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Abstract

Hybrid wireless mesh networks are more suitable to tunnels in underground mines because mesh clients can perform the routing functionality and provide end-user applications. Types of data transmitted among hybrid wireless mesh networks in underground mines are diverse and power supply of clients is limited. Using virtual potential field, a routing algorithm is proposed to support data-differentiated service in hybrid wireless mesh networks. Based on network parameters, the hybrid wireless mesh networks are abstracted as potential fields. The hop count is used to build the depth potential field. The residual energy of nodes is converted into penalty factor to symbolize the used buffer spaces of nodes, which is used to construct resource potential field to support different types of data. According to the different demands of data transmission, the proportion of these two potential fields is adjusted by a regulatory factor to form a hybrid potential field. The data packets are driven to move toward the gateway in the hybrid potential field at the same time to achieve high quality of service. Simulation results demonstrate that the proposed routing algorithm has shown better performance on end-to-end delay, delivery ratio, and network lifetime, compared with similar algorithms.

Keywords

Hybrid wireless mesh networks routing algorithm data-differentiated service underground mine quality of service

Introduction

Wireless mesh networks (WMNs) will play an increasingly important role in the next-generation network, which can be divided into three categories: infrastructure/backbone WMNs, client WMNs, and hybrid WMNs.¹ In infrastructure/backbone WMNs, mesh clients (MCs) cannot directly communicate with each other and must connect to mesh routers (MRs) to access the backbone network. MRs connect to the Internet via mesh portals (MPs). In client WMNs, composed by MCs, which perform routing and configuration functionalities and provide end-user applications to customers. Hybrid WMNs have achieved a combination of infrastructure/backbone WMNs and client WMNs.² The prime advantage of hybrid WMNs is its high-level network connectivity and is more suitable for the complex environment, such as underground mines, due to its flexibility and extensibility.

In underground mines, there are many narrow tunnels and coal mining faces and tunnel excavating faces are constantly moving. Wired networks are unable to cover all regions, so using wireless networks is a better solution.³ Adapted to the long-strip structure of the tunnels, wireless networks in coal mines have the long-chain topologies.⁴ Therefore, wireless networks in coal mines can only transfer information through multiple hops, as shown in Figure 1.

Figure 1.

Wireless networks in a coal mine.

For traditional wireless networks in a coal mine, it is difficult to find an alternate node if the router is broken, so its ability of self-repair is weak. In hybrid WMNs, MCs can participate in networking and routing, which can effectively solve these problems, as shown in Figure 2. Hybrid WMNs have higher reliability than traditional wireless networks in underground mines.

Figure 2.

Link repair of hybrid WMNs in a coal mine.

However, there are some special characteristics of application scenarios in underground mines. The information with different types needs to be monitored in coal mine. Different types of data have different requirements for network services in terms of delay, throughput, and so on. If a routing protocol can dynamically adjust to the data types, it can make full use of the advantages of hybrid WMNs to improve the quality of service. At the same time, the power supply of nodes in underground mines is different. MRs employ wired power supply, while MCs use battery power.⁵ Node energy is crucial to prolonging the network lifetime. The limited capacity of a battery will constrain the running time of MCs and further affect the network lifetime. If the corresponding strategies can be adopted to save MC’s energy as much as possible, the network lifetime can be prolonged and the network operation cost can be reduced. So, the energy harvesting and prolonging of the network lifetime are two key elements and the energy supply of nodes should be considered to optimize the utilization of different types of nodes.

In this article, considering these characteristics of application scenario, we propose a routing algorithm using virtual potential field for supporting data-differentiated service (RADD) to satisfy the service requirements of different types of data and optimize the utilization of different types of nodes to prolong the lifetime of hybrid WMNs in underground mines. With analogy to potential field in physics, through designing penalty mechanism, RADD takes into account hop count, residual energy, and buffer space as routing metrics to construct hybrid potential field to achieve the multi-parameter routing decision.

The remainder of this article is organized as follows: section “Related work” reviews related work. Section “Preliminaries” presents the preliminary of this study. Section “Design of RADD” details the design of RADD. Section “Characteristics and Implementation of RADD” discusses the characteristics and implementation of RADD. Section “Simulation experiment and performance evaluation” presents the results of the simulation experiments. The conclusions are presented in section “Conclusion.”

Related work

With the development of WMNs, research on routing protocols has gained more and more attention. Destination sequenced distance vector routing (DSDV) is a proactive routing protocol based on the classical Bellman–Ford algorithm.⁶ Ad hoc on-demand distance vector routing (AODV) is an improvement of DSDV. However, the route discovery of AODV is initiated only when it is needed; thus, it is a reactive routing protocol.⁷ Moreover, AODV is a kind of shortest path routing protocol, which is not traffic aware, therefore, the used path is vulnerable to congestion and long queuing delay. The hybrid wireless mesh protocol (HWMP) is a combination of proactive and reactive routing protocol.⁸ Back-pressure routing protocols work to schedule the packet transmissions based on queue length.⁹ However, there are still some problems that prevent it from being widely deployed in the real world, including its high computational complexity and poor delay performance.

The idea of ad hoc network routing protocols is adopted in the design of WMNs’ routing protocols. But it did not consider the characteristics of WMNs.^10,11 The application field of WMNs is constantly expanding and existing routing protocols cannot satisfy fast-changing and sophisticated application requirements.¹²

Learning from the principle of potential fields in physics, a framework of multi-strategy routing protocol in wireless sensor networks (WSNs) using virtual potential fields is proposed.¹³ In this manner, multiple network performances can be synthetically evaluated.^14,15 The energy-balanced routing protocol (EBRP) has constructed a mixed virtual potential field in terms of depth, energy density, and residual energy.¹⁶ A distributed energy optimized routing using a virtual potential field (DERVP) has been designed.¹⁷ The goal of these approaches is to achieve the energy balance in the network, but it did not consider the other demands of the quality of network services, such as delay and throughput. The potential-based real-time routing (PRTR) protocol supports real-time routing using multi-path transmission.¹⁸ PRTR minimized delay for real-time traffic but did not involve other network requirements. A two-step algorithm called minimized upgrade batch VM scheduling and bandwidth planning (MSBP) is designed to minimize the number of upgrade batches. Shortest trajectory first and least bandwidth utilization first are considered to reduce the bandwidth consumption and contention of trajectories.¹⁹

In WSNs, the data sensed by sensor nodes need to be transmitted through multiple hops to the sink. Similar to WSNs, data in hybrid WMNs are forwarded to the gateway in the same manner. Thus, the theory of potential field can be introduced in the design of routing protocol in the hybrid WMNs to satisfy the specific application requirements.

Autonomous load-balancing field-based any-cast routing (ALFA) has effectively balanced loads among multiple gateways and has brought minimal control overhead to mesh nodes.²⁰ Enhanced optimized field-based routing (EOFBR) enables each node to determine the neighboring nodes’ position, velocity, and congestion in macro-mobility and to maintain least cost routing.²¹ Novel temporal, functional, and spatial big data computing framework for large-scale smart grid were designed. The method has achieved a promising computing efficiency approaching to the optimal solution, and it has saved the in-path bandwidth.²² The field-based any-cast routing (FAR) protocol has achieved rapid dynamic routing that are inspired by an electrostatic potential field governed by Poisson’s equation.²³ This routing protocol has provided a robust solution to meet video transmission requirements, such as load balancing for the high data rate and delay requirements, which is similar to the video surveillance application scenarios in underground mines.

Various types of data in hybrid WMNs in underground mines have different transmission requirements, which requires the routing protocol to provide data-differentiated service to achieve stable and efficient data transmission. Existing routing protocols cannot satisfy the requirements of different types of data regarding the quality of network service.^24–26

The proposed algorithm RADD provides a robust solution to meet urgent data transmission requirements such as minimized delay and to meet large amount of data transmission requirements such as load balancing and congestion aware. Moreover, it has constructed the resource potential field for different types of data to support data-differentiated service and has provided better network service for data transmission compared with FAR protocol in the similar application scenarios.

Preliminaries

The potential energy stored in a system is related to the position or state of an object in a potential field and can be released or converted into other forms of energy. Under the independent influence of the potential field, an object will choose the path with the maximum gradient and move from the region with high potential energy to low potential energy. Similar to the phenomenon of water flowing, it will choose the steepest path and eventually converge at the lowest point.

In contrast with a general application scenario, the data transmission in hybrid WMNs in underground mines has a specific flow direction, which will converge at a gateway. These networks contain a low number of gateways, and the data transmission exhibits a many-to-one characteristic, which renders them suitable for combination with a potential field. If the potential value of a gateway is set to the lowest value, the data packets will converge from other nodes to the gateway. Considering the converging characteristics, multiple virtual potential fields will be constructed by different network parameters. A hybrid potential field, which is formed by the superposition of multiple potential fields, will drive data packets along the direction with the maximum potential gradient. The data packets will eventually converge at the gateway to achieve the basic function of routing. According to the demands of different data, the proportion of each virtual potential field can be adjusted to realize the various optimized goals, such as energy balance, congestion avoidance, and data-differentiated service, by adding adaptive adjusting parameters to the hybrid potential field.

The routing protocol proposed in this article based on virtual potential fields in hybrid WMNs in underground mines has considered the characteristics of special applications. MCs in hybrid WMNs can not only support terminal application but also serve as intermediate nodes to forward data, which will provide a large number of redundant routing nodes. MCs can participate in constructing alternative paths for the routing decision, which can enhance the robustness and flexibility of hybrid WMNs. The data will converge at a gateway showing a many-to-one characteristic, which can be effectively combined with a potential field. In the virtual potential field abstracted from the hybrid WMNs in underground mines, the path selection with the maximum potential gradient depends on the potential difference between neighbors. This means that the routing protocol only needs information about neighbors to make routing decisions. This distributed routing protocol can effectively reduce network overhead and increase extendibility.

The location of a node in a network determines its hop count to a gateway. Farther from the gateway, the hop count of the node increases, as shown in Figure 3. $H (x)$ indicates the hop count of node x to the gateway. If $H (gateway)$ is set to 0, $H (x)$ can be abstracted as the virtual depth potential field, as shown in Figure 4. According to the theory of physics, the potential difference between nodes can be transformed into force, which can drive an object to move from a position with high potential value to a position with low potential value. After the network is abstracted into a virtual depth potential field, the data packets can spontaneously move from the node with high potential value to the gateway, which will realize the basic function of routing.

Figure 3.

Hop count of nodes.

Figure 4.

Virtual depth potential field.

In the independent role of the depth potential field, we can only find the shortest path. However, the data type, node energy, and link load are not considered in the routing decision. If the shortest path with the maximum potential gradient is selected by a large number of data, the path may become overloaded. Therefore, multiple factors must be considered in the routing process, and various virtual potential fields should be constructed based on different network parameters.

Different potential fields are superimposed to form a hybrid potential field, in which the neighbor node with maximum virtual force is selected to forward the packet, guaranteed the packet flowing toward the gateway and achieving multiple policy routing. In this article, two potential fields, the depth potential field and the resource potential field, are constructed. The resource potential field is built by the nodes’ available buffer spaces and residual energy. The residual energy has been converted into a penalty factor, which is added to the used buffer space. The lower is the residual energy, the larger is the penalty factor and the less of opportunity of the node to be selected as the next hop. The depth potential field and resource potential field are combined into the hybrid potential field. According to the requirements of different types of data, the proportion between these two potential fields is adjusted to support data-differentiated service.

Design of RADD

The potential difference between different positions in the potential field can be transformed into forces to drive the object to move. Assume that v and w are two points in the potential field and their potential values are $P (v)$ and $P (w)$ , respectively. We set $P (v) > P (w)$ . The distance between v and w is $Δ d$ . The virtual force from v to w is defined as follows

$F (v, w) = \frac{P (v) - P (w)}{Δ d}$ (1)

The larger is $F (v, w)$ , the greater is the gradient variation. The object in the potential field will choose the steepest path to move from a high potential position to a low potential position.

The RADD proposed in this article has abstracted hybrid WMNs into virtual potential fields. When a node has calculated the potential difference and the force, it will compare them with its neighbors. Thus, the distance is one hop. The value of $Δ d$ is set to 1, and the equation (1) can be simplified as follows

$F (v, w) = P (v) - P (w)$ (2)

Depth potential field

To drive data packets to the gateway and realize the basic function of routing, it is necessary to build a depth potential field. The depth potential value of node v is defined as

$P_{d} (v) = H (v)$ (3)

where $H (v)$ denotes the hop count from node v to the gateway. According to equation (2), the force produced by the difference of the depth potential between v and w is defined as follows

$F_{d} (v, w) = P_{d} (v) - P_{d} (w) = H (v) - H (w)$ (4)

Since v and w are neighbors, the difference between their hop count is −1, 0, or 1, and the value of $F_{d} (v, w)$ is −1, 0, or 1.

The depth potential field can drive the data packet to move toward the gateway. With this single potential field, the path selected by the routing algorithm is the shortest path, which will inevitably cause an increase of traffic on the shortest path and network congestion. The fast-speed consumption of node energy on the shortest path will reduce the network lifetime. Therefore, the construction of multiple virtual potential fields through different network status parameters and the comprehensive evaluation of the link performance are necessary to satisfy different requirements of the quality of network service.

Resource potential field

The data transmitted in hybrid WMNs in underground mines have different types. According to the different requirements for network delay and link load, the data are divided into two types: urgent data and non-urgent data. Urgent data, such as warnings about transfinite gas, power failure, abnormal feed, and other information on emergent events, should be transmitted in real time with short network delay. Non-urgent data, such as environmental monitoring data and video, can be transmitted within a stipulated time. However, non-urgent data with a large data amount have a significant impact on the link load, and its transmission will consume a large amount of node energy. Therefore, a routing algorithm realized by virtual potential fields in hybrid WMNs should distinguish data types to support data-differentiated service and choose appropriate network parameters to construct the resource potential field.

RADD sets different priorities for urgent data and non-urgent data. The priorities of urgent data and non-urgent data are set to 1 and 0, respectively. Data packets are sorted according to their priorities when they are stored in the buffer space of nodes. If data packets have the same priorities, they are sorted according to their arrival times.

The buffer space and residual energy of nodes are primarily considered when constructing the resource potential field. For different data types, different methods will be employed to calculate the resource potential values.

Resource potential for urgent data

When transmitting urgent data, the data should arrive the MPs as soon as possible by decreasing the hop count of path or the queue delay. So, to construct the resource potential field, the number of urgent data packets buffered should be counted. The resource potential value of node w for urgent data $P_{r} (w)$ is defined as follows

$P_{r} (w) = \frac{Q_{u} (w)}{N (w)}$ (5)

where $Q_{u} (w)$ represents the number of urgent packets in the buffer queue of node w, and $N (w)$ is the maximum number of packets that w can buffer. The range of $P_{r} (w)$ is [0, 1]. The node with less urgent packets in the buffer queue will have less potential value. The urgent data will be transmitted to MPs along the path with less urgent data load under the independent driving of resource potential field.

Resource potential for non-urgent data

In hybrid WMNs in an underground mine, MRs are powered by cable power, whereas MCs use batteries. The limited capacity of a battery will constrain the running time of MCs and affect the network lifetime. When transmitting non-urgent data, the occupied node buffer space should be calculated and the residual energy of a node should be considered to optimize the energy consumption of MCs and prolong the network lifetime. In the construction of the resource potential field, a node’s residual energy is converted to a penalty factor, which is added to the occupied node buffer space. The penalty factor of node w— $pf (w)$ —is defined as follows

$pf (w) = lo g_{a} E (w)$ (6)

where $E (w)$ refers to the percentage of residual energy of node w, whose range is [0, 1]. “a” refers to the base of $lo g_{a}$ , which represents the low energy threshold and is set to 0.1. If $E (w)$ is equal to 0.1, then the value of $pf (w)$ is 1, which is shown in Figure 5. In this situation, we assume that the buffer space of node w is full, which indicates that this node will stop forwarding data and can only be employed as a source node when its residual energy is less than 10%.

Figure 5.

Penalty mechanism.

To control the value of the penalty factor within the range of [0, 1], we set $E (w)$ to 0.1 when it is less than 0.1.

After the residual energy has been transformed into a penalty factor, the resource potential of node w for non-urgent data— $P_{r} (w)$ —is defined as

$P_{r} (w) = \frac{1}{2} (\frac{Q (w)}{N (w)} + pf (w))$ (7)

where $Q (w)$ represents the number of packets in the buffer queue of node w, including urgent packets and non-urgent packets. If $Q (w) / N (w)$ or $pf (w)$ is equal to 1, which indicates that the node’s buffer space is full or its residual energy is less than 10%, the value of $P_{r} (w)$ will be set to 1.

In the resource potential field, the resource potential difference between node v and its neighbor w is defined as follows

$P_{r} (v, w) = P_{r} (v) - P_{r} (w)$ (8)

Since the distance between v and w is one hop, the virtual force between them is expressed as

$F_{r} (v, w) = P_{r} (v, w)$ (9)

The value of $F_{r} (v, w)$ falls within the interval of [0, 1] as the same with $F_{d} (v, w)$ .

Hybrid potential field

The main purpose of the depth potential field is to drive data packets to move toward the gateway, and the role of the resource potential field is to balance traffic load and optimize the energy consumption of MCs. RADD constructs a hybrid virtual potential field by superimposing these two potential fields. The potential value of node v in the hybrid potential field is defined as

$P_{h} (v) = α P_{d} (v) + (1 - α) P_{r} (v)$ (10)

The potential difference between node v and its neighbor w is

$P_{h} (v, w) = α (P_{d} (v) - P_{d} (w)) + (1 - α) (P_{r} (v) - P_{r} (w))$ (11)

Therefore, the virtual force between v and w is defined as

$F_{h} (v, w) = α F_{d} (v, w) + (1 - α) F_{r} (v, w)$ (12)

In these equations, α is the ratio adjusting factor for the depth potential field and the resource potential field, which is set between 0 and 1. The proportion of these two potential fields can be adjusted by α according to the data type when making routing decisions. A large α indicates a greater effect by the depth potential field and a greater probability that a data packet will choose the shortest path. A small α indicates a greater influence by the resource potential field and a greater probability that a data packet will choose a path with more energy and less load.

Characteristics and implementation of RADD

Parameter adjustment strategy

RADD provides different services for different types of data according to the actual needs of hybrid WMNs in underground mines. The two virtual potential fields are assigned different proportions to satisfy the urgent data service and non-urgent data service by adjusting the value of α.

Urgent data service

Urgent data packets with high priority are processed first when they arrive at the node. The waiting time in the buffer space has minimal effect on the delay of urgent data packets. Thus, RADD focuses on the depth potential field when transmitting urgent data and adjusts α to ensure that urgent data are transmitted along the shortest path.

Assume that $w_{1}$ and $w_{2}$ are two neighbors of node v, so the value of $F_{d} (v, w_{1})$ and $F_{d} (v, w_{2})$ is within the scope of {–1, 0, or 1} as defined in section “Depth potential field.” If $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 1$ or $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 2$ , it indicates that $w_{2}$ is closer to the gateway than $w_{1}$ . To ensure that only $w_{2}$ is selected as the next hop when transmitting urgent data, $F_{h} (v, w_{1}) < F_{h} (v, w_{2})$ is required even if $F_{r} (v, w_{1}) > F_{r} (v, w_{2})$ , which can be simplified as follows

$\begin{matrix} α F_{d} (v, w_{1}) + (1 - α) F_{r} (v, w_{1}) \\ < α (F_{d} (v, w_{1}) + 1) + (1 - α) F_{r} (v, w_{2}) \\ F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < \frac{α}{1 - α} \end{matrix}$ (13)

The value of $F_{r} (v, w)$ falls in the range of [0, 1], thus, $0 < F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < 1$ . The sufficient condition for the equation (13) is $(α / 1 - α) > 1$ , then $α > 1 / 2$ . If this assumption is $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 2$ , which can be simplified as follows

$\begin{matrix} α F_{d} (v, w_{1}) + (1 - α) F_{r} (v, w_{1}) \\ < α (F_{d} (v, w_{1}) + 2) + (1 - α) F_{r} (v, w_{2}) \\ F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < \frac{2 α}{1 - α} \end{matrix}$ (14)

The value of $F_{r} (v, w)$ falls in the range of [0, 1], thus, $0 < F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < 1$ . The sufficient condition for the equation (14) is $(2 α / 1 - α) > 1$ , then $α > 1 / 3$ . Thus, RADD sets $α \in (1 / 2, 1)$ when transmitting urgent data.

Non-urgent data service

RADD not only considers the hop count but also measures the utilization of buffer space and energy when transmitting non-urgent data. Thus, the neighbor with the higher depth potential value can be selected as the next hop.

When $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 1$ (or $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 2$ ) and $F_{r} (v, w_{1}) > F_{r} (v, w_{2})$ , $F_{h} (v, w_{1}) > F_{h} (v, w_{2})$ may be valid, that is, $w_{2}$ is closer to the gateway but $w_{1}$ has more resources, which makes it possible to select $w_{1}$ as the next hop.

In the case of $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 1$ , the range of α can be deduced by reduction to absurdity. Assume that $w_{1}$ is not selected as the next hop; even if $F_{r} (v, w_{1}) > F_{r} (v, w_{2})$ , $F_{h} (v, w_{1}) < F_{h} (v, w_{2})$ remains valid. The range of α is determined by

$\begin{matrix} α F_{d} (v, w_{1}) + (1 - α) F_{r} (v, w_{1}) \\ < α (F_{d} (v, w_{1}) + 1) + (1 - α) F_{r} (v, w_{2}) \end{matrix}$ (14)

That is

$F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < \frac{α}{1 - α}$ (15)

Because $0 < F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < 1$ , the sufficient condition for the equation (15) is $α > 1 / 2$ . Therefore, $w_{1}$ can be selected as the next hop if $α \leq 1 / 2$ .

In the case of $F_{d} (v, w_{2}) = F_{d} (v, w_{1}) + 2$ , the range of α can also be deduced by reduction to absurdity. Assume that $w_{1}$ is not selected as the next hop; even if $F_{r} (v, w_{1}) > F_{r} (v, w_{2})$ , $F_{h} (v, w_{1}) < F_{h} (v, w_{2})$ remains valid. The range of α is determined by

$F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < \frac{2 α}{1 - α}$ (16)

Because $0 < F_{r} (v, w_{1}) - F_{r} (v, w_{2}) < 1$ , the sufficient condition for the equation (16) is $α > 1 / 3$ . Therefore, $w_{1}$ can be selected as the next hop if $α \leq 1 / 3$ .

Combining these proofs, if $α \in (0, 1 / 2]$ , the neighbor with one hop higher than other neighbors can be selected as the next hop. In some extreme situations, such as the situation in which the node’s buffer space is full or the MCs have low residual energy, the routing algorithm can set the value of α to less than or equal to $1 / 3$ , which enables the neighbor with two hops higher than other neighbors to be selected as the next hop.

Implementation of RADD

The routing algorithm that is based on the virtual potential field needs to calculate and maintain the potential value of the node. The following fields are stored in the node’s local memory.

{hop_self; resource_urgent; resource_non-urgent},

where hop_self represents the hop count to the gateway, and resource_urgent and resource_non-urgent record the node’s resource potential values when handling urgent data and non-urgent data, which are calculated according to equations (5) and (7), respectively.

Construction of depth potential field

The depth potential field is constructed by using HELLO packets, which are initiated by the gateway. Nodes receive and process HELLO packets and then continue forwarding them until all nodes determine their respective depth potential values. The hop_hello field in the HELLO packet is used to record the hop count of the node that sends this packet. The structure of the HELLO packet is shown in Figure 7. The construction process of the depth potential field is shown in Figure 6.

Figure 6.

Construction process of depth potential field.

The TTL of the HELLO packet is set to 1, which indicates that all nodes only exchange information with their neighbors, which can prevent HELLO packets from being repeatedly forwarded and save network resources. The depth potential field will be established after the hop count of each node is determined. The frequency of sending HELLO packet will be controlled by the resource potential field in the next step.

Construction of resource potential field

The resource potential values are closely related to the data types. Therefore, resource_urgent and resource_non-urgent fields in the HELLO packet are added to record the node’s resource potential values for urgent data and non-urgent data, respectively, as shown in Figure 7. The field of node IP Address records the IP address of the node which sent the HELLO packet.

Figure 7.

Structure of HELLO Packet.

Creation of routing table

RADD supports data-differentiated services and needs to dynamically adjust the routing according to the data types; thus, the nodes maintain two routing tables: urgent_RT and non-urgent_RT. When nodes create routes, they select the next hop according to their neighbors’ potential values; thus, the Neighbor_table needs to be constructed to record and maintain the potential values of neighbors.

The fields of the routing tables and neighbor table are as follows:

urgent_RT/non-urgent_RT: {Activated, Lifetime, Next Hop IP Address, Force, Locally Repairable};

Neighbor_table: {Neighbor IP Address, hop, resource_urgent, resource_non-urgent};

The creation process of the routing tables is as follows:

After receiving the HELLO packet, the node searches Neighbor_table to find the Neighbor IP Address, which is the same as the Node IP Address in the received HELLO packet. If the value of hop_hello, resource_urgent or resource_non-urgent in the HELLO packet is less than the value of the corresponding field in Neighbor_table, then Neighbor_table will be updated.

When Neighbor_table is updated, the Force will be calculated according to equation (12) and compared with the existing routing records in the routing table. If the new Force is larger than the old one, the routing table will be updated.

To distinguish the data type, the priority field is added to the head of the data packet. The value of priority for urgent data is set to 1, and the value of priority for non-urgent data is set to 0. The data packets are stored in the buffer space in descending order by the value of priority; thus, the urgent data packets can be forwarded before the non-urgent data packets. According to the value of priority, the routes in urgent_RT or non-urgent_RT will be selected to transmit urgent data packets or non-urgent data packets, respectively.

Information exchange cycle

Due to the dynamic character of a node’s potential value, the information should be updated in a timely manner. In general routing protocols, HELLO packets are sent every second. Since node’s potential value is always dynamic, in order to collect the needed information in time to make the most appropriate routing decision, we set nodes to send HELLO packets to their neighbors in two cases:

(a) The variation range of the resource potential exceeds 5%.

(b) The last HELLO packet has been sent for one second.

When either of the above conditions occurs, the HELLO packet will be sent. This method can ensure that even if the node’s resource potential is suddenly changed or unchanged for a long time, its neighbors can acquire the node’s information in a timely manner.

Avoid routing loop

RADD allows packets to return when transmitting non-urgent data, so it is possible to form a routing loop. This strategy proposed in this article helps to avoid routing loops. Data packets record nodes which forwarded them and add these nodes to the blocked nodes table.²⁷ Nodes in this table will be avoided when selecting the next hop. The resource potential values of nodes are constantly updated. If there is a large routing loop, it means that the potential value of the loop region is lower than its surrounding area. In this case, even if the blocked nodes table can avoid the loop, it is difficult to select a better path, but to increase the loads of neighbors which around the routing loop. Therefore, the data packets only record the latest three nodes. Simulation experiments show that recording the latest three nodes can achieve the better performance (in section “Parameter of RADD”). If a large loop is repeated, the nodes can find a new path after the congestion is alleviated or the fault is repaired.

Example of RADD

An example is given to illustrate the execution process of RADD and the network topology is shown in Figure 8, where S is the source node and GW is the gateway.

Figure 8.

Example of RADD: (a) initial status of network, (b) general status of network, and (c) deteriorated status of network.

(a) The depth potential $P_{d}$ and virtual force $F_{d}$ are shown in Table 1. As shown in Figure 8(a), in the initial stage of the network, there is no buffered packets and the residual energy of node is equal, so the routing selection is only related to the depth virtual force $F_{d}$ .

Table 1.

Parameters of Example (a) (*refers the selected one).

Node	S	A	B	C	D	E	F	G	H	I	J	K	L	GW
$P_{d}$	3	3	2	1	2	1	3	2	1	4	3	2	2	0
$F_{d}$	$F_{d} (S, A) = 0$ $F_{d} (S, D) = 1^{*}$ $F_{d} (S, F) = 0$				$F_{d} (D, A) = - 1$ $F_{d} (D, B) = 0$ $F_{d} (D, E) = 1^{*}$ $F_{d} (D, G) = 0$ $F_{d} (D, F) = - 1$					$F_{d} (E, B) = - 1$ $F_{d} (E, C) = 0$ $F_{d} (E, GW) = 1^{*}$ $F_{d} (E, H) = 0$ $F_{d} (E, G) = - 1$

Results in Table 1 show that the path S→D→E→GW is the shortest path, which is selected to transmit urgent and non-urgent data.

The urgent data should be sent before non-urgent data. When transmitting urgent data, the residual energy of node will not be considered and the shortest path will be selected. Therefore, Path S→D→E→GW is still selected to transmit urgent data with running of the network. The routing decision process, when transmitting non-urgent data, will be analyzed in the following paragraph.

(b) With the increase of data transmission in the network, there will emerge some buffered packets and the energy will be consumed gradually. The depth potential $P_{d}$ is shown in Table 1, and the resource potential $P_{r}$ , depth virtual force $F_{d}$ and resource virtual force $F_{r}$ are shown in Table 2.

Table 2.

Parameters of Example (b) (* refers the selected one).

Node	S	A	B	D	E	F	G	H	I	J	K	L	GW
$P_{r}$	1	0	0	0.5	0.7	0.1	0	0	0	0	0	0	0
$F_{d}$	$F_{d} (S, A) = 0$ $F_{d} (S, D) = 1$ $F_{d} (S, F) = 0$			$F_{d} (A, B) = 1$ $F_{d} (A, D) = 1$			$F_{d} (B, C) = 1$ $F_{d} (B, E) = 1$ $F_{d} (B, D) = 0$				$F_{d} (C, GW) = 1$ $F_{d} (C, E) = 0$
$F_{r}$	$F_{r} (S, A) = 1$ $F_{r} (S, D) = 0.5$ $F_{r} (S, F) = 0.9$			$F_{r} (A, B) = 0$ $F_{r} (A, D) = - 0.5$			$F_{r} (B, C) = 1$ $F_{r} (B, E) = 0.3$ $F_{r} (B, D) = 0.5$				$F_{r} (C, GW) = 1$ $F_{r} (C, E) = 0.3$
$F_{h}$	$F_{h} (S, A) = 0 . 7^{*}$ $F_{h} (S, D) = 0.65$ $F_{h} (S, F) = 0.63$			$F_{h} (A, B) = 0 . 3^{*}$ $F_{h} (A, D) = - 0.05$			$F_{h} (B, C) = 1^{*}$ $F_{h} (B, E) = 0.51$ $F_{h} (B, D) = 0.35$				$F_{h} (C, GW) = 1^{*}$ $F_{h} (C, E) = 0.21$

When transmitting non-urgent data, the value of α in equation (12) is set as 0.3, which is determined by experiments in section “Parameter of RADD.” The calculated hybrid virtual force $F_{h}$ is shown in the last line of Table 2. Path S→A→B→C→GW will be selected to transmit non-urgent data, which is shown in Figure 8(b). The depth potential value of A is higher than that of D, but the resource potential value of A is lower than that of D. Node A is selected as the next hop rather than D although it is on the shortest path because there are buffered packets in D or its residual energy is low.

(c) If the buffer of some nodes are near full of packets or their residual energy is very low, such as B, E, and G in Figure 8(c), RADD will avoid these nodes when transmitting non-urgent data. Supposing that the depth potential $P_{d}$ is shown in Table 1, and the resource potential $P_{r}$ , depth virtual force $F_{d}$ , and resource virtual force $F_{r}$ are shown in Table 3, the hybrid virtual force $F_{h}$ can be calculated according to equation (12), as shown in the last line of Table 3.

Table 3.

Parameters of Example (c) (* refers the selected one).

Node	S	A	B	C	D	E	F	G	H	I	J	K	L	GW
$P_{r}$	1	0.2	0.6	0.1	0.5	1	0.1	0.7	0.1	0	0	0.1	0	0
$F_{d}$	$F_{d} (S, A) = 0$ $F_{d} (S, D) = 1$ $F_{d} (S, F) = 0$		$F_{d} (D, A) = - 1$ $F_{d} (D, B) = 0$ $F_{d} (D, E) = 1$ $F_{d} (D, G) = 0$ $F_{d} (D, F) = - 1$		$F_{d} (F, G) = 1$ $F_{d} (F, J) = 0$ $F_{d} (F, I) = 0$			$F_{d} (J, I) = 1$ $F_{d} (J, G) = 1$ $F_{d} (J, K) = 1$		$F_{d} (K, G) = 0$ $F_{d} (K, H) = 1$ $F_{d} (K, L) = 0$			$F_{d} (H, GW) = 1$ $F_{d} (H, L) = - 1$
$F_{r}$	$F_{r} (S, A) = 0.8$ $F_{r} (S, D) = 0.5$ $F_{r} (S, F) = 0.9$		$F_{r} (D, A) = 0.8$ $F_{r} (D, B) = 0.4$ $F_{r} (D, E) = 0$ $F_{r} (D, G) = 0.3$ $F_{r} (D, F) = 0.9$		$F_{r} (F, G) = 0.3$ $F_{r} (F, J) = 1$ $F_{r} (F, I) = 0.9$			$F_{r} (J, I) = 1$ $F_{r} (J, G) = 0.3$ $F_{r} (J, K) = 0.9$		$F_{r} (K, G) = 0.3$ $F_{r} (K, H) = 0.9$ $F_{r} (K, L) = 1$			$F_{r} (H, GW) = 1$ $F_{r} (H, L) = 1$
$F_{h}$	$F_{h} (S, A) = 0.56$ $F_{h} (S, D) = 0 . 65^{*}$ $F_{h} (S, F) = 0.63$		$F_{h} (D, A) = 0.26$ $F_{h} (D, B) = 0.28$ $F_{h} (D, E) = 0.3$ $F_{h} (D, G) = 0.21$ $F_{h} (D, F) = 0 . 33^{*}$		$F_{h} (F, G) = 0.51$ $F_{h} (F, J) = 0 . 7^{*}$ $F_{h} (F, I) = 0.63$			$F_{h} (J, I) = 0.4$ $F_{h} (J, G) = 0.51$ $F_{h} (J, K) = 0 . 93^{*}$		$F_{h} (K, G) = 0.21$ $F_{h} (K, H) = 0 . 93^{*}$ $F_{h} (K, L) = 0.7$			$F_{h} (H, GW) = 1^{*}$ $F_{h} (H, L) = 0.4$

If the $P_{r}$ of other neighbors are too high, such as B, E, and G, node D will choose neighbor F with lower $P_{r}$ but higher $P_{d}$ than itself as the next hop. So the Path S→D→F→J→K→H→GW will be selected to transmit non-urgent data, as shown in Figure 8(c). This strategy can alleviate excessive link load.

Simulation experiment and performance evaluation

Based on QualNet 7.1, simulation experiments are performed to evaluate the performance of RADD, and the results of RADD are compared with multi-criteria routing metric (MRM), AODV, and FAR. The parameters of the simulation network are listed in Table 4. In the simulation, we set the network in a long and narrow area of 1000 × 10 m² to simulate the tunnel in an underground mine.

Table 4.

Simulation Parameters.

Simulation area	1000 × 10 m²
Simulation time	300–900 s
Number of gateways	2
Number of MRs	5–20
Number of MCs	23
Initial energy of each MC	8000 J
Energy consumed per packet	0.1 J
Transmission range	200 m
Traffic type	CBR (UDP)
Packet size of CBR	512 bytes
Number of CBR flows	From 2 to 20
Physical data rate	2 Mbps

MC: mesh clients; MR: mesh routers; CBR: constant bit rate; UDP: user datagram protocol.

Parameter of RADD

The value of α

Section “Parameter adjustment strategy” can only prove the range of α, whereas the following experiments will determine its optimal value. The experimental parameters are listed in Table 4, where the traffic type is set as constant bit rate (CBR) over user datagram protocol (UDP) and the number of CBR flows is 12. The value of α changes from 0.1 to 0.9 with the step set to 0.02. The evaluation standards are the delay and delivery ratio.

For urgent data, as shown in Figures 9 and 10, the delay is lowest and the delivery ratio is highest when the value of α is set to 0.6 and 0.58, respectively. However, the performance of these two indicators becomes worse when the value of α is larger than 0.6. To increase the stability of the routing algorithm, the value of α is set to 0.6 in the following experiments when transmitting urgent data. For non-urgent data, as shown in Figure 11, the delay increases slowly when α changes from 0.02 to 0.4 and then increases rapidly. As shown in Figure 12, when α changes from 0.02 to 0.36, the delivery ratio increases and reaches the maximum when α is 0.36 and then drops dramatic. In addition, only α with the value less than or equal to 1/3, will achieve the selection of a neighbor with one hop higher than the current node as the next hop, which is proved in section “Parameter adjustment strategy.” Therefore, the value of α is set to 0.3 in the following experiments when transmitting non-urgent data.

Figure 9.

Delay of urgent data.

Figure 10.

Delivery ratio of urgent data.

Figure 11.

Delay of non-urgent data.

Figure 12.

Delivery ratio of non-urgent data.

The number of blocked nodes

RADD allows packets to return when transmitting non-urgent data, so it is possible to form a routing loop. Data packets record nodes which forwarded them and add these nodes into the blocked nodes table to avoid routing loops. Nodes in this table will be avoided when selecting the next hop. The following experiments will determine the optimal number of blocked nodes. The experimental parameters are listed in Table 4, and the number of CBR flows is 12. Source nodes only send non-urgent data because this strategy is used for transmitting non-urgent data. The evaluation standards are the end-to-end delay and delivery ratio.

Figures 13 and 14 are end-to-end delay and delivery ratio with different number of blocked nodes when transmitting non-urgent data. Simulation experiments show that the end-to-end delay of two or three blocked nodes is shorter than others, but the delivery ratio of two blocked nodes is lower than that of three. So, recording the latest three nodes can achieve the better performance.

Figure 13.

End-to-end delay of non-urgent data.

Figure 14.

Delivery ratio of non-urgent data.

Performance analysis

Average end-to-end delay

In Figures 15 –17, the average end-to-end delay of RADD is the shortest, MRM is the second short, FAR is the third short and AODV is the longest. This trend becomes more distinct with an increase in CBR flows. Because AODV always selects the shortest path, the path will overload or even become congested if the buffered packets increase, which prolongs the end-to-end delay. FAR uses the Poisson equation and iterative calculation to evaluate the potential values of the nodes. The iterative process runs through the entire network running period, and FAR is a centralized routing algorithm. RADD is similar to FAR in initializing the depth potential field, but RADD adopts the distributed routing algorithm to establish the resource potential field and exchange information. Thus, the network delay of RADD is shorter than FAR. RADD is optimized for the parameters on the basis of MRM. The advantage of RADD is more prominent when transmitting urgent data because the routing algorithm sets higher priority for urgent data, which can be sent prior to non-urgent data, so it is faster than MRM.

Figure 15.

End-to-end delay of urgent data.

Figure 16.

End-to-end delay of non-urgent data.

Figure 17.

End-to-end delay of all data.

In order to analyze the performance of the protocol in more detail, the number of MRs and the simulation time are added in the simulation experiments. The experimental parameters are listed in Table 4, and the CBR number is set to 12. The simulation time is set to 300 s in the experiment of end-to-end delay with different number of MRs. The number of MRs is set to 5 in the experiment of end-to-end delay with different simulation time. The end-to-end delay of all data is compared among different algorithms.

Figure 18 shows that the more MR nodes, the shorter the delay. All protocols have the same trend because the processing capacity of MR is stronger than that of MC. Although the trend is the same, the delay of RADD is the shortest at the same number of MR because data-differentiated strategy sets different priorities for different types of packets and selects different transmission paths to improve the overall transmission performance. Figure 19 shows that the longer the simulation time, the longer the delay because the energy of MCs is gradually consumed. The delay of RADD is the shortest compared with other protocols at the same simulation time because the parameter adjustment strategy adjusts the usage frequency of MCs according to the resource potential to balance energy consumption of MCs.

Figure 18.

End-to-end delay with different number of MRs.

Figure 19.

End-to-end delay with different simulation time.

Delivery ratio

Figures 20 –22 show that the delivery ratio of RADD is the highest, which is followed by MRM. The delivery ratio of FAR is the third. The delivery ratio of AODV is the lowest. RADD considers the path load based on the used buffer spaces of nodes. If the load of the selected path is heavier, RADD will choose another path to balance the network load, which will improve the quality of service. With an increase in CBR flows, the delivery ratio of RADD can be guaranteed at a ratio above 90% for transmitting the urgent data. FAR and AODV exhibit a rapid downward trend when transmitting urgent data, as shown in Figure 20, because RADD provides a priority strategy for urgent data. If the network load is too heavy, it will sacrifice the delivery rate of non-urgent data to ensure that of urgent data. Therefore, the delivery ratio of RADD for non-urgent data decreased at a rapid rate for a large number of CBR flows and a significant network load. However, the ratio remains higher than FAR and AODV, as shown in Figure 21. Compared with MRM, RADD is more accurate in adjusting node load and node energy, and calculates more exactly when choosing the next hop.

Figure 20.

Delivery ratio of urgent data.

Figure 21.

Delivery ratio of non-urgent data.

Figure 22.

Delivery ratio of all data.

Figures 23 and 24 show the delivery ratio with different number of MRs and different simulation time respectively. The experimental parameters are listed in Table 4, and the CBR number is set to 12. The simulation time is 300 s in Figure 23 and the number of MRs is set to 5 in Figure 24.

Figure 23.

Delivery ratio with different number of MRs.

Figure 24.

Delivery ratio with different simulation time.

As shown in Figures 23 and 24, the delivery ratio of RADD is still better than other protocols. Figure 23 shows that the more MRs, the higher the delivery ratio. All protocols have the same trend because the processing capacity of MR is stronger than that of MC. Although the trend is the same, the delivery ratio of RADD is the highest at the same number of MRs and it is the most stable one with the changing of the number of MRs. MCs can be used to relay data in hybrid WMNs. RADD can decrease the opportunity for low-energy MCs to relay data so as to reduce packet loss. Figure 24 shows that the longer the simulation time, the lower the delivery ratio, because the energy of MCs is gradually consumed and the load is aggravated, resulting in packet loss. The delivery ratio of RADD is the highest at the same simulation time for the reason that the parameter adjustment strategy adjusts the energy consumption of MCs according to the resource potential.

Network lifetime

The following figures show the network lifetime with different number of CBR flows and different number of MRs. The experimental parameters are listed in Table 4. The number of MRs is set to 5 in Figure 25 and the CBR number is set to 12 in Figure 26. The network lifetime of transmitting all data is compared among different algorithms.

Figure 25.

Network lifetime with different CBR flows.

Figure 26.

Network lifetime with different number of MRs.

In this experiments, the network’s effective working time until the appearance of the first energy-exhausted node is defined as the network lifetime, so the simulation time of each routing protocol has been extended to 6 h, as shown in Figures 25 and 26. Compared with MRM, AODV, and FAR, RADD has the longest network lifetime. The network lifetime has been prolonged by approximately 12%–84% in RADD because the residual energy of node is considered in the routing decision. When transmitting non-urgent data, if the residual energy of node is less than 10%, its neighbors will assume that it is unavailable and will select another path. As shown in Figure 26, with the increase of the number of MRs, the advantage of RADD is not obvious because the energy of MRs has been set to 100% in the simulation experiment for its wired power supply. When the number of MRs is very large, the difference of network lifetime caused by energy is no longer prominent.

Residual energy of MCs

The standard deviation of residual energy of MCs is employed to reflect the balance degree of the nodes’ utilization, as shown in Figures 27 and 28. The standard deviation of AODV is the highest, MRM is the second, FAR is the third and RADD is the lowest, which indicates that the utilization of MCs is most balanced in RADD. When constructing the resource potential field, RADD transforms the residual energy of a node into a penalty factor and adds it to the resource potential value. RADD tends to choose a node with high residual energy to balance the energy consumption among MCs, so its standard deviation of residual energy is the lowest. With the increase in the CBR flows, the advantage of RADD is more distinct. In Figure 28, with the increase of the number of MRs, the advantage of RADD is not obvious, because the energy of MRs is always one hundred percent. The more the number of MRs, the smaller of the difference in residual energy.

Figure 27.

Standard deviation of residual energy with different CBR flows.

Figure 28.

Standard deviation of residual energy with different number of MRs.

Conclusion

To satisfy the requirements of different types of data and optimize the energy consumption of nodes in underground mine hybrid WMNs, the concept of the potential field in physics is introduced in this article, and a routing algorithm employing virtual potential fields to support data-differentiated service is proposed. The network parameters, such as hop count, buffer occupancy, and residual energy of nodes, are selected to construct the depth potential field and resource potential field by the proposed. A parameter adaptive adjustment mechanism is designed based on different types of data, and the proportion of different potential fields is adjusted to form a hybrid potential field for different applications. The routing protocol designed in this article only requires neighbor’s information to make routing decisions without obtaining the whole network parameters. This distributed routing algorithm has a smaller network overhead and better extendibility. The simulation results show that the proposed routing algorithm has achieved better performance in end-to-end delay and the delivery ratio and has prolonged the network lifetime and improved the quality of network service.

Although most of the nodes in underground mine networks are static, there are some mobile nodes, such as the terminals used in the personnel positioning system or the wireless sensors on transport equipment. If some nodes on the routing path move out of the communication area, the source node has to search a new route after receiving an error report. In the future, we will focus on the node mobility and use the prediction of the movement trend of nodes in the design of routing protocols.

Footnotes

Handling Editor: Pengpeng Chen

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: The financial support for this work provided by the Fundamental Research Funds for the Central Universities (no. 2017XKQY077) is gratefully acknowledged.

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