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Energy hole is an inherent problem caused by heavier traffic loads of sensor nodes nearer the sink because of more frequent data transmission, which is strongly dependent on the topology induced by the sensor deployment. In this paper, we propose an autonomous sensor redeployment algorithm to balance energy consumption and mitigate energy hole for unattended mobile sensor networks. First, with the target area divided into several equal width coronas, we present a mathematical problem modeling sensor node layout as well as transmission pattern to maximize network coverage and reduce communication cost. And then, by calculating the optimal node density for each corona to avoid energy hole, a fully distributed movement algorithm is proposed, which can achieve an optimal distribution quickly only by pushing or pulling its one-hop neighbors. The simulation results demonstrate that our algorithm achieves a much smaller average moving distance and a much longer network lifetime than existing algorithms and can eliminate the energy hole problem effectively.

A typical wireless sensor network (WSN) is composed of hundreds of sensor nodes reporting their data to the information collector, referred to as the sink node. Sensor nodes are usually of low cost and low power, having limited sensing, computing, and communication capabilities. In recent years, with the rapid progress in advanced VLSI and radio frequency (RF) technologies, WSNs have attracted lots of interest due to their potential use in various applications such as military surveillance, target tracking, emergency navigation, and large scale systems [

Sensor deployment is an important issue in designing a WSN since it affects the communication cost, detection capability, coverage, and connectivity [

As sensor nodes are usually battery driven, they can survive for only a limited lifetime with nonrenewable batteries. Taking it one step further, the limited constraints of the sensor nodes restrict the use of high complexity algorithms and protocols. How to balance energy consumption is one of the fundamental issues arising in WSN. To address this issue, much work has been done during recent years. Among them, taking advantage of sensor mobility to enhance network lifetime has attracted extensive attention [

In this paper, we try to solve the energy hole problem by proposing an autonomous coverage-driven sensor redeployment scheme. We first develop the energy hole problem with nonuniform node distribution in WSN theoretically. By importing the energy-aware transmission mechanism and the accessibility condition of energy-balanced depletion in our pervious approach [

More recently, there has been growing interest in optimizing the sensor movement to maintain full coverage and prolong the network lifetime for mobile sensor networks. In [

In [

Energy-aware sensor redistribution was also proposed to mitigate or avoid the energy hole problem in WSNs. In [

Overall, though most of the algorithms discussed above intended to maximize coverage rate, minimize deployment density, and eliminate the energy hole, they did not answer a fundamental question in sensor redeployment: what type of node layout and communication pattern that could provide the maximum coverage with the smallest overlap and gap and guarantee that all the working sensors die simultaneously with nearly zero residual energy? We will deal with this issue in the next section.

In this section, we will present our network model and basic assumptions. Assume that a set of

In this paper, periodic data gathering monitoring is considered, where the network is working in rounds. Each round is further divided into two phases: the node redistribution phase and stability monitoring phase. We will provide a detailed description of the first stage issues in the next section. During the second phase, each working node should send their sensing messages to the sink node per unit time via multihop communication. For the theoretical analysis, we use a simplified power consumption model and an ideal MAC layer with no collisions and retransmissions. The initial energy of each sensor is set as

When using traditional transmission mechanism, the redundant sensing messages for the same area will be retransmitted by more than one sensor, consuming a considerable amount of energy [

As the sensors in corona

The optimal energy consumption state means that all the sensors in the network deplete their energy in the constant ratio; namely, all the sensor nodes have the same lifetime which is identical with the corresponding network lifetime. In particular, if the optimal energy depletion is achieved, there is no energy wasted and the network lifetime can be given by

Optimal energy depletion is possible, if all the working nodes take the energy-aware transmission mechanism, and the node density

Without loss of generality, suppose that (

Since

Theorem

The lifetime comparison of energy–balanced redeployment with traditional uniform approaches is

Suppose that these two schemes run with the same initial conditions. The node density of each corona obeys (

This completes the proof of Theorem

Therefore, compared with traditional uniform distribution strategy, the network lifetime can raise as much as

In this section, we first introduce equivalent sensing radius. Then we develop the uniform sensor distribution for corona-shaped area. Further, we propose a novel autonomous sensor redeployment approach to balance energy depletion.

Equivalent sensing radius is defined as the sensing radius when the given distribution density

According to [

Optimal energy depletion can be achieved, where

According to the definition of equivalent sensing radius, we can combine it with the energy balance condition. Thus we have

Since the equivalent sensing radius is only determined by corona number

If

If

Figure

Optimal sensor redeployment with different equivalent sensing radii

Therefore, the optimal sensor redeployment to balance energy depletion can be transformed into a uniform distribution problem with given deployment density and equivalent sensing radius. The novel sensor redeployment algorithm mainly contains two parts: (1) sensor redeployment control among the coronas to regulate the number of nodes for each corona and (2) sensor redeployment control inside coronas to guarantee that each corona achieves the given node density.

As sensors are randomly deployed in the target area, the deployment uncertainty may cause the number of deployed nodes to be more or fewer than the corona really needs. Movement control of sensor nodes will satisfy the desired deployment density for each corona and its rings. To avoid consuming much energy during the moving process, the nodes are only allowed to move to the adjacent coronas. After the needed number of sensors is achieved in each corona, a certain number of sensors should move between different rings to achieve uniform distribution. Define the number of sensors deployed in corona

For each corona

If

Move

Elseif

Select

Move these nodes straight to

For each ring

Move

Sensor redeployment inside coronas mainly focuses on how to redistribute the nodes locating on the median line of these rings in each corona to a perfect layout. Here, it is executed simply with its neighbour nodes. The straightforward idea is to adjust the angle between any two neighbours to

For each round

For each node

Let

Move node

While there exists node

Move node

While there exists node

Move node

Sensor redeployment in the ring.

The sensor redeployment algorithm ends in finite rounds and can achieve uniform layout in the ring.

As long as the angle between any two nearest neighbours is not equal to

Let

Thus the total covered angle of

If all the sensor nodes are distributed in an optimal layout, we can get the upper bound for

Denote the angle between

If

If

Thus we have

If

Clearly, in all the cases,

Illustration of sensor redeployment in one working round.

In this section, we will present the simulation results of our algorithm for both random and Gaussian deployment models. Three metrics, including coverage rate, the average moving distance, and the network survival lifetime, are imported to evaluate the performance of the algorithm.

First, a random deployment is considered in the circular area of radius 100 with 627 potential sensors. We assume that all the sensors are homogeneous, that is, having the same initial energy reserve ^{3} J/bit and ^{3} J/bit. The total number of working rounds for sensor node

The sensing data forwarding strategy is similar to [

Figure

Illustration of network distribution in different rounds using random deployment model.

Initial distribution

10th round

20th round

30th round

The second assumption examined is the Gaussian distribution, and the simulation environment is the same as the first experiment. In this distribution, each sensor's coordinate

Figure

Illustration of network distribution in different rounds using Gaussian deployment model.

Initial distribution

10th round

20th round

28th round

Further, we compare the performance of our algorithm with VEC in terms of coverage rate and average moving. Figure

Comparisons of network performance in different rounds.

Comparisons of coverage rate

Comparisons of moving distance

We further compare the performance of our algorithm with traditional uniform and nonuniform sensor deployment in terms of network lifetime and energy efficiency. In addition, the performance of our energy-aware transmission mechanism (

Since the node densities for all the coronas are the same in uniform deployment, the number of sensors distributed from

Figure

Comparison of average energy consumption in a sampling period.

Comparison with uniform deployment

Comparison with the nonuniform deployment

Figure

Comparison of energy unused ratio for each node.

Table

Comparison of the number of working rounds.

Algorithm | The number of working rounds |
---|---|

Uniform deployment with |
3 |

Uniform deployment with |
17 |

Nonuniform deployment with |
33 |

Nonuniform deployment with |
61 |

Our proposed algorithm | 104 |

In this paper, we have investigated the problem of sensor redeployment to achieve optimal energy depletion and minimize sensor movement. We have given a theoretical analysis on energy consumption using nonuniform distribution strategy. Formally, we have proved that, the optimal energy consumption can be achieved through calculating the node densities for different regions of the target area. As a contribution, we have proposed an autonomous coverage-driven sensor redeployment algorithm to produce an optimal solution, which can maximize the network lifetime and minimize total movement of sensors. In addition, extensive simulation results have been presented to demonstrate the effectiveness of our proposed techniques.It also should be noted that we only consider the two dimensional (2D) case in this paper. As part of our future work, we will design new algorithms for the sensor redeployment problem in 3D space.

The authors declare that they have no conflict of interests regarding the publication of this paper.

This work is supported by the National Natural Science Foundation of China under Grant no. 61173153 and no. 60903159, the National Science Foundation for Distinguished Young Scholars of China under Grant no. 61225012 and no. 71325002, the Fundamental Research Funds for the Central Universities under Grant nos. N130504007, N110318001, N110204003, N100218001, and N120104001, the China Postdoctoral Science Foundation funded project under Grant no. 20110491508 and no. 2012T50248, the Specialized Research Fund of the Doctoral Program of Higher Education for the Priority Development Areas under Grant no. 20120042130003, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant no. 20110042110024.