- Research
- Open Access
ENCP: a new Energy-efficient Nonlinear Coverage Control Protocol in mobile sensor networks
- Zeyu Sun^{1, 2}Email author,
- Guozeng Zhao^{1} and
- Xiaofei Xing^{3}
https://doi.org/10.1186/s13638-018-1023-7
© The Author(s). 2018
- Received: 17 October 2017
- Accepted: 2 January 2018
- Published: 15 January 2018
Abstract
The node deployment in mobile sensor networks (MSNs) is mostly performed in a random method. However, a large number of redundant nodes may exist due to the randomness. As a result, severe data congestion may be caused and the quality of coverage (QoC) is undermined. In order to solve this QoC problem, we propose an Energy-efficient Nonlinear Coverage Control Protocol (ENCP). This protocol utilizes the normal distribution to calculate the minimal number of sensors which is required to guarantee coverage over the monitoring area. We also balance the node energy consumption and achieve the collaborative scheduling among all the sensor nodes. Meanwhile, when a certain QoC is guaranteed, we present the calculation model for the normal distribution of the sensing ranges and the proportional relationship between different parameters in the QoC function. Finally, simulation results show that the ENCP could not only improve the network QoC and network coverage rate but also effectively control the energy exhaustion at the nodes. Therefore, the network lifetime can be effectively prolonged.
Keywords
- Mobile sensor network
- Nonlinear coverage
- Quality of coverage
- Networks coverage rate
- Network lifetime
1 Introduction
Mobile sensor networks (MSNs) are composed of tens of thousand sensor nodes whose processing ability, communication bandwidth, and energy are quite limited. Usually, the high-density node deployment strategy is employed to improve the network performance [1]. The node density can be as high as 200 nodes/m^{2}. However, a series of problems are brought about in terms of scalability, information redundancy, wireless channel interference, and energy wastes. Since the sensors are mostly battery-powered, it is often impractical to replace the batteries due to the limits of the application environment. However, the network is expected to work over a long period of time without further energy supply, which makes the energy management a key problem for the study of sensor networks.
The sensing characteristics for the same kind of sensors are investigated in the realistic environment. We also study the coverage problem for the randomly deployed sensor network where the sensing ranges for the nodes satisfy the normal distribution. The calculation model with no location information required is presented for the redundancy degree. Also elaborated is the calculation model for the minimal number of working nodes with a desired QoC. Based on QoC problem, we present a new Energy-efficient Nonlinear Coverage Control Protocol (ENCP) in mobile sensor networks. Under the premise of a certain QoC, we can use the minimum sensor node to complete the effective coverage of the monitoring area, thus suppress to the network energy consumption and a longer network lifetime.
2 Related work
Dong et al., node scheduling scheme using spatial resolution of wireless sensor networks [16]. The sensors calculate the sponsored area by the neighbors according to the location information. Then, the coverage relationship can be derived. However, this algorithm fails to consider the case of overlapped sensing area, which may cause a large number of working nodes and extra energy waste. Xing et al. proposed target coverage scheme using linear programming [17]. The probing method is as follows. Every sleeping node would regularly check whether working nodes exist within its probing area. If no, this sleeping node will switch to the work state. Otherwise, it will remain sleeping. Obviously, some nodes may keep working consistently according to the PEAS protocol, which leads to an early node failure and unbalanced network energy consumption. Therefore, the QoC is affected. Wang et al. proposed saluting of scheduling mobile sensor and fixed sensors for target tracking algorithm. (MTTA) [18]. The node closest to the optimal location is chosen as the working node according to this protocol. Therefore, the QoC is guaranteed with the smallest number of working nodes. However, the calculation of the optimal location relies on rigorously accurate positioning technique and high computational complexity. Sun et al. proposed a linear programming optimization coverage scheme (LPOCS) [19] which divides all of the sensor nodes into many subsets. The connectivity and coverage for a specific target within every subset can then be guaranteed.
Energy-efficient sleep schedule with service coverage guarantee is firstly given by Zhang et al. in [20]. The mathematical relationships among the QoC, the number of working nodes, the size of the sensing area, and the sensing ranges of the sensor nodes are derived while no location information is required in this algorithm. Based on the mathematical relationship, three scheduling strategies are proposed, i.e., Efficient Coverage Algorithm Based on Node Scheduling Strategy (ECNSS) [21], Energy-efficient Multi-target Coverage Control Protocol (EMCCP) [22], and Efficient Rendezvous algorithms for mobility-enabled (ERME) [23]. In these three scheduling schemes, the working nodes are chosen in completely a random method, which may result in the instability of the QoC. Furthermore, the limited delay mechanism is employed in the scheduling schemes to ensure that all the data can be collected within the monitoring area. Liu et al. [24] derived the mathematical relationships among the QoC, the size of the network monitoring area, the sensing range of the nodes, and the node density. Again, the location information is not needed for the QoC during the derivation. Also included are three methods to evaluate the coverage, i.e., partial coverage, node coverage, and monitoring ability. A further modification was made based on the protocol in [25], and the energy balance strategy was introduced. The working nodes are chosen according to the remained energy, and optimization is performed on the distribution of working nodes. Therefore, the network lifetime is further prolonged. An extension of the results in [26] was made in [27], and the influence of edge effects is considered. As a result, the analytical results are more accurate and many multiple-fold coverage problems can be analyzed. Zeng et al. [28] studied the coverage problem for the sensor network where the node deployment satisfies the two-dimension normal distribution. Wu et al. [29] proposed a probability-based calculation method for the node redundancy degree, according to which, the node could independently calculate its own redundancy degree. Furthermore, a node scheduling protocol, lightweight deployment-aware scheduling (LDAS) is proposed with no location information required. However, the sponsorship of the two-hop neighbors for the sensing area of the nodes is neglected. As a result, many of the working nodes chosen by the LDAS algorithm are redundant. A joint scheduling algorithm is proposed by Chen et al. [30] which adds more working nodes to guarantee the network connectivity with the required QoC.
Cheng et al. derived the minimal number of working nodes and the corresponding node deployment location for the simultaneous guarantee of k coverage and network connectivity [31]. The QoC and connectivity quality are guaranteed with the minimal number of working nodes by deploying the mobile sensor nodes to the designated positions. Therefore, the network energy is saved. Lu et al. presented the sensor node deployment scheme which guarantees the full coverage over the monitoring area and the network 2 connection [32]. It was also proven that the proposed deployment is optimal regardless of the value of R_{ c }/R_{ s } (R_{ c } is the communication range and R_{ s } is the sensing range).
All the studies stated above are based on different assumptions [33–37]. The sensing range of the node varies according to its own characteristics and the influence of other external factors such as the environment. This paper focuses on the realistic sensing characteristics of randomly deployed MSNs and studies the coverage problem for the MSNs where the sensing range of the node satisfies the normal distribution and no location information is required.
3 Network model and problem description
3.1 Basic assumptions
- (1)
The node density is sufficiently high. When all the nodes are working nodes, the QoC can be guaranteed and a large number of redundant nodes will exist in the mobile sensor network.
- (2)
Boolean sensing model is adopted by the nodes. In other words, if the sensing range of an arbitrary node i is R_{ i }, then, the sensor area of node i is circle with center i and radius R_{ i }. The sensing area is denoted as Θi (R_{ i }).
- (3)
The sensing ranges for all the nodes in the network satisfy the normal distribution N (R_{0}, δ^{2}) where R_{0} is the average of the sensing ranges, i.e., the rated sensing range, δ is the standard deviation, and R_{0} ≥ 3.3δ so that the sensing ranges concentrate in the interval [0, 2R_{0}].
- (4)
The monitoring area is large enough so that the boundary effect can be neglected.
- (5)
The communication range of the node is no smaller than 4R_{0}, i.e., the communication range is at least twice times the maximal sensor range.
- (6)
No GPS or other locating techniques are required for each node to acquire the location information.
- (7)
The sensor nodes are randomly deployed in the monitoring areas with high density, and the sensor nodes are independent from each other.
In large scale MSNs, the random deployment scheme is both practical and low in cost [38–40]. Therefore, the random deployment scheme is employed in this network model. Although all the nodes have been the same rated sensor range R_{0} in the binary sensing model, the actual sensing range would still be affected by the characteristics of the nodes and the environment. Therefore, we employ the normal assumption N (R_{0},δ^{2}) on the distribution of the actual sensing range. Since the actual sensing range is no smaller than 0, we have the limitation R_{0} ≥ 3.3δ so that the probability that the actual sensing range lies in [−∞, 0] is smaller than 5 × 10^{−5}. Due to the symmetry of the normal distribution, we can derive that the probability that the actual sensing range lies in [0, 4R_{0}] is larger than 99.99%, which approximately makes it a certain event.
3.2 Definitions and problem description
where S is the set of all the nodes deployed within the monitoring area M, d (i, j) is the Euclidean distance between sensor node i and sensor node j, R_{ i }, and R_{ j } are the sensing ranges of sensor node i and sensor node j, respectively.
where φ is the set of all the working sensor nodes, S_{ i } and S_{ j } are the monitoring area for sensor node i and sensor node j, respectively, \( \mathrm{area}\left(\left(\underset{j\in \left(S(i)\cap \varphi \right)}{\cup }{S}_j\right)\cap {S}_i\right) \) is the overlapped monitoring area, and S_{ i } is the monitoring area for node i.
where φ is the set of all the working nodes, S_{ i } is the monitoring area for node i, area(M) is the size of the whole monitoring area, \( \mathrm{area}\left(\left(\underset{i\in \varphi }{\cup }{S}_i\right)\cap M\right) \) is the intersection between M and the monitoring area of all the working nodes. As a matter of fact, the quality of coverage is also equivalent to the network coverage probability.
where Δt_{ i } is a time slice which is close to 0, Δt_{i + 1} is the subsequent slice after Δt_{ i }, \( {\eta}_o^{\Delta {t}_j} \) is the quality of coverage obtained within Δt_{ j }, and η_{ d } is the desired QoC.
It is assuming that a large number of working sensor nodes are randomly deployed within the sensing area M, and the sensing ranges of all the sensor nodes must satisfy the normal distribution N (R_{0}, δ^{2}). Furthermore, R_{0} ≥ 3.3δ. All the redundant nodes are shut down on the condition that the desired QoC η_{ d } is satisfied, i.e., a minimal set of working nodes φ is found which can guarantee the satisfaction of \( \mathrm{area}\left(\left(\underset{i\in \varphi }{\cup }{S}_i\right)\cap M\right)/\mathrm{area}(M)\ge {\eta}_d \). A calculation model is constructed for the node redundancy degree. We also design the node scheduling strategy for the setφ, which can be employed to prolong the effective network lifetime.
4 Problem analysis and research methods
4.1 ENCP problem solution
Two questions have to be answered for the node scheduling strategy in the MSNs. The first one is how to determine whether a node is redundant [41–43]. The second one is the specific scheduling of the nodes. We mainly deal with the first question here while the second one is left for the next section. The calculation of node redundancy degree based on location information employs the geometry knowledge and offers the accurate coverage relationship between nodes [44–46]. However, when the location information is not available, it is hard for the nodes to derive the node redundancy degree. Still, we could still utilize the number of neighbor sensors of a node and calculate the expectation for the node redundancy degree based on the probability theory.
In order to further simplify Eq. (14), set \( t=-{r}^2/2{\delta}^2,{c}_1={R}_0^2/{\delta}^2 \). So, \( E\left({P}_{b-a}\right)=\frac{c_1}{4}{\int}_{-\frac{c_1}{2}}^0\frac{{\mathrm{e}}^t}{t+{c}_1}\mathrm{d}t=\frac{c_1}{4{\mathrm{e}}^{c_1}}{\int}_{\frac{c_1}{2}}^{c_1}\frac{{\mathrm{e}}^t}{t}\mathrm{d}t \).
Set \( {I}_1=\sum \limits_{n=1}^{\infty}\frac{t^n}{nn!} \), we have \( {tI}_1-{I}_1=-t+\sum \limits_{n=2}^{\infty}\frac{t^n}{n!}+\sum \limits_{n=2}^{\infty}\frac{t^n}{\left(n-1\right) nn!} \). So, \( {I}_1=\frac{{\mathrm{e}}^t-3}{t-1}-2+\sum \limits_{n=2}^{\infty}\frac{t^n{\left(t-1\right)}^{-1}}{\left(n-1\right) nn!} \).
Set \( p\left({c}_1\right)=\frac{c_1}{4{e}^{c_1}}\cdot \left(\frac{3}{c_1-1}+\frac{2{e}^{c_1/2}-6}{c_1-2}\right),q\left({c}_1\right)=\frac{c_1}{4{e}^{c_1}}\cdot \sum \limits_{n=1}^{\infty}\frac{c_1^{n+1}/\left({c}_1-1\right)-{\left({c}_1/2\right)}^{n+1}/\left({c}_1/2-1\right)}{n\left(n+1\right)\left(n+1\right)!} \), p(c_{1}) and q(c_{1}) are monotonically decreasing in [10, +∞).
Substitute Eq. (19) into Eq. (18) and the proof of Lemma1 is completed.
Substituting the conclusion in Theorem 1 into Eq. (23), we have \( E\left({\xi}_n\right)=1-{\left(\frac{3{R}_0^2-4{\delta}^2}{4\left({R}_0^2-{\delta}^2\right)}\right)}^n \).
Therefore, the proof of Theorem 2 is completed.
The expectation of redundancy nodes and the number of sensing neighbors
Sensor neighbors | Expectation of redundancy nodes (R_{0} = 10)/% | ||||
---|---|---|---|---|---|
δ = 0 | δ = 1 | δ = 2 | δ = 3 | δ = 4 | |
6 | 72.36 | 73.41 | 73.98 | 74.33 | 75.08 |
7 | 72.92 | 74.26 | 75.03 | 75.86 | 76.29 |
8 | 74.12 | 74.95 | 76.21 | 77.08 | 78.13 |
9 | 78.89 | 80.06 | 82.56 | 83.91 | 85.49 |
10 | 85.16 | 87.42 | 89.51 | 90.61 | 92.07 |
11 | 91.63 | 93.08 | 94.87 | 95.69 | 97.80 |
12 | 94.06 | 96.50 | 97.28 | 98.57 | 98.82 |
13 | 95.74 | 97.05 | 98.25 | 98.97 | 99.03 |
14 | 96.09 | 97.71 | 98.68 | 99.02 | 99.51 |
15 | 97.15 | 98.28 | 99.36 | 99.57 | 99.86 |
This completes the proof.
4.2 Process of NECP implementation
This node is then regarded as a redundant node which can be shut down to save energy.
The initial power is equal for all the nodes. A management node is randomly chosen in an arbitrary alliance. Centered by this management node, the routing protocol is transmitted in a single-hop or multiple-hop method. Assuming that the management node is deployed in advance with unlimited power, it could communicate directly with all the member nodes. However, the member nodes need to perform single-hop or multiple-hop routing to reach the management node. This is an optimization problem which minimizes the cost from the source to the destination. Since the energy consumption models, i.e., the calculation model for the communication energy, the calculation model for the data processing energy and the calculation model for the environment sensing energy, are definite, upon receiving one message, the management node could trace the energy change of all the nodes processing this message according to energy models, the message length and the data quantity. For each round of cycles, the nodes in the alliance are divided into three states according to the protocol, i.e., work, election, and sleep. Sensing nodes only take charge of monitoring the environment and collecting data. Relay nodes are in charge of relaying data while sensing relay nodes possess both of these two functions. When inactive nodes are switched to the sleep state, the management node determines the state of each node according to the node energy, topology, and network task. When the routing is established, the management node broadcasts the node state and routing information to all the nodes. Due to message loss and data processing delay, there may be errors in the energy calculation model for the management node. Therefore, the member nodes are required to transmit the energy update message on the present energy to the management nodes. Then, the optimal routing is calculated and broadcasted to the members in the alliance by the management node.
4.3 Set value of k
At the beginning, since all the nodes have the same initial energy and the management node is chosen randomly, the energy are consumed by all the nodes to some extent after one or several working rounds. According to the proposed algorithm, the node with more remained energy is chosen as the management node for the next round. Meanwhile, the rank of all the nodes is updated in the link. During the establishment of the alliance, each node randomly chooses a real number between 0 and 1. If this number is smaller than a certain threshold, this node is chosen as the management node. Then, the identification of this management node is broadcasted to all the nodes. Each node determines its own alliance according to the amplitude of the receiving signal and broadcasts its membership to all of the alliance members. During the data transmission period, all the member nodes transmit data to the management nodes in Time Division Multiple Access (TDMA) slots while the management nodes integrate the receiving data and broadcast them to the base station. After several working rounds, the network is restarted. Then, the next round of election for the management nodes is performed and the new alliances are established.
At the beginning of each round, in order to reduce the density of working sensor node, k nodes are firstly chosen as candidates. Therefore, k nodes should not be too dense or too sparse. k value should be at least larger than the minimal number of working sensor nodes which could guarantee the expectation of QoC.
In ENCP, we choose K = ⌈2E(k)⌉ so that globally, it can be guaranteed that there are enough nodes to satisfy the desired QoC. Then, by the local node scheduling of the ENCP, redundant nodes are switched to the sleep node to achieve the uniform coverage within the monitoring range. To balance the node energy consumption in the network, the K candidate nodes are chosen in the same way the cluster heads are chosen in [24].
5 ENCP evaluation systems
In order to verify the validity and performance for the ENCP, we perform simulations based on the OPNET Modeler platform. The monitoring area for the simulation is 200 × 200 m^{2} and the sensing ranges of the nodes satisfy the normal distribution N (10,δ^{2}), where 10 ≥ 3.3δ. The node energy consumption model is the same as the physical model in [25], i.e., the energy consumption ratio for the transmitting state. The transmission rate for the node is 56 kb/s. The time for each round is 200 s while the durations for T_{1}, T_{2}, and T_{3} are 5 s. The probability P for each candidate node to elect itself into the start_work state is 10%. The initial energy for each node is sufficient to last 190–210 rounds of consistent receiving state.
Figures 8, 9, 10, and 11 depict the relationship between the network lifetime and the target nodes within different sensing fields. The algorithms we focus on are the Multiple Target Tracking Algorithm (MTTA) [18] and linear programming optimization coverage scheme (LPOCS) [19]. It can be observed from Fig. 8 that at the initial stages of the program, the network lifetime of the three algorithms increases with the number of nodes. However, due to the limit of the value range of this algorithm and the inactive state of the redundant nodes, the network lifetime of the ENCP is lower than the other algorithms when the equalization is finally achieved for the network energy. During the coverage process for the target node, less network energy is required for the ENCP, which can be explained as above. In Fig. 10, parts of the redundant nodes are transitioned to the state of work due to the increase of the area of the sensing fields. As a result, the network lifetime is prolonged. When δ = 3, the network lifetime of the ENCP is longer than that of the LPOCS algorithm. When δ = 4, the network lifetime of the ENCP is longer than those for both of the other two algorithms. The network lifetime during the coverage for the target node is depicted in Fig. 11. It can be observed that the network lifetime of three algorithms decreases with the increase of target nodes. Finally, the energy tends to be equalized. However, the ENCP exhibits a lower decrease speed during the decline process. This is due to the fact that when a part of the sensing field is densely deployed with the sensor nodes, i.e., the coverage expectation is higher for this region, some redundant nodes are awakened via the scheduling mechanism of the sensor nodes. These awakened nodes are transitioned to the state of work to enhance the coverage intensity and further prolong the network lifetime.
6 Conclusions
Focusing on the sensing characteristics of randomly deployed MSNs, we analyzed the coverage redundancy problem for the MSNs where the sensing ranges satisfy the normal distribution. We also presented the calculation model for the node redundancy degree for which no location information is needed and the calculation model for the minimal number of working nodes to guarantee the network QoC. According to the analytical result, we proposed the ENCP which shut down all the redundant nodes satisfying the redundancy condition. Based on the ENCP, it enables the collaborative scheduling of distributed sensor nodes and balances the energy consumptions of each sensor nodes. The purpose of energy conservation of the networks is achieved since the ENCP maintains the least number of sensor nodes, as working nodes to provide the desired QoC. Simulation results show that the ENCP could not only accurately guarantee the desired QoC, but also efficiently reduce the network energy consumption to prolong the effective network lifetime.
Declarations
Acknowledgements
This work was supported by the National Natural Science Foundation of China under grant no. 61628210, Henan Province Education Department Cultivation Young Key Teachers in University of under grant no. 2016GGJS-158, Henan Province Education Department Natural Science Foundation under grant no. 17A520044, Luoyang Institute of Science and Technology High-level Research Start Foundation under grant no. 2017BZ07, Natural Science and Technology Research of Henan Province Department of Science Foundation under grant no. 162102210113, Guangdong Natural Science Foundation of China under grant no. 2016A030313540, Guangzhou Education Bureau Science Foundation under grant no. 1201430560, Science and Technology Planning Project of Guangzhou under grant no. 201707010284, and Shaanxi Education Bureau Science Foundation under grant no. 2016SF-428. Finally, great thank to the anonymous reviewers for their valuable suggestions to improve the quality of the paper.
Funding
This work was sponsored by the National Natural Science Foundation of China under grant no. 61628210, Henan Province Education Department Cultivation Young Key Teachers in University of under grant no. 2016GGJS-158, Henan Province Education Department Natural Science Foundation under grant no. 17A520044, Luoyang Institute of Science and Technology High-level Research Start Foundation under grant no. 2017BZ07, Natural Science and Technology Research of Henan Province Department of Science Foundation under grant no. 162102210113, Guangdong Natural Science Foundation of China under grant no. 2016A030313540, Guangzhou Education Bureau Science Foundation under grant no. 1201430560, Science and Technology Planning Project of Guangzhou under grant no. 201707010284, and Shaanxi Education Bureau Science Foundation under grant no. 2016SF-428.
Authors’ contributions
ZYS and XFX contributed to the conception and algorithm design of the study. ZYS and GZZ contributed to the acquisition of the simulation. All authors contributed to the analysis of the simulation data and approved the final manuscript.
Authors’ information
Zeyu Sun received a M.S. and Ph.D degree from Lanzhou University and Xi’an Jiaotong University, in 2010 and 2017. He is an assistant professor in the School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, Henan, China. He is a member of China Computer Federation. His research interests lie in wireless sensor networks, parallel computing, mobile computing, and Internet of things (e-mail: lylgszy@163.com).
Guozeng Zhao received a M.S. degree from Taiyuan University of Technology in 2010. He is a lecturer in School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China. His research interests include wireless sensor networks and cloud computing (e-mail:ly_zgz@163.com).
Xiaofei Xing received BS degree in computer science and technology from Henan University of Science and Technology in 2003, and an MS and Ph.D. degrees in Central South University, China, in 2008 and 2012, respectively. He has been a Research Fellow at University of Tsukuba, Japan, and he had been also a post-doctorate researcher in Applied Mathematics. He is an assistant professor in the School of Computer Science and Educational Software, Guangzhou University, Guangzhou, China. His research interests include wireless sensor networks, mobile computing, and network performance analysis (e-mail:xxfcsu@163.com).
Competing interests
The authors declare that they have no competing interests.
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