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Deployment quality and cost are two conflicting aspects in wireless sensor networks. Random deployment, where the monitored field is covered by randomly and uniformly deployed sensor nodes, is an appropriate approach for large-scale network applications. However, their successful applications depend considerably on the deployment quality that uses the minimum number of sensors to achieve a desired coverage. Currently, the number of sensors required to meet the desired coverage is based on asymptotic analysis, which cannot meet deployment quality due to coverage overestimation in real applications. In this paper, we first investigate the coverage overestimation and address the challenge of designing coverage-guaranteed deployment strategies. To overcome this problem, we propose two deployment strategies, namely, the Expected-area Coverage Deployment (ECD) and BOundary Assistant Deployment (BOAD). The deployment quality of the two strategies is analyzed mathematically. Under the analysis, a lower bound on the number of deployed sensor nodes is given to satisfy the desired deployment quality. We justify the correctness of our analysis through rigorous proof, and validate the effectiveness of the two strategies through extensive simulation experiments. The simulation results show that both strategies alleviate the coverage overestimation significantly. In addition, we also evaluate two proposed strategies in the context of target detection application. The comparison results demonstrate that if the target appears at the boundary of monitored region in a given random deployment, the average intrusion distance of BOAD is considerably shorter than that of ECD with the same desired deployment quality. In contrast, ECD has better performance in terms of the average intrusion distance when the invasion of intruder is from the inside of monitored region.

Wireless sensor networks have many applications, including environment monitoring, intrusion detection and tracking, precision agriculture,

Determining the required number of sensors to be deployed is a critical decision for wireless sensor networks. The art gallery problem is to determine the minimum number of guards required to cover all points in a gallery [_{a}_{a}

However, these researches assume that the sensors are deployed on an infinite region, rather than boundary region which is more relevant to real application scenarios. Therefore, this asymptotic analysis fails to guarantee the required network coverage in real world applications due to boundary effects [

Motivated by the coverage overestimation associated with uniform random deployment, in this paper, we propose two novel random deployment strategies for sensor nodes with coverage-oriented requirement, namely, Expected-area Coverage Deployment (ECD) and BOundary Assistant Deployment (BOAD).

The main contributions of this paper are the following: (1) we formulate the coverage overestimation for random deployed sensor networks; (2) we propose two deployment strategies to solve the coverage overestimation problem and analyze the lower bound on the number of deployed sensor nodes for each strategy to fulfill the deployment quality; (3) we carry out performance evaluation and demonstrate that the proposed deployment strategies can effectively alleviate the coverage overestimation and achieve user-specified desired deployment quality; (4) we apply two strategies to the application of intrusion detection to investigate the tradeoff between the deployed quality and average intrusion distance under two intrusion scenarios.

The remainder of this paper is organized as follows. In Section 2 related works are outlined. Section 3 describes the system models and problems. Random deployment strategies are proposed and the impact of deployment on coverage is discussed in Section 4. In Section 5, the performance of the deployment strategies is evaluated and compared. In Section 6, we discuss some practical issues, such as the extensibility of our work. Finally, we draw the conclusion, and point out the future work in Section 7.

Sensor deployment is a critical issue since it reflects the cost and the surveillance capability of a wireless sensor network. Therefore, a great deal of research has studied the deployment problem related to sensing coverage. The problem of sensor placement in a monitored field has been investigated in depth in [

Random deployment refers to the situation in which sensor nodes are uniformly and independently distributed across the monitored field. In [

Recently, most researches have extended the above analysis to coverage verification or coverage analysis. Tsai [

In addition, the theory of asymptotic analysis also has a great impact on coverage based node scheduling, active node selecting and applications such as intrusion detection. Given the assumption that the nodes are densely deployed, the research in [

All these random deployment strategies and their corresponding applications focused on the analysis results that the number of sensor nodes deployed or selected can achieve desired coverage requirement. Unfortunately, as shown in the empirical study in [

In this paper, we intend to study random sensor node deployment strategies concerning with coverage guaranteed. The goal of our design is to meet the coverage requirement of a sensor network by using a minimum number of sensor nodes randomly deployed in a certain area.

In this section, we describe the network model and give some definitions to simplify the analytical process in Section 4.

We consider the sensor nodes randomly and uniformly deployed in the monitored field. Assume that the sensing area is the disk of radius centered at the sensor with sensing radius

To facilitate later discussion, we introduce the following definitions.

_{i}

Given a monitored region Ω, and the sensing area of each sensor _{i}

The notations used in this paper are listed in

In this section, we proposes two novel deployment strategies, namely, Expected-area Coverage Deployment (ECD) and BOundary Assistant Deployment (BOAD), respectively.

In practical applications, the points near the boundary of monitored region for an area coverage deployment (ACD) strategy have a smaller chance to be covered by the sensor, which would decrease network coverage requirement. Therefore, the analytical expressions of

For an arbitrary node ^{2}. For the nodes where 0 ≤ ^{2}. Therefore, we wish to determine the expected area covered by

For _{r}_{r}_{r}

We use the variable

Using Fubini’s theorem, we have:

For an arbitrary point x∈Ω, let ^{2}. Point

To measure _{xi}_{r}_{r}_{r}_{xi}_{r}_{r}

For _{r}

The computing of _{r}_{r}

Then,

Therefore, when

Based on above analysis, we give the theorem 1.

From

An alternative, and possibly more counter-intuition, approach is deploying sensor nodes outside the monitored region for dealing with the above coverage overestimation. In this section, we propose boundary assistant deployment strategy (BOAD). In contrast to the ECD strategy, sensor nodes are deployed not only in the monitored region but also in a boundary assistant region in BOAD strategy. First of all, we give the definition of boundary assistant region as following.

^{2}.

From the

Therefore, any point _{xi}

Obviously, for the given number of sensor nodes

Finally, when sensor nodes are uniformly and randomly deployed within

In this section, the performance of two deployment strategies was evaluated using simulations and compared with the deployment strategy analyzed in [

We first investigate the performance of the three deployment strategies. The simulations are maked on a 100 m × 100 m monitored field with a sensing radius of 15 m, and the desired deployment quality

The minimum number of deployed sensor nodes: a measure of deployment cost to achieve the desired deployment quality.

Deployment quality achieved and deployment errors: a measure of efficiency for deployment quality.

In

Meanwhile, the minimum number of sensor nodes that have to be deployed increases drastically when the desired deployment quality reaches a certain threshold for three strategies. When

From

Intrusion detection in a wireless sensor network can be regarded as a monitoring system for detecting the intruder that is invading the monitored region [

To conduct a convincing performance evaluation and a fair comparison, we use the average intrusion distance as a metric to explore and compare the performance of the three deployment strategies. In the simulations, the sensors with sensing radius

In the simulations, we assume that the intruder’s physical size can be neglected, and the intruder in the monitored region moves along a straight line at a constant speed. Based on the starting point where the intruder makes its initial intrusion, we conclude two intrusion manners proposed in [

From

It is worth noting that the average intrusion distance is longer when

In intrusion detection applications, the intruder may appear in a location with the lowest detection probability or the longest intrusion distance. The results in this section indicate that for a given applications, we can make appropriate choices among the two strategies above according to different application. For example, in applications of border or perimeter surveillance against hostile elements such as embassies, and factories, BOAD has better surveillance performance. In precision agriculture, fire monitoring applications, the ECD can be up to the task.

In order to verify the validity of our theoretical results, we investigated the design parameters by performing extensive simulations. Apparently, there are three factors influencing the desired deployment quality: the monitored region, the number of sensor nodes and the sensing range. We assume a monitored region 100 m × 100 m, and the analytical and simulation results are compared by varying the number of deployed sensor nodes and the sensing radius.

First, we examine the impact of the number of deployed sensor nodes with different sensing range on the desired deployment quality of the three strategies.

In fact, we found that ACD match for the ECD when the radius is small compared to the length or width of the rectangle.

From

From

The simulation results can be summarized as follows:

Both BOAD and ECD can efficiently alleviate the coverage overestimation in terms of the desired deployment quality, which can ensure the surveillance quality.

Both BOAD and ECD reduce the average intrusion distance compared to ACD in intrusion detection applications. Furthermore, BOAD, which uses a boundary assistant region, has the best performance in terms of the average intrusion distance when the invasion of intruder is from the boundary of a monitored region. ECD has the best performance in terms of the average intrusion distance when the invasion of intruder is from the inside of monitored region.

Achieved desired deployment quality increases when the number of sensor nodes or radius increases. BOAD achieves the lower desired deployment quality compared to ECD under the same number of sensor nodes and sensing radius, the analysis and simulations have slight discrepancy which efficiently alleviate coverage overestimation.

So far, we have analyzed the lower bound number of sensors deployed to achieve a desired deployment quality. In this section, we address two practical issues with random deployment strategies. We first discuss how to apply the derivations in Section 4 to a sensing field of a more general shape and the sensing model to real applications.

We first remark that the validity of the derivations of the deployment strategies is not limited to any particular shape of the monitored region. The derivations in Section 4.1 and 4.2 assume that the monitored region is rectangular. However, the methods and the derivations can be extended to the case where the monitored field is of arbitrary convex shape. Assume that the shape of the brim is not too rugged, from Section 4.1, it is apparently introduced boundary effects when 0 ≤ ^{2}^{2}. When 0 <

Using

On the other hand, concerning the boundary assistant deployment strategy discussed in Section 4.2, we can easily extend to arbitrary convex monitored region by using parallel convex sets [

_{Ω} be an area of the monitored region with parameter _{Ω} and let sensors with sensing radius _{r}_{r}

This study assumes that the sensing models of deployed sensor nodes are deterministic and the monitored region is rectangular. In practice, due to the randomness in sensing, ambient noise, interference and obstacles in monitored region, probabilistic models describe a sensor’s sensing ability more accurately.

In wireless sensor networks, the sensing capability is mandatory for monitoring applications that immediately response to detect the event. With unit disk sensing model analyzed in Section 2, we can derive the minimum number of sensors to achieve the required deployment quality. However, the sensing capabilities are affected by the distance between the sensor and the measuring point [

To sense an event in monitored region, the sensor nodes should sense the emitted signal from the sensing area. Considering the nodes sensing range _{target}_{rev}_{i}_{0}_{0}_{σ}

In shadowed environments, the sensing area of a sensor is not a disk, and the sensing radius is not _{0}_{σ}_{ave}_{sen}

Therefore, given the _{ave}

Balancing the deployment quality and deployment cost is a challenging task in sensor networks under random deployment. Aiming at reducing coverage overestimation, we proposed two node deployment strategies in wireless sensor networks. Specifically, we studied network coverage by randomly deployed sensor nodes, and obtained the lower-bound of number of sensor nodes which can accurately meet the deployment requirement. The performance study of the deployment strategies shows the new strategies have significant advantages to the area coverage deployment. We also evaluate the performance in an intrusion detection application. Boundary assistant deployment strategy showed the best performance when the invasion of intruder comes from the boundary of monitored region. On the other hand, expected-area coverage deployment strategy has the best performance when the invasion of intruder happens from inside of a monitored region. Moreover, the theorems that we have derived characterize the interactions among network parameters. The results obtained in this paper will provide important guidelines for the random deployment of typical application of wireless sensor networks and our analysis can help to plan a sensor network meeting deployment quality requirements at a low budget cost.

Network connectivity, in addition, reflects how well the sensor nodes communicate with each other in reporting detected events or the sensed data to the sink node. For our future work, we plan to study the connectivity under two deployment strategies and give a detail analysis and simulation when extended to general monitored region and probabilistic sensing model.

The authors would like to thank the reviewers for valuable comments and suggestions, which have helped to improve the manuscript. This work is sponsored by the National Natural Science Foundation of China under Grants No. 60973139 and 60773041; The Natural Science Foundation of Jiangsu Province under Grant No. BK2008451; Special Fund for Software Technology of Jiangsu Province; Special fund for the Development of Modern Service Industry of Jiangsu Province; Postdoctoral Foundation under Grants No. 0801019C, 20090451240 and 20090451241; Science & Technology Innovation Fund for higher education institutions of Jiangsu Province under Grants No.CX09B_153Z and CX08B_086Z; The six kinds of Top Talent of Jiangsu Province under Grant No.2008118.

In order to compute _{r}_{r}

Let _{r}

A sensor node located in sub-region Ω_{r}

Since 0 ≤ _{r}_{Ωr(1)}(

Hence, after few steps of mathematical simplification, we derived:

Let the distance from a node located in Ω_{r}

Case 1. The distance to the corner is less than

Case 2. The distance to the corner is larger than or equal to

Two cases of a sensor’s location in sub-region Ω_{r}

Let _{r1}[_{r2}[

We then compute _{r1}[

Let _{Ωr1(2)}(

Then, we have:

By simplifying, we get:

Compute _{r2}[

Let _{Ωr2(2)}(

Similar technique used in computing _{r1}[

Since

We have:

A monitored region and its sub-region.

A sensor deployment region.

The minimum number of sensors deployed to meet desired deployment quality.

Desired deployment quality and achieved deployment quality.

Deployment error.

Intrusion scenarios. (a) The intrusion from the boundary of the monitored region.

Comparison average intrusion distance of three deployment strategies with sensing radius

Comparison average intrusion distance of three deployment strategies with sensing radius

Effects of number of deployed sensor nodes on the DDQ for

Effects of number of deployed sensor nodes on the DDQ for

Effects of number of deployed sensor nodes on the DDQ for

Effects of sensing range on the DDQ for

Notation and definition.

Notation | Definition |
---|---|

Ω | the monitored region |

the deployed region | |

the boundary assistant region | |

the number of deployed sensor nodes | |

^{k} |
the lower bound number of deployed sensor nodes for strategy |

_{i} |
the sensing radius of sensor |

the circular area centered at given point | |

the distance to the boundary of monitored region of sensor | |

the effective coverage area of sensor | |

_{r} |
the expected area of |

Ω_{r} |
the sub-region |