A fuzzy-rule-based packet reproduction routing for sensor networks

Abstract

It is a major challenge to transfer target sensing data efficiently to sink in Internet of things. The low-efficiency data transmission can cause low quality of service. To realize the emergent detection and periodic data gathering, the sensed data should be transferred to the sink efficiently and quickly. Recently, there are many related studies. However, there are few researches taking energy efficiency, transport delay, and network reliability into comprehensive consideration. In this article, a novel adaptive green and reliable routing scheme based on a fuzzy logic system is proposed in consideration of energy efficiency, end-to-end transport delay, and network transmission reliability. The key idea of the proposed scheme is to generate different number of renewed packet copies after certain steps according to the fuzzy inference. The fuzzy inference reflects the knowledge that the nodes in the region far to the sink and with more remaining energy initiate and transmit more packet copies concurrently by multiple routing paths to ensure the success rate of data transmission, whereas less. Thus, the high energy efficiency and low latency are obtained for data collection. Our analysis and simulation results show that adaptive green and reliable routing is more superior than the existing scheme.

Keywords

Internet of things fuzzy logic packet reproduction reliability delay lifetime

Introduction

The emergence of low-power processors, smart wireless networks, low-power sensors, and cloud computing as well as big data analysis has led to the increase in the interest on the Internet of things (IoT).^1–5 By combining these techniques, a large number of sensors could be placed anywhere to collect any valuable information, including the where or what information relating to the monitoring object behavior, such as military, environmental science, home automation, health care, architecture, and urban management.^6–8 One of the important technology in industrial wireless sensor network (WSN) is efficient data gathering.^1–3,6 For data gathering of industrial WSN, there are several key requirements that make industrial WSN distinctive:

Reliability. Reliability is vital for industrial applications. Due to the unreliable wireless links, it is important to avoid packet loss and to ensure the reliable communications for most applications in industrial WSNs.^9–11 There are mainly two kinds of solutions to ensure the transmission reliability, including avoiding and recovering packet loss. The typical solutions are Automatic Repeat-reQuest (ARQ) protocol and multi-path routing.^8,12–14 In the ARQ, the data transmission reliability is guaranteed by retransmitting the lost data. In the multi-path routing, data packets are transmitted by multiple paths to achieve reliable data transmission. However, these schemes are poor at end-to-end (E2E) successful transmission rate or energy efficiency.

Delay. For industrial surveillance and control, the timeliness of its data is crucial.^15–18 The E2E delay is defined as the time required for sensor nodes transmitting the monitoring data to the sink. In applications such as emergency and hazard monitoring, they require the sensed information transmitted to the sink quickly and continuously. The bigger delay may cause the inaccuracy of the decision and even serious production accidents. This is unacceptable for industrial WSN.

Energy efficiency. The industrial WSN consists of spatially distributed sensors capable of sensing, data processing, and communication. The sensors are usually powered by battery. If the wireless nodes need to be plugged in or recharged every few hours or months, the deployment cost is prohibitive and it is impractical. In addition, some sensor nodes are not rechargeable. Thus, from the consideration of economic benefits, the energy consumption is one of the most concerned topics in the network design. However, reducing the energy consumption of data collection protocols cannot necessarily improve the network lifetime effectively.^19,20 There is a special phenomenon of energy holes or hotspots in WSN. The network lifetime depends entirely on the nodes’ energy cost of hotspots. To improve the network lifetime effectively, the energy cost of hotspots should be reduced. Hence, it suggests that we should minimize the energy cost of nodes in hotspots as many as possible, in addition to minimizing the total energy consumption of data collection schemes. Therefore, industrial WSN has the key challenge to design data gathering scheme of high energy efficiency in order to prolong the network lifetime.

Intelligence. Recently, people have paid great attention to the improvement of object intelligence. Intelligence of terminal sensor nodes is an important operation technology in industrial WSN. For example, to meet the low power requirements to extend the battery life, it is necessary for sensor nodes to automatically adapt to changes in the available power and adopt intelligent forwarding scheme according to the current characteristic of the entire network.^21–23 Since both software and hardware resources are limited for WSN nodes, it is challenging to improve the intelligence level of sensor nodes.

To address these issues, the proliferation routing (PR) scheme is proposed to recover the lost packet by the in-middle recovery.⁹ In the PR approach, the source node has multiple copies of data packets and transmits them concurrently through multiple routes. In the routing process, data are reproduced at the appropriate time and is forwarded through multiple paths routing until arriving at the sink. Although PR scheme could ensure the transmission reliability, it has the following drawbacks:

The packet loss is recovered by the in-middle recovery or packet reproduction for PR. It ensures the data multiplication and concurrent transmission to guarantee the network transmission reliability. But, to guarantee the network transmission reliability, the number of multiple routing paths is often calculated according to the worst case for PR. This leads to more energy consumption and affects the network lifetime.

Nodes with different distances to sink may have different data loads to forward, which causes different energy consumption and remaining energy (RE). The sensors located at the area closer to the sink often consume their energy faster than other sensors, because these sensors must relay data from other nodes, which causes their batteries depleted very quickly. In the PR, it does not consider the factors affecting the energy efficiency, such as distance and energy level.

The number of renewed data packets of sensor nodes cannot be adaptively adjusted according to node energy and distance to sink. The adaptive data collection is not implemented. The PR scheme is lack of intelligence.

Based on the above analysis, in this article, we propose a novel adaptive data gathering scheme based on fuzzy logic in consideration of energy efficiency, E2E delay, and transmission reliability. It is called adaptive green and reliable routing (AGRR). Compared with the existing study, we make several contributions follows:

The proposed scheme has no special requirements for hardware system. In order to ensure the reliability of data transmission and reduce the energy consumption of nodes in data collection, many of the current algorithms are too complex to be implemented. Because they have high requirements for hardware system, it is difficult to run and implement on the existing hardware system. Fuzzy inference is based on rule inference. It directly uses language inference rules, reflecting the operator knowledge of the experience or relevant experts in the field. In the design, there is no need to establish an accurate mathematical model of the studied object. In addition, the inference mechanism and strategy are easy to be accepted and understood. And, the design is simple and easy to use. The implementation and operation of fuzzy logic require very small storage space.²⁴ Therefore, it is suitable for sensors without special requirements for hardware.

A fuzzy-rule-based scheme considering reliable communication and energy efficiency is proposed. Reducing delay with the guarantee of network reliability and network lifetime is very challenging. In this article, the data collection scheme named AGRR is proposed. In order to realize efficient data gathering, the proposed method calculates the number of transmitted packet copies based on fuzzy inference. A fuzzy logic system is designed based on heuristic knowledge and language decision rules. Thus, it is beneficial to simulate the process and method of artificial control, which enhances the adaptability of routing scheme and makes it have a certain level of intelligence. In addition, it is easy to find the choice of compromise using these fuzzy reasoning rules. In this article, the fuzzy inference is based on the knowledge that the nodes in the region far to the sink and with more RE initiate and transmit more packet copies concurrently by multiple routing paths to ensure the success rate of data transmission. And, in order to extend the network lifetime, the number of reproduced packet copies is calculated depending on the distance to the sink and the node’s RE. The network lifetime under the reliability guaranteed can be prolonged by reproducing different number of packet copies inferenced from fuzzy language rules.

We offer theoretical performance analysis. The theoretical analysis on the maximum number of reproduced packet copies under certain cases is presented. The data loads and energy cost of each node are analyzed. In addition, the transmission delay is discussed. Finally, we describe the selection of AGRR parameters as a multi-objective optimization issue under the constraint of the network reliability.

Comprehensive simulation experiments are carried out to evaluate the effectiveness of the AGRR scheme. The simulation results show that the proposed AGRR outperforms the compared scheme. The optimization objective of network lifetime and transport delay with the satisfaction of network reliability is achieved. In the simulation, the maximum energy cost could be reduced by 23.05% in one round of data gathering and without the transport E2E delay increased simultaneously compared with PR, which presents the superiority of the strategy. Therefore, the network lifetime could be improved without the increase in the transport delay through obtaining the optimized parameters.

The rest of this article is organized as follows: section “Related work” reviews the related works. Section “System model and problem statements” describes the system model. The design of the novel AGRR scheme is presented in section “The design of AGRR scheme.” Section “Performance analysis of AGRR scheme” formulates the performance analysis. The simulation results are presented in section “Simulation results” to evaluate the efficiency of the proposed AGRR scheme. A conclusion is given in section “Conclusion and future work.”

Related work

There are many research efforts devoted to provide an efficient data gathering for industrial WSN. The studies mainly focus on the three aspects of reliable transmission, energy efficiency, and latency. It is necessary to provide reliable transmission service for industrial WSN.^9–11 There are two typical categories of avoiding and recovering lost packets to ensure reliable transmission in the existing works. The multi-path routing or concurrent multi-path routing is one typical way of avoiding packet loss. It uses multiple alternative paths through a network to ensure reliable transmission. It is evident that the schemes will cause more energy cost. In addition, these schemes based on packet-loss avoidance are usually costly. So, it is not widely applied in practice. The reliable transmission protocols by recovering the lost packets are more widely adopted, such as the ARQ protocol. It is a typical method of the packet-loss recovery. In the scheme, the network transmission reliability is ensured by retransmitting the lost packets once or many times.^12,14 Although ARQ schemes could improve the transmission reliability, the packet-loss retransmission could lead to high delay for working in the poor industrial field.

Many of the existing research on data gathering integrate network delay and reliability,^{3,14,18,25,26} or integrate network lifetime and delay,^8,16,17 or network lifetime and reliability.^19,20,22 For example, in order to improve transmission reliability and reduce transmission delay, PR scheme appeared, in which the packet loss is recovered by the in-middle recovery. In the PR approach, the source node transmits multiple copies of data packets and forwards them concurrently through multiple routes. Some packets lost in the routing paths due to the unreliable links are reproduced at their arriving nodes after certain routing hops. Then, all the packets including the renewed are forwarded through multiple paths continually. The procedure is repeated until they arrive at the destination node sink. Although PR scheme could guarantee transmission reliability by packet reproduction and reduce the unnecessary waiting time for packet-loss retransmission in the routing process to the destination, it is evident that it increases the energy cost, and the network lifetime may not be improved effectively. As far as we know, there are few researches taking network reliability, delay, and network lifetime into consideration.

Prolonging the network lifetime is a challenging issue in the case of ensuring high transmission reliability and low latency. Some researches focus on applying the modern artificial intelligent algorithms to realize the goal of multi-objective optimization. In order to improve the reliability and energy efficiency of data delivery, Rosset et al.²² studied the application of swarm intelligence in large-scale WSNs. The artificial bee colony algorithm is also studied in application of data collection for WSNs, such as path planning in Chang et al.²³ It is undeniable that these algorithms are effective. However, these algorithms are complicated, and it is complex to implement in terminal nodes with limited resources, because they generally have high requirements of the hardware. Therefore, it is difficult to implement on the sensor nodes without changing the current hardware. Recently, because fuzzy logic adopts fuzzy sets instead of fixed and exact value for approximate reasoning, it has many advantages, such as easy implementation, strong robustness, and strong ability to approximate non-linear mapping. It is widely applied in fields, such as adaptive control systems and system identification.²⁷ In addition, it has no special requirement on hardware. The implementation and operation of fuzzy logic require very small storage space. Thus, it is suitable for terminal sensors. Combining the advantages of the PR in ensuring reliable transmission and low E2E delay and the fuzzy logic in easy implementation, the fuzzy-rule-based packet reproduction routing scheme is studied in the article to achieve the prolongation of the network lifetime and decrease in E2E transport delay when the transmission reliability is satisfied.

System model and problem statements

System model

We consider a typical and the most used planar periodic data gathering WSN, which consists of $N$ sensor nodes. The nodes are randomly distributed in a planar circular network with the radius of $R (m)$ , the area of $W (m^{2})$ , and the node density of $ρ (m^{- 2})$ . Once the nodes are deployed, they will no longer move. Each node has an identical transmission range of $r (m)$ . To monitor and detect an event, the sensor node will periodically generate a packet and forward the message contained in the packet to one node called sink through multi-hop relays. We assume the location of the sink node is at the center of the network. The data packet has the length of $σ bits$ . Each sensor node is assumed to know about the distance to the sink, and sensor nodes also know about their one hop neighbors.

In this article, the energy consumption model is based on the typical energy consumption model studied in Gupta and Kumar.²⁸ In the model, the energy consumed for sending one packet is calculated as follows

{\begin{matrix} E_{t} = σ E_{elec} + σ ε_{fs} d^{2} (d < d_{0}) \\ E_{t} = σ E_{elec} + σ ε_{amp} d^{4} (d \geq d_{0}) \end{matrix}

(1)

And, the energy consumed for receiving one packet is computed by

E_{r} = σ E_{elec}

(2)

where σ and $E_{elec}$ , respectively, indicates the sending data packet length (bits) and the transmitting circuit loss energy. We use $d_{0}$ to represent the transmitting distance threshold (m). The parameters $ε_{fs}$ and $ε_{amp}$ are, respectively, used to denote the energy required by power amplifier in the cases of transmitting distance less and no less than the threshold $d_{0}$ . Table 1 shows the parameters and the corresponding values generally adopted in energy consumption model.²⁸ Based on the model, the energy consumed for sending or receiving data packets could be calculated. Therefore, each sensor node has its own RE information.

Table 1.

Parameters and values.

Parameter	Value
Threshold (d₀), m	87
E_elec (nJ/bit)	50
$ε_{fs}$ (pJ/bit/m²)	10
$ε_{amp}$ (pJ/bit/m⁴)	0.0013

Problem statements

For realizing the emergency detection and periodic data gathering, the perception data should be collected to sink efficiently and quickly. Concerning the network performance, our goal in this article is to design an efficient data gathering scheme optimizing the overall performance including the guarantee of network reliability, the reduction of transport delay, and the improvement of energy efficiency. Considering that the network lifetime depends largely on the node with the largest energy consumption of the network, we use the first node death time to approximately represent network lifetime and denoted by $T$ . Because of the unreliable wireless communication, the packet may be lost in the transmission. Network reliability is used to represent the success rate of packet delivered to sink from all source nodes to sink in quality-of-service (QoS) level. It indicates the transport service quality. If we use $δ$ to indicate the guarantee of network reliability and let $φ_{i}$ denote the success rate of packets transmitted from source node $i$ to sink, $φ_{i} \geq δ$ . That means that each sensed data transmitted to the sink with a probability not less than $δ$ . In order to ensure the transmission reliability, the lost packet is reproduced in the transmission procedure as in Liu et al.⁹

Each initiated packet carries the information (ID, time to live (TTL), DELAY), where ID describes the information associated with the packet. The packet carries the value of TTL to record the route length. Therefore, packet lifetime or packet TTL is defined as the number of steps needs to be forwarded before reproduction. It represents the route length. In addition, DELAY denotes the transmission time took in transferring procedure. We called the transport delay or E2E delay denoting the time required for a packet to finish its successful transmission to the sink. In the transmission, the packet needs time to finish one hop route and packet reproduction. The total time needed for the transmission and reproduction is recorded to make the final statistics of DELAY. Following the network model in Xu et al.,¹⁶ we assume the transmission reliability of node $i$ is $ε_{i}$ and the length of the routing path from the source node $i$ to the sink is $h$ hops. Let $P_{i}$ denote the nodes contained in the routing path and $P_{i} = {V_{h}^{i}, V_{h - 1}^{i}, \dots, V_{1}^{i}}$ , where $V_{h - m}^{i} (m = 0, 1, h - 1)$ denotes the node with distance of $h - m$ (hops) to the sink. We denote the reliability at each node by $[ε_{h}, ε_{h - 1}, \dots, ε_{1}]$ . Therefore, the network reliability of packet transmitted to the sink from node $i$ is $φ_{i} = [1 - \sum_{k = 1}^{h} (1 - ε_{k})]$ . Similarly, if we assume the routing length or the packet TTL is $τ$ hops and each node is with the same reliability of $ε$ , the reliability of transmitted packet is $ε^{τ}$ after $τ$ steps. Considering that there are $λ$ data copies or routing paths, the total reliability $φ$ is calculated by formula (3). According to the relation contained in formula (3), the number of data copies $λ$ is derived and represented by formula (4). Figure 1 shows the relations among the parameters. From Figure 1, we can see that when the packet TTL $τ$ increases, the corresponding data copies $λ$ generated by source or relay nodes should be increased to ensure the transmission reliability. In addition, it can be seen that the reliability $φ$ is decreased with the increase in the number of hops $τ$ when the number of regenerated packets $λ$ is fixed

φ = 1 - {(1 - ε^{τ})}^{λ}

(3)

λ = \log_{a} (1 - φ) / \log_{a} (1 - ε^{τ})

(4)

where $a > 1$ .

Figure 1.

Relation between the number of data copies $λ$ and packet lifetime $τ$ under the given node reliability $ε = 0.8$ and $a = 10$ .

Thus, the focuses of our article are to meet the requirements that each sensed data transmitted to the sink with a probability not less than $δ$ . That is, $φ_{i} \geq δ$ . Simultaneously, we try to maximize the network lifetime. Considering the network lifetime depends largely on the node with the largest energy consumption of the network, the key issue is to minimize the energy cost of the node with the largest energy consumption. Therefore, the research objective is to obtain the satisfaction that for any node $i$ in the network it needs to ensure the following formula

{\begin{matrix} max (T) = min [max_{0 < i < n} (Co s_{i})] \\ Co s_{i} = N_{i}^{t} E_{t} + N_{i}^{r} E_{r} \\ φ_{i} = 1 - Π_{k = 1}^{h} (1 - ε_{k}) \geq δ \end{matrix}

(5)

where $N_{i}^{t}$ and $N_{i}^{r}$ , respectively, represent the number of sending and receiving data packets of node $i$ . $E_{t}$ and $E_{r}$ , respectively, denote the energy consumed for transmitting and receiving one data packet. And, $Co s_{i}$ denotes the total energy consumption of node $i$ . Hence, our optimization goal is minimizing the largest node energy consumption without the maximum transport delay increased and ensuring the network reliability, for example, $φ_{i} \geq δ$ .

The design of AGRR scheme

Overview of the proposed scheme

In this section, we describe the overall approach. In order to achieve an efficient data gathering, the number of the reproduced packet copies is decided based on a fuzzy logic system. The overall approach is illustrated in Figure 2.

Figure 2.

Illustration of the AGRR scheme.

In Figure 2, an example is given to illustrate the procedure of the AGRR scheme. It presents how data packets initiated from a source node $S$ transmitted to the destination sink. First, in order to ensure transmission reliability, several data copies carrying their TTL are initiated by the source node $S$ based on a fuzzy logic system. Second, the packets are dispersed over the network by one or several steps until arriving at the intermediate nodes. Finally, packets are traversed over the network following the shortest path routing until finishing their TTL. Packets are to be reproduced at the arriving nodes. These nodes are called reproducing nodes. The number of the reproduced data copies is inferenced considering the distance of the reproducing nodes to the sink and their RE. So, the proposed AGRR scheme in the article integrates three parts of fuzzy-rule-based packet generation or reproduction, packets dispersing and shortest path routing. The whole transmission process of the packets from the source node to the sink consists of many rounds of the three parts.

Fuzzy-rule-based packet generation or reproduction. For ensuring the transmission reliability and energy efficiency, the source node generally initiates $M$ copies of data packet based on the fuzzy logic system. The $M$ value depends on the source node RE and distance to the sink. During the transmission procedure, some packets may be lost because of the unreliable elements. Thus, the $M$ copies of packets could be reduced to $M' (M' < M)$ copies after several hops. To make up for the lost packets, several new copies of data packets are reproduced based on fuzzy logic inference, for example, the number of new copies is $Q$ . Then, $Q + M'$ data copies are continuously forwarded to the destination.

Direction dispersity and shortest path routing. The goal of dispersity is to transmit the reproduced packets to different nodes around the source or reproducing node. Thus, the packets could be transmitted to the destination by multi-path. When the data copies are dispersed by direction dispersity to the intermediate nodes, they will finish their TTL following the traditional shortest path routing schemes.

The implementation of the proposed scheme

Section “Overview of the proposed scheme” is an overview of the proposal. The proposed method is described in detail in the section, including fuzzy-rule-based packet generation or reproduction, direction dispersity, and shortest path routing:

Fuzzy-rule-based packet generation or reproduction.

In the proposed AGRR scheme, the number of the renewed copies of each node is decided based on the distance of reproducing node distance to the sink and its RE. The result is calculated applying a fuzzy logic system. The fuzzy inference is as follows. If the source or relay node has longer distance to the sink and more RE, it would have more data copies and the packet carries a corresponding longer TTL, which means the packet has longer path route before the next reproduction. Otherwise, there are less data copies and shorter packet TTL. A special case is that if the source or reproducing node has one or less than one hop distance to the sink, the packet is transmitted directly to the sink.

The fuzzy-logic-based packet reproduction consists of two inputs and one output, as shown in Figure 3. The inputs include the RE of the reproducing node and its distance to the sink. That means the fuzzy logic system is based on two factors of RE and distance from the reproducing node to the sink (DIS). The output of the fuzzy logic is the number of the reproduced packet copies. On the whole, the fuzzy logic system consists of three parts: (1) fuzzification, (2) fuzzy inference, and (3) defuzzification.

Figure 3.

Two inputs and one output fuzzy logic system.

In the fuzzification phase, the crisp input values are converted to corresponding fuzzy sets through fuzzy membership functions. Fuzzy sets are represented by linguistic terms, such as “small,”“medium,” and “large.” The simple membership function types, such as trapezoidal, triangular, and sigmoid are used in the article and they are defined as shown in Figures 4 –6, which allocate the truth values to a domain ranging between 0 and 1. In fuzzy membership functions, the fuzzy variables are represented as follows:

RE (remaining energy) = {XS (extreme small), S (small), M (medium), L (large), XL (extreme large)}.

DIS (distance to sink) = {XS (extreme small), S (small), M (medium), L (large), XL (extreme large)}.

The output value of the number of the renewed data packet is determined by these two factors. The output fuzzy variables are represented as follows:

RST (result) = {XXS (extreme, extreme small)), XS (extreme small), S (small), M (medium), L (large), XL (extreme large), XXL (extreme, extreme large)}.

Figure 4.

Membership function of input “RE.”

Figure 5.

Membership function of input “DIS.”

Figure 6.

Membership function of output “RST.”

The knowledge of the packet reproduction is reflected by fuzzy rules, and the fuzzy rules are applied to process the fuzzy values in the fuzzy inference phase. The packet is reproduced based on the knowledge as follows: if the source or reproducing node has longer distance to the sink and more RE, it would have larger number of data copies and the packet carries a corresponding longer TTL. Otherwise, there are less number of data copies and shorter packet TTL. As we know from the above that the fuzzy logic system is based on two factors of RE and DIS, two input factors of RE and DIS are combined for each variable, and 25 rules are obtained in the fuzzy if-then rules. In this article, the constructed fuzzy if-then rules are shown in Table 2. The interpretation of the fuzzy logic rules is as following. Based on the fuzzy logic system, in the packet reproduction phase, if RE for the reproducing node is extreme small and the DIS is extreme small, the number of reproduced packet copies (RST) is extreme, extreme small (Rule 1). That means the reproducing node renews extreme, extreme small number of data packet copies to improve energy efficiency. This rule is usually selected to reproduce data packets in the area close to the sink for reducing energy consumption. In contrast, if RE for the reproducing node is extreme large and DIS is extreme far from the sink, (Rule 25), the RST is extreme, extreme large to guarantee the statistical network reliability. The fuzzy inference surface derived from fuzzy rules is shown in Figure 7.

Table 2.

Fuzzy rules.

RE/DIS	XS	S	M	L	XL
XS	XXS	XXS	XS	XS	XS
S	XS	S	S	S	S
M	XS	S	M	M	M
L	XS	M	L	L	XL
XL	S	M	L	XL	XXL

RE: remaining energy; XS: extreme small; S: small; M: medium; L: large; XL: extreme large; XXS: extreme, extreme small; XXL: extreme, extreme large.

Figure 7.

Surface of fuzzy inference.

In the defuzzification phase, a single crisp output value is obtained using the centroid method based on the fuzzy solution space. Because the output domain is ranging from 0 to 1, in the defuzzification case, the renewed number of data copies is multiplied by a coefficient and is calculated by

λ = ψ \cdot [RST]

(6)

where $ψ$ is the coefficient. The range of $ψ$ value will be discussed in the following section.

Therefore, the fuzzy-rule-based packet generation or reproduction is implemented in packet routing as shown in Figure 8. The detailed implementation is explained in Algorithms 1 and 2, respectively.

Figure 8.

Packet reproduction based on fuzzy logic system in packet routing.

Algorithm 1.

Generating the initiated packets.

1: Begin
2: //

φ

: the network reliability
3: //

ε

: the node reliability
4: // node_list: the set of the nodes in the sensor network
5: For each node in node_list
6: calculate distance to the sink

l

(m) and

h

(hop)
7: If

h

<=1
8:

λ

=1
9: Else
10: calculate

λ

according to formula (6)
11: End
12: return

λ

13: End for
14: End

Algorithm 2.

Reproducing packets.

1: Begin
2: //

packet_list

: the set of the transmitted packet
3: For each packet in

packet_list

arriving one node
4: If TTL <1 && the packet is not lost
5: calculate distance to the sink

l

(m) and

h

(hop)
6: If

h

<=1
7:

λ

=1
8: Else
9: calculate

λ

according to formula (6)
10: End If
11: End If
12: return

λ

13: End for
14: End

2. Direction dispersity and shortest path routing.

The objective of direction dispersity carried out by source or reproducing nodes is to transmit the reproduced data copies to $λ$ intermediate nodes to realize multi-path routing. The intermediate nodes are around the source or reproducing nodes and they have the distance of $X_{h}$ , where $X_{h}$ represents the maximum hops of the disperse. In the process of realizing the packets dispersity, the packets are dispersed along the X direction and Y direction simultaneously as illustrated in Figure 9. As we know that the number of packet copies is $λ$ , $λ$ angles are randomly selected from 360° first, which, respectively, represents the disperse direction. If we assume one selected angle is $θ_{1}$ , it means that the packet is transmitted $\tan θ_{1}$ hops along the Y direction whenever it is transmitted by one hop along X direction, which is illustrated by the red routing path in Figure 9. As shown in Figure 9, there are four data packets dispersed to four intermediate nodes, which are intermediate nodes of S1, S2, S3, and S4. In the article, we assume the dispersing distance is one hop along the X direction. And, the dispersing direction is different according to the randomly selected dispersing angle. The detailed implementation of dispersing one packet is presented in Algorithm 3. After packet dispersed to intermediate nodes, the typical shortest path routing is implemented to transmit the packet to the destination sink or the next reproducer.

Figure 9.

Procedure of packet dispersed to intermediate nodes.

Algorithm 3.

Dispersing the packets.

1: Begin
2: For each packet in initiated or reproduced

λ

packets
3: select one angle

θ

randomly from 2

π

4: If 0<

θ

π / 2

x

1

y = \tan θ

6: Else If

π / 2

θ

π

x

- 1

y = - \tan θ

8: Else If

π

θ

3 π / 2

x

- 1

y = - \tan θ

10: Else

π

θ

3 π / 2

11:

x

1

y = \tan θ

12: End If
13: return

x, y

14: End for
15: End

Therefore, the procedure of the proposed AGRR scheme is shown in Algorithm 4.

Algorithm 4.

Procedure of the AGRR.

1: //

φ

: the network reliability
2: //

ε

: the node reliability
3: Begin
4: generating the initiated

λ

packets following algorithm 1
5: packet ttl

τ

is calculated by formula (4)
6: If

λ

=1
7: trans packet directly to sink
8: Else
9: dispersing following algorithm 2
10: For each packet in dispersing node set
11: If the packet is not lost
12:

τ

- = 1
13: If intermediate distance to the sink

h

<1
14: trans packet directly to sink
15: Else
16: If

τ

>1
17: route to next hop by shortest path routing
18: Else
19: reproducing packet following algorithm 3
20: go to 9
21: End if
22: End if
23: End if
24: End for
25: End if
26: End

Performance analysis of AGRR scheme

The core idea of the proposed AGRR scheme is to determine the number of reproduced packet copies based on fuzzy logic system in order to realize the network delay reduction and network lifetime prolonged under the assurance of transmission reliability. In this section, the parameters and its performance of the strategy are discussed.

The maximum number of reproduced packets

Theorem 1

If we assume $R = ℜ r$ , $\sum_{k = 1}^{χ} τ_{k} \leq ℜ$ is obtained, where $R$ represents the radius of the planar network, $r$ indicates the transmission range of sensor nodes, $χ$ denotes the reproduced times of the packet initiated by one source node in the transmission process to the sink, and $τ_{k}$ represents the TTL (hops) before reproduction in the transmission path of the kth renewed packet. The maximum number of reproduced packets $λ_{\max}$ can be expressed as follows

λ_{\max} < \frac{\log_{a} (1 - ε - a^{ℜ})}{\log_{a} (1 - φ)} (a > 1)

(7)

Proof

As we know that $\sum_{k = 1}^{χ} τ_{k} \leq ℜ$ and $χ \geq 2$ , $τ_{\max} \leq ℜ$ is derived. According to the relation among the network reliability $φ$ , node reliability $ε$ , the number of reproduced data copies $λ$ , and TTL $τ$ shown by formula (4). The following formula is obtained

τ = \frac{\log_{a} [1 - {(1 - φ)}^{1 / λ}]}{\log_{a} ε}

(8)

Therefore, we have the following result

τ_{\max} = \frac{\log_{a} [1 - {(1 - φ)}^{1 / λ_{\max}}]}{\log_{a} ε} < ℜ

(9)

After further simplification, the maximum number of the renewed data packet copies satisfies the following formula: $λ_{\max} < (\log_{a} (1 - ε - a^{ℜ}) / \log_{a} (1 - φ))$ .

In short, the number of renewed data packets has the maximum value. After exceeding the maximum value, the TTL or the route length of the packets exceeds the network topology radius hop, and the packet in-middle recovery cannot be realized.

The maximum energy consumption

In this part, we discuss the number of packets that each node needs to transmit after one round of data gathering.

Theorem 2

Considering the transmission range of sensors is $r$ and the network circular width or the packet lifetime $τ$ , each node finds its next forwarding node by the shortest path routing. We assume that the distance of one node to the sink is $l$ and $l = hr + μ$ , where $h$ represents hops to the sink and $μ$ denotes the remaining distance less than $r$ . In the case of packet generated based on fuzzy logic system, the data loads of one node with the distance $l$ to the sink are calculated as following

\begin{matrix} κ_{l_fuzzy} = \frac{l \cdot ds \cdot ρ \cdot λ_{0} + \sum_{m = 1}^{h} (l + mr) \cdot ds \cdot ρ \cdot λ_{m}}{l \cdot ds \cdot ρ} \\ = \sum_{m = 0}^{h} (1 + \frac{mr}{l}) λ_{m} \end{matrix}

(10)

where $λ_{m}$ denotes the number of data copies generated by source or reproducing nodes based on fuzzy logic system. It is calculated by formula (6).

Proof

If the number of packet generated by source or reproducing node is fixed $λ$ , the packet lifetime is $τ$ . According to the study on the data loads of each node needs to transmit in the literature,^16–18 the data loads borne by the node with distance $l$ to sink is approximately equal to the result in the literature^16–18 multiplied by $λ$ for PR scheme (taking into account of packet loss, it actually should be smaller than this value). Thus, the data loads are approximately calculated by the following

\begin{matrix} κ_{l} = \frac{l \cdot ds \cdot ρ \cdot λ + \sum_{m = 1}^{h} (l + mr) \cdot ds \cdot ρ \cdot λ}{l \cdot ds \cdot ρ} \\ = \sum_{m = 0}^{h} (1 + \frac{mr}{l}) λ \end{matrix}

(11)

In this case of packet generated based on fuzzy logic system, the number of packets forwarded by one node with distance $l$ to the sink is calculated as following

\begin{matrix} κ_{l_fuzzy} = \frac{l \cdot ds \cdot ρ \cdot λ_{0} + \sum_{m = 1}^{h} (l + mr) \cdot ds \cdot ρ \cdot λ_{m}}{l \cdot ds \cdot ρ} \\ = \sum_{m = 0}^{h} (1 + \frac{mr}{l}) λ_{m} \end{matrix}

(12)

where $λ_{m}$ denotes the number of data copies generated by source or reproducing nodes based on fuzzy logic system. And, it is calculated by formula (6).

From the above analysis, we can see that the energy cost is different for each node in industrial WSN because of the different data loads. There is more energy cost in hotspots and less energy consumption in non-hotspots. Therefore, we could fully exploit the energy cost characteristic to generate more data copies for nodes in the area far to the sink and with more RE. Correspondingly, the generated packets take longer path route or longer TTL to be forwarded. Otherwise, the opposite is true. This is the superiority of the packet reproduction based on fuzzy logic. Compared with PR, we can get the final result

κ_{l} - κ_{l_fuzzy} = \sum_{m = 0}^{h} (1 + \frac{mr}{l}) (λ - λ_{m})

(13)

The research goal is to minimize the energy cost of the node with the largest energy consumption. Therefore, if $Max (κ_{l} - κ_{l_{fuzzy}}) > 0$ , the proposed AGRR scheme is more energy efficient than the PR scheme.

The maximum transmission delay

In this part, we do analysis on the relation between the number of reproducing times and E2E delay. From section “The maximum number of reproduced packets,” we know the total length of network radius is $ℜ$ hops. That is, $R = ℜ r$ . According to $τ = \log_{a} [1 - (1 - φ)^{1 / λ}] / \log_{a} ε$ , the maximum TTL of the reproduced data packet is $τ_{m} = \log_{a} [1 - (1 - φ)^{1 / λ_{m}}] / \log_{a} ε$ . Because $\sum_{k = 1}^{χ} τ_{k} \leq ℜ$ , the number of renew times in the whole transmission is $χ$ . We assume $ν$ denotes the time needed for one hop transmission and $υ$ represents the time required for one packet reproduction. Because $υ >> ν$ , the E2E delay of data packets mainly depends on the number of reproduction times. It is calculated approximately as following

ζ = χ υ

(14)

Considering the time required for once packet reproduction is much longer than the time needed for packet one hop transmission, the larger number of packet reproduction times means the greater E2E delay.

From the above discussion, we can see that the larger number of packet copies leads to longer packet TTL and less number of reproduction times. In the case, the E2E delay is reduced and the energy cost may be increased due to the larger number of reproducing packets. Thus, it is also a trade-off optimization issue to find the optimized parameters of AGRR to ensure E2E delay reduction without the increase in the energy cost.

Simulation results

The goal of the proposed scheme is to prolong the network lifetime and reduce the E2E delay under the constraint of the network reliability. In this section, the simulation results are illustrated to evaluate the proposed AGRR scheme from three performance metrics including the network reliability, the maximum energy cost, and the maximum E2E delay after one round of data gathering. First, the network model parameter setting applied in simulation experiment is described. Then, the evaluation results are presented for the proposed routing scheme. Finally, it is compared with the existing PR routing mechanism to prove the effectiveness.

Parameter settings

The simulation scenario is a WSN consisting of 800 sensor nodes that are uniformly and randomly scattered in a two-dimensional circular plane with the radius of R = 400 m. The network is shown in Figure 10. In the network, the sink is located at the center of the circular plane. In addition, the transmission range is assumed r = 60 m in maximal. The packet size is fixed 100 bits. And, we assume the time for one hop transmission is 1 ms and for packet reproduction is 3 ms. All the nodes except the sink have the identical initial energy of 2 J. The node and network reliability are assumed with the same value $φ = ε = 0.85$ . Other parameters are shown in Table 1. As illustrated in the design of the proposed AGRR scheme, if the distance from source or reproducing nodes to the sink is just one or less than one hop, the packets are transmitted directly to the sink. In the simulation, the data loads of each node include the number of receiving and sending data packets. The energy cost of each node is calculated according to formulas (1) and (2) based on the data loads. The E2E delay from one source node to the sink equals to the average time required for all packets generated in the transmission procedure and successfully transmitted to the sink. Each simulation runs 1000 times and we take the average results.

Figure 10.

Network topology with 800 nodes scattered in a circular planar with the radius of R = 400 m.

As shown in Figure 4, the fuzzy logic system is based on two input factors of RE and distance from the node to the sink to deduce the output value of the number of the renewed data packet. The linguistic terms of the fuzzy variables are RE = {VS, S, M, L, VL}, DIS = {VS, S (small), M, L, VL}, and RST = {VVS, VS, S, M, L, VL, VVL}. In the simulation, the simple types of trapezoidal, triangular, and sigmoid fuzzy membership functions are applied as shown in Figures 5 –7, respectively. The maximum and minimum values are determined by considering conditions of the sensor network. In the article, the domain of inputs and output are {0, 1}, {0, 1}, and {0, 1}, respectively. The fuzzy logic rules are as shown in Table 2. In the fuzzy inference, the simple logical operation methods, such as AND, OR and Prober are applied for the implication and aggregation. In the defuzzification phase, the centroid method is selected.

Evaluation on the parameter $ψ$ in the scheme

In the proposed AGRR scheme, the number of the reproduced packets is decided by fuzzy logic system. Because the output domain is ranging from 0 to 1, the output of the fuzzy system is multiplied by a coefficient $ψ$ to calculate the renewed number of data copies. In this section, we evaluate the influence of parameter $ψ$ on the performance of the proposed scheme. We, respectively, do simulation on performance metrics of reliability, energy cost, and delay. According to formula (7), we know that the number of the renewed data packets has the maximum value. In view of the current experimental parameters and formula (6), the value of parameter $ψ$ are integers and $ψ_{\max} = 6$ . Thus, the performance is evaluated under the several cases of $ψ = {2, 3, 4}$ .

Under the three different cases, our simulation results on metrics of reliability, energy cost, and delay are shown in Figures 11 –16. Table 3 shows the specific detailed comparison results. Figure 11 presents the network transmission success rates or the network reliability in QoS level under different coefficients of $ψ = 2$ , $ψ = 3$ , and $ψ = 4$ after one round of data gathering. As shown in the figure, it can be seen that the bigger value of $ψ$ leads to the higher network reliability. This means that the larger number of reproduced packet copies transmitted in the network provides the higher reliable transmission, which is in consistent with the facts. The number of packets transmitted by each node is shown in Figure 12(a). In order to clearly state the result, the performance of the domain with the distance in range [0,200] (m) is illustrated in Figure 12(b). From Figure 12, we can see that there are more data packets to be forwarded for nodes in the area closer to the sink as a whole. The larger value of $ψ$ leads to larger amount of the transmitting data for source or reproducing nodes, which is caused by more reproduced data copies in the transmission. For example, compared with $ψ = 3$ , the number of transmitting packets is increased for nodes when $ψ = 4$ in general. Moreover, as illustrated in Figure 12, when the coefficient $ψ = 2$ , the amount of transmitting data in the area close to sink is the smallest compared with $ψ = 3$ and $ψ = 4$ . And, when $ψ = 4$ , it has the largest amount of transmitting data compared with $ψ = 2$ and $ψ = 3$ . Figure 13(a) illustrates the energy cost of each node after one round of data gathering and Figure 13(b) demonstrates the results of the key range. In our simulation, they need energy cost only in sending and receiving data packets. So, the energy cost presents a similarly changing trend with the data loads carried by each node. In order to clearly compare the energy cost, the maximum energy cost comparison after one round of data gathering is demonstrated in Figure 14. From the figure, it is clear to see that the maximum energy cost is larger with the bigger coefficient $ψ$ . This is in consistent with the above-mentioned data loads analysis. The transport E2E delay of each node is shown in Figure 15(a) and (b) shows the key regional results after one round of data gathering. In addition, the maximum transport delay comparison is shown in Figure 16. As can be seen from Figures 15 and 16, the delay is longer when the distance to the sink becomes much farther as a whole. From Figure 16, we can see that the delay is reduced when the coefficient is becoming larger. This is because that the number of the reproducing times is reduced and packet reproduction needs more time than that required for packet transmission in the whole path route to sink. So, in the whole transmission from source nodes to the sink, the number of packet reproduction times is reduced. And, it means that the network E2E delay is reduced. Therefore, we can reduce network E2E delay by reducing the number of reproducing times.

Figure 11.

Comparisons of reliability.

Figure 12.

Comparisons of data loads of each node: (a) all nodes in the network and (b) nodes in the key region of the network.

Figure 13.

Comparisons of energy cost of each node: (a) all nodes in the network and (b) nodes in the key region of the network.

Figure 14.

The maximum energy cost comparison.

Figure 15.

Comparisons of transport delay of each node: (a) all nodes in the network and (b) nodes in the key region of the network.

Figure 16.

The maximum transport delay comparison.

Table 3.

Performance under different $ψ$ .

Parameters	Performance
Parameters	Reliability (%)	Maximum energy cost (J)	Maximum E2E delay (ms)
2	71.62	0.0964	21.6000
3	84.18	0.1425	18.4000
4	90.00	0.2193	18.0000

E2E: end-to-end.

Therefore, as can be seen from Figures 12 –16, the bigger coefficient $ψ$ leads to more data packets copies forwarded and smaller number of packet reproduction times in the path route from source nodes to the destination sink. Moreover, the transport delay could be reduced by reducing the number of reproducing times, which, however, may result in additional energy cost.

Comparison

The research problem of our article is similar to the PR scheme, and our work is advanced research based on the scheme. In this part, we compare the proposed AGRR scheme with the existing PR scheme through the above-mentioned circular planar network, focusing on performance metrics of the network reliability, the maximum energy cost, and the maximum E2E delay after one round of data gathering.

The detailed comparison results of the network reliability are shown in Table 4. Figure 17 clearly shows the comparisons of reliability between AGRR and PR when one round of data gathering finishes. From the results, it can be seen that there are not obvious differences of reliability when PR = 2 and $ψ = 2$ . Similarly, it is with the other two cases. However, with the increase in the number of the reproduced packet copies, the transmission success rate is becoming higher. Figures 18 –20 show the comparison of the data loads of each node after one round of data gathering under different cases. The corresponding comparisons of energy cost of each node are shown in Figures 21 –23. Table 5 shows the detailed comparison results of the maximum energy cost. To clear state the comparison, Figure 24 shows the maximum energy cost comparison. From tables and figures, we can see that there is less energy cost for AGRR compared with PR. The maximum energy cost is reduced by 15.50%, 23.05%, and 11.15%, respectively.

Table 4.

Reliability comparisons.

Parameters	Reliability (%)
Parameters	AGRR	PR
2	71.62	72.42
3	84.18	84.00
4	90.00	89.35

AGRR: adaptive green and reliable routing; PR: proliferation routing.

Figure 17.

Reliability comparisons of AGRR with PR under different parameters.

Figure 18.

Data loads comparison of each node of AGRR with PR under PR = 2 and $ψ = 2$ .

Figure 19.

Data loads comparison of each node of AGRR with PR under PR = 3 and $ψ = 3$ .

Figure 20.

Data loads comparison of each node of AGRR with PR under PR = 4 and $ψ = 4$ .

Figure 21.

Energy cost comparison of each node of AGRR with PR under PR = 2 and $ψ = 2$ .

Figure 22.

Energy cost comparison of each node of AGRR with PR under PR = 3 and $ψ = 3$ .

Figure 23.

Energy cost comparison of each node of AGRR with PR under PR = 4 and $ψ = 4$ .

Table 5.

Maximum energy cost comparisons.

Parameters	Maximum energy cost (J)
Parameters	AGRR	PR
2	0.0964	0.1141
3	0.1425	0.1852
4	0.2193	0.2468

AGRR: adaptive green and reliable routing; PR: proliferation routing.

Figure 24.

The maximum energy cost comparisons of AGRR with PR under different parameters.

Figures 25 –27, respectively, show the transport E2E delay comparison between the proposed AGRR and the existing PR scheme after one round of data gathering. It is evident from the figures that the transport E2E delay changes alternately for nodes with different distances to sink. Table 6 shows the comparison result of the maximum E2E delay. For the maximum transport delay, the difference is not obvious, as shown in Figure 28.

Figure 25.

E2E delay comparison of each node of AGRR with PR under PR = 2 and $ψ = 2$ .

Figure 26.

E2E delay comparison of each node of AGRR with PR under PR = 3 and $ψ = 3$ .

Figure 27.

E2E delay comparison of each node of AGRR with PR under PR = 4 and $ψ = 4$ .

Figure 28.

The maximum E2E delay comparison of each node of AGRR under different parameters.

Table 6.

Maximum E2E delay comparisons.

Parameters	Maximum E2E delay (ms)
Parameters	AGRR	PR
2	21.6000	21.6000
3	18.4000	18.4000
4	18.0000	18.4000

E2E: end-to-end; AGRR: adaptive green and reliable routing; PR: proliferation routing.

From the above comparison and analysis, we can see that the proposed AGRR scheme outperforms the existing PR scheme in energy efficiency. Simultaneously, it is superior in ensuring the transmission reliability without the increase in the E2E delay.

Conclusion and future work

In this article, we studied the problem of efficient data gathering in consideration of energy efficiency, data reliability, and E2E transport delay in industrial WSN. In the existing scheme, the energy cost is quite high. This could lead to the energy of some nodes in the network is exhausted quickly. In addition, to give nodes a certain degree of intelligence and adaptability, a novel fuzzy-rule-based AGRR scheme is proposed in the article. In the AGRR scheme, the number of reproduced packet copies is decided based on a fuzzy logic system to achieve an efficient data gathering. In the fuzzy inference, it takes the RE and distance to the sink of the source or reproducing node as its inputs. So, it can adaptably tune the number of reproducing packet copies. Therefore, the energy efficiency is improved. The theoretical analysis and the simulation results show that our method outperforms the existing method PR in reducing the maximum energy cost and prolonging the network lifetime under the guarantee of transmission reliability. Simultaneously, the E2E delay is not increased. However, the designing membership functions, arranging the inference rules and their influence on system performance are worth further research studies.

Footnotes

Handling Editor: Renato Ferrero

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: This work was supported, in part, by the Natural Science Foundation of Hunan Province (2017JJ3417), the Science and Technology Plan of Hunan (2016TP1003), the National Natural Science Foundation of China (61472450), and the National Basic Research Program of China (973 Program) (2014CB046305).

ORCID iD

Anfeng Liu

References

Atzori

Iera

Morabito

. The Internet of things: a survey. Comput Netw 2010; 54(15): 2787–2805.

Lee

Park

. Energy efficient and accurate monitoring of large-scale diffusive objects in Internet of things. IEEE Commun Lett 2017; 21(3): 612–615.

Hossain

Muhammad

. Cloud-assisted industrial Internet of things (IIoT)—enabled framework for health monitoring. Comput Netw 2016; 101: 192–202.

Velandia

DMS

Kaur

Whittow

et al . Towards industrial Internet of things: crankshaft monitoring, traceability and tracking using RFID. Robot Comput Integrated Manuf 2016; 41: 66–77.

Dong

Ota

Liu

. RMER: reliable and energy efficient data collection for large-scale wireless sensor networks. IEEE Internet Things 2016; 3: 511–519.

Sethi

Sarangi

. Internet of things: architectures, protocols, and applications. J Electr Comput Eng 2017; 2017: 9324035.

Ibayashi

Kaneda

Imahara

et al . A reliable wireless control system for tomato hydroponics. Sensors 2016; 16: E644.

Mohanty

Kabat

. Energy efficient reliable multi-path data transmission in WSN for healthcare application. Int J Wireless Inform Network 2016; 23: 162–172.

Liu

Zhu

et al . A reliability-oriented transmission service in wireless sensor networks. IEEE T Parall Distr 2011; 22: 2100–2107.

10.

Kafi

Ben Othman

Badache

. A survey on reliability protocols in wireless sensor networks. ACM Comput Surv 2017; 50(2): 31.

11.

Kim

Lee

Park

et al . Security challenges in recent Internet threats and enhanced security service model for future IT environments. J Internet Technol 2016; 17(5): 947–955.

12.

Kwok

. A new multipath routing approach to enhancing TCP security in ad hoc wireless networks. In: 34th international conference on parallel processing (ICPP), Oslo, 14–17 June 2005.

13.

Liu

et al . A time and location correlation incentive scheme for deeply data gathering in crowdsourcing networks. Wirel Commun Mob Com 2018; 2018: 8052620.

14.

Liu

et al . APMD: a fast data transmission protocol with reliability guarantee for pervasive sensing data communication. Pervasive Mob Comput 2017; 41: 413–435.

15.

Saifullah

et al . Real-time wireless sensor-actuator networks for industrial cyber-physical systems. Proc IEEE 2016; 104: 1013–1024.

16.

Mao

et al . A delay-efficient algorithm for data aggregation in multihop wireless sensor networks. IEEE T Parall Distr 2011; 22(1): 163–175.

17.

Huang

Liu

Wang

et al . Green data gathering under delay differentiated services constraint for Internet of things. Wirel Commun Mob Com 2018; 2018: 9715428.

18.

Joo

Shroff

. On the delay performance of in-network aggregation in lossy wireless sensor networks. IEEE ACM T Network 2014; 22: 662–673.

19.

Boulfekhar

Benmohammed

. A novel energy efficient and lifetime maximization routing protocol in wireless sensor networks. Wireless Pers Commun 2013; 72(2): 1333–1349.

20.

Tang

Liu

Zhao

et al . An aggregate signature based trust routing for data gathering in sensor networks. Secur Commun Netw 2018; 2018: 6328504.

21.

Liu

et al . Learning based synchronous approach from forwarding nodes to reduce the delay for Industrial Internet of things. EURASIP J Wirel Comm 2018; 2018: 10.

22.

Rosset

Paulo

Cespedes

et al . Enhancing the reliability on data delivery and energy efficiency by combining swarm intelligence and community detection in large-scale WSNs. Expert Syst Appl 2017; 78: 89–102.

23.

Chang

Zeng

Chen

et al . An artificial bee colony algorithm for data collection path planning in sparse wireless sensor networks. Int J Mach Learn Cyb 2015; 6: 375–383.

24.

Adnan

MRHM

Sarkheyli

Zain

et al . Fuzzy logic for modeling machining process: a review. Artif Intell Rev 2015; 43(3): 345–379.

25.

Zhang

Long

Zhao

et al . Minimized delay with reliability guaranteed by using variable width tiered structure routing in WSNs. Int J Distrib Sens N 2015; 11: 1–12.

26.

Zhang

Long

Zhang

et al . A delay-aware and reliable data aggregation for cyber-physical sensing. Sensors 2017; 17: 395.

27.

Nam

Cho

. A fuzzy rule-based path configuration method for LEAP in sensor networks. Ad Hoc Netw 2015; 31: 63–79.

28.

Gupta

Kumar

. The capacity of wireless networks. IEEE T Inform Theory 2000; 46(2): 388–404.

A fuzzy-rule-based packet reproduction routing for sensor networks

Abstract

Keywords

Introduction

Related work

System model and problem statements

System model

Problem statements

The design of AGRR scheme

Overview of the proposed scheme

The implementation of the proposed scheme

Performance analysis of AGRR scheme

The maximum number of reproduced packets

Theorem 1

Proof

The maximum energy consumption

Theorem 2

Proof

The maximum transmission delay

Simulation results

Parameter settings

Evaluation on the parameter ψ in the scheme

Comparison

Conclusion and future work

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Evaluation on the parameter $ψ$ in the scheme