) Average Hop Count (AHC): AHC is defined as the average hop count on the routing path from source to the sink for forwarding data packets. 3) Packet Delivery Ratio (PDR): PDR is defined as the ratio of the number of packets successfully received at the sink to the number of data packets generated by source nodes. 4) Network Lifetime (NL): NL is defined as the time (in seconds) from the simulation starting moment to the moment that the first node completely depletes its energy.

5.2. Effect of Control Parameters

According to formular 19, the routing quality is the multiplication product of three factors, i.e., ${\tilde{\theta }}_{i,j}$, ${\tilde{d}}_{i,j}$ and ${\tilde{\epsilon }}_{i,j}$. Therefore, increasing the value of any control parameter will enhance the impact of the corresponding factors on routing performance. The control parameters $({\alpha }_{\theta },{\alpha }_d,{\alpha }_{\epsilon })$ can be adjusted to meet the requirements of the various application for post-disaster MIoT. However, there may be a factor that is ineffective in routing in some cases. In order to select the optimal forwarders in the routing process, the setting of control parameter values should ensure that they have a certain effect on three factors. Besides, in order to maximize the lifetime of the post-disaster network, the value of the energy control parameter ${\alpha }_{\epsilon }$ should be larger than the other two parameters $({\alpha }_{\theta },{\alpha }_d)$. In the simulation, the number of nodes is set to 200, the communication range of nodes varying from 30m to 50m, the two control parameters is set to ${\alpha }_{\theta }={\alpha }_d=1$, and the value of ${\alpha }_{\epsilon }$ varying from 1 to 6. We can clearly see that when the communication range r is fixed, the network lifetime increases with the larger of ${\alpha }_{\epsilon }$. When ${\alpha }_{\epsilon }=5$ , the growth of network lifetime tends to be stable. Therefore, the DEOR algorithm ensures good performance in terms of network lifespan for different control parameters ${\alpha }_{\epsilon }$ values.

Figure 8. Network lifetime varying control parameters.

Figure 8. Network lifetime varying control parameters.

5.3. Performance for Varying Communication Ranges

According to formular 3, it can be seen that for a given sensing area, the network density $D$ is determined by the number of nodes $N$ and the communication range $r$. The more network nodes or the larger the communication range, the higher the network density. Accordingly, we evaluate the network performance of the DEOR algorithm by varying the communication ranges $r$ and the number of nodes $N$. In the simulation, the control parameter is set to ${\alpha }_{\theta }={\alpha }_d={\alpha }_{\epsilon }=1$, the number of nodes is set to 200, and the communication range $r$ is varied from 30m to 50m. Other parameters are listed in Table 3. The results can be found in Figure 9, Figure 10, Figure 11 and Figure 12.

Figure 9. Energy consumption varying communication range.

Figure 9. Energy consumption varying communication range.

Figure 10. Average number of hops varying communication range.

Figure 10. Average number of hops varying communication range.

Figure 11. Packet delivery ratio varying communication range.

Figure 11. Packet delivery ratio varying communication range.

Figure 12. Network lifetime varying communication range.

Figure 12. Network lifetime varying communication range.

Figure 9 illustrates the influence of the communication range on the energy consumption. From Figure 9, we can see that the energy consumption of all four routing algorithms decreases with the increase of communication range $r$. This is because as the communication range $r$ increases, the number of hops for packets forwarding to sink will correspondingly decrease, which means that the number of nodes involved in forwarding decreases, and therefore the total energy consumption of the network is reduced. The network energy consumption in ORR is the highest because ORR is a centralized routing algorithm that through utilizing a large number of control packets to transmit nodes information to the sink when calculating routing metrics, resulting in significant energy consumption. Compared with OBRN and ECSOR, DEOR has the least energy consumption. This is because in DEOR, the number of forwarding nodes is restricted by the directional forwarding zone, see formular 6. The sender will dynamically adjust the number of candidate forwarders based on the current communication range $r$, thereby reducing the number of packet replicas. In addition, based on formular 17, DEOR balances the load of nodes close to the sink and improves the energy utilization efficiency of nodes. Therefore, DEOR has better energy efficiency than ORR, OBRN, and ECSOR.

Figure 10 illustrates the influence of the communication range on the average hop count of delivered packets. It can be clearly seen that as the communication range $r$ increases, the number of routing hops decreases for all four algorithms. This is because the larger the communication range $r$, the greater the transmission distance of nodes, which means that the packets routing path from the source node to the sink is shortened, and therefore fewer nodes are involved in forwarding. Compared with ORR, OBRN, and ECSOR, DEOR has the least number of hops because the DEOR can adjust the density of candidate nodes in the target area based on the communication range $r$, and thus dynamically select the appropriate number of forwarders. Besides, DEOR considers the relationship between link length and transmission range, thus ensuring a lower number of hops in the routing path.

Figure 11 illustrates the influence of the communication range on the packet delivery ratio. It is obvious from Figure 11 that DEOR is better than ORR, OBRN and ECSOR, because the PDR of the network is related to the link quality and the number of forwarding nodes. The DEOR algorithm takes into account the effect of transmission distance $d_{i,j}$ on routing when selecting relay nodes, ensuring better path quality of packets throughout the entire routing process. Moreover, DEOR makes each node have multiple forwarders through a recovery mechanism for void routing, which means that when a sender encounters a void node, it can quickly find recovery relay nodes, which in turn improves the packet delivery rate. However, ORR, OBRN, and ECSOR only consider the energy and load factors to make routing decisions. When encountering void nodes, a large number of control packets need to be sent to update network information to calculate new forwarders set, see formular 24, which leads to a higher probability of packet loss. As a result, the DEOR algorithm outperforms the other three algorithms in terms of PDR.

Figure 12 illustrates the influence of the communication range on the network lifetime. As can be seen in Figure 12, the network lifetime of all four algorithms increases as the communication range $r$ becomes larger. Compared to ORR, OBRN, and ECSOR, DEOR achieves the longest network lifetime, while ORR has the shortest network lifetime. In OBRN and ECSOR, the remaining energy of nodes around the sink is not considered when selecting forwarders. There exits that node near the sink participating in excessive packets forwarding, leading to the hotspot problem. Thus, premature depletion of energy by critical routing nodes causes network connection interruption. However, in DEOR, only nodes in the upward path to the sink are eligible to forwarding packets, which effectively reduces the number of redundant packets and shortens the routing path. Meanwhile, DEOR balances the load of nodes through transmission distance factor ${\tilde{d}}_{i,j}$ in routing decisions, thereby reducing energy consumption. As a result, DEOR has a longer network lifetime than ORR, OBRN and ECSOR.

5.3. Performance for Varying Number of Nodes

In this section, we evaluate the network performance of the DEOR algorithm by varying the numbers of nodes from 200 to 300. In the simulation, the control parameter is set to ${\alpha }_{\theta }={\alpha }_d=1$, ${\alpha }_{\epsilon }=5$, and the communication range is set to 40m. Other parameters for this simulation are listed in Table 3. The results can be found in Figure 13, Figure 14, Figure 15 and Figure 16.

Figure 13. Energy consumption varying number of nodes.

Figure 13. Energy consumption varying number of nodes.

Figure 14. Average number of hops varying number of nodes.

Figure 14. Average number of hops varying number of nodes.

Figure 15. Packet delivery ratio varying number of nodes.

Figure 15. Packet delivery ratio varying number of nodes.

Figure 16. Network lifetime varying number of nodes.

Figure 16. Network lifetime varying number of nodes.

Figure 13 illustrates the influence of the number of nodes on the energy consumption. It is clearly seen that as the number of nodes becomes larger, the energy consumption of all four routing algorithms increases. This is because when the size of the monitoring area is fixed, more nodes in the network imply a higher network density, then the number of nodes involved in forwarding increases. Excessive forwarding nodes will generate more redundant packets in the network, which in turn leads to higher energy consumption. DEOR has the smallest increase in energy consumption among the four algorithms, due to the number of forwarders in DEOR is controlled by the network density $D$. According to formular 4, when the network density $D$ increases, the width $w_i$ of the forwarding area will decrease, thereby limiting the number of nodes in the CFS. However, for ORR, OBRN, and ECSOR algorithms, as the number of nodes in the network increases, the number of nodes participating in forwarding will also increase, generating more redundant packets and therefore leading to more energy consumption.

Figure 14 illustrates the influence of the number of nodes on the average hop count of delivered packets. It is observed that the average hop count in all four algorithms gradually decreases as the deployment density of nodes increases. This is because when the communication radius $r$ of nodes is fixed, the number of nodes in the network is small leading to a sparse local topology and packets need to pass through a large number of relay nodes to enter the coverage range of the sink. Therefore, the average number of hops for packets forwarding is higher. On the contrary, when the number of nodes is higher, there are fewer void nodes and packets are theoretically able to enter the coverage of the sink through the shortest path, resulting in fewer average number of hops. Compared with ORR, OBRN, and ECSOR, DEOR has the fewest number of hops. According to formular 23, DEOR updates the transmission distance metric in the routing decision. DEOR selects optimal relay nodes closer to the void node by adopting a recovery mechanism, thereby shortening the length of the communication link.

Figure 15 illustrates the influence of the number of nodes on the packet delivery ratio. Obviously, the PDR of all four algorithms gradually increases as the number of nodes becomes larger. When the deployment density of nodes is higher, the probability of routing void areas will decrease, and there are more available candidate nodes for packet forwarding. As a result, the probability of packet loss is reduced and the packet delivery success rate is improved. ORR has the lowest PDR among the four routing algorithms. This is because only the residual energy of nodes is considered in ORR. If there are fewer nodes in the network, it is prone to a large amount of packet loss. Additionally, as shown in Figure 15, when the number of nodes approaches 300, the PDR of OBRN, ECSOR, and DEOR algorithms are close to the same, approximately 90%. However, when the number of nodes is less than 300, the DEOR algorithm is significantly better than OBRN and ECSOR. This is because when a sparse topology appears in the network, DEOR can increase the number of forwarders, thereby improving the reliability of successful packet forwarding.

Figure 16 illustrates the influence of the number of nodes on the network lifetime. From Figure 16, it can be seen that the network lifetime of the four routing algorithms increases as the number of network nodes increases. This is because DEOR designs a candidate forwarding zone (FZ) for all senders to make appropriate routing decisions. DEOR can limit the number of nodes involved in packets forwarding based on the current network density $D$, reducing the number of redundant packets generated in the network and thus reducing network energy consumption. Furthermore, DEOR utilizes a routing quality function to balance the traffic load of forwarding nodes, overcoming the problem of hot spots caused by critical routing nodes near sink, and thus improving the network lifetime.

6. Conclusions

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