Distributed deployment schemes for mobile wireless sensor networks to ensure multilevel coverage

Distributed Deployment Schemes for Mobile

Wireless Sensor Networks to Ensure

Multilevel Coverage

You-Chiun Wang, Member, IEEE, and Yu-Chee Tseng, Senior Member, IEEE

Abstract—One of the key research issues in wireless sensor networks (WSNs) is how sensors can efficiently be deployed to cover an area. In this paper, we solve the k-coverage sensor deployment problem to achieve multilevelðkÞ coverage of the area of interest I . We consider two subproblems: the k-coverage placement problem and the distributed dispatch problem. The placement problem asks how the minimum number of sensors required and their locations inI can be determined to guarantee that I is k-covered and the network is connected, while the dispatch problem asks how mobile sensors can be scheduled to move to the designated locations according to the result computed by the placement strategy if they are not in the current positions such that the energy consumption due to movement is minimized. Our solutions to the placement problem consider both the binary and probabilistic sensing models and allow an arbitrary relationship between the communication distance and the sensing distance of sensors, thereby relaxing the limitations of existing results. For the dispatch problem, we propose a competition-based scheme and a pattern-based scheme. The competition-based scheme allows mobile sensors to bid for their closest locations, while the pattern-based scheme allows sensors to derive the target locations on their own. Our proposed schemes are efficient in terms of the number of sensors required and are distributed in nature. Simulation results are presented to verify their effectiveness.

Index Terms—Mobile sensors, network planning, pervasive computing, sensor coverage problem, topology control, wireless sensor networks.

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I

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microsensing MEMS and wireless communication tech-nologies, wireless sensor networks (WSNs) have been studied intensively for various applications such as environment monitoring, smart home, and surveillance. A WSN usually consists of numerous wireless devices deployed in a region of interest, each able to collect and process environmental information and communicate with neighboring devices.

Sensor deployment is an essential issue in WSN, because it not only determines the cost for constructing the network but also affects how well a region is monitored by sensors. In this paper, we consider the sensor deployment problem for a WSN with multilevel coverage. In particular, given a region of interest, we say that the region is k-covered if every location in that region can be monitored by at least ksensors, where k is a given parameter. A large amount of applications may impose the requirement of k > 1. For instance, military or surveillance applications with a stronger monitoring requirement may impose that k  2 to avoid leaving uncovered holes when some sensors are broken. Positioning protocols using triangulation [1] require at least three sensors (that is, k  3) to detect each location

where an object may appear. Moreover, several strategies are based on the assumption of k  3 to conduct data fusion [2] and to minimize the impact of sensor failure [3]. In addition, to extend a WSN’s lifetime, sensors are separated into k sets, each capable of covering the whole area, to work in shifts [4], [5], [6].

In this paper, we address the sensor deployment problem with the following requirements:

1. Multiple-level coverage of the area of interest is required.

2. Connectivity between sensors (in terms of their communications) should be maintained.

3. The area of interest may change over time.

4. Sensors are autonomous and mobile and thus can be dispatched to desired locations when being in-structed so.

We call this the k-coverage sensor deployment problem, where the k-level coverage of a given area of interest I is needed. We consider two subproblems: the k-coverage sensor placement problemand the distributed sensor dispatch problem. The placement problem asks how we can decide on the minimum number of sensors required and their locations in I to ensure that I is k-covered and that the network is connected. Note that coverage is affected by sensors’ sensing distance, while connectivity is determined by their commu-nication distance. Considering that sensors are mobile and the area I may change over time, the objective of the dispatch problem is to schedule sensors to move to the designated locations (according to the result computed by the placement

. The authors are with the Department of Computer Science, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan 300, R.O.C. E-mail: {wangyc, yctseng}@cs.nctu.edu.tw.

Manuscript received 20 Apr. 2007; revised 8 Nov. 2007; accepted 14 Nov. 2007; published online 21 Nov. 2007.

Recommended for acceptance by J.-P. Sheu.

For information on obtaining reprints of this article, please send e-mail to: tpds@computer.org, and reference IEEECS Log Number TPDS-2007-04-0119. Digital Object Identifier no. 10.1109/TPDS.2007.70808.

strategy) such that the total energy consumption of sensors due to movement can be minimized.

In the literature, one related area is the art gallery problem [7] in computational geometry. It intends to use the minimum number of observers to monitor a polygon area. The problem assumes that an observer can watch any point, as long as line of sight exists, and it does not address the (wireless) communication issue between observers. An-other relevant issue is the base station (BS) placement problem. This problem discusses how we can determine the optimal number and locations of BSs within an environment so as to satisfy the coverage and throughput requirements [8]. To solve this problem, many studies propose their discrete optimization models by multiobjective genetic algorithms [8], [9], parallel evolutionary algorithms [10], and simulated annealing [11] to determine the optimal placement of BSs. However, these results cannot be directly applied to our sensor placement problem.

Sensor placements for 1-coverage have been studied in several works. For example, the works in [12] and [13] consider placing sensors in a gridlike fashion to satisfy some coverage requirements, while [14] suggests placing sensors strip by strip to achieve both coverage and connectivity. In [15], a 1-coverage sensor placement method for the sensing field with obstacles is proposed. Several studies have also considered the sensor placement problem of multilevel coverage. In [3], a hexagonlike placement is proposed to guarantee that the sensing field is k-covered, under the assumption that the communication distance of sensors rcis not smaller than twice their sensing distance rs.

The work in [16] models the sensing field by grids and considers two kinds of sensors with different costs and sensing capabilities to be deployed in the sensing field. The objective is to make every grid point k-covered, and the total cost is minimum. However, both [3] and [16] do not address the relationship between rc and rs. How the coverage level

of a given placement can be computed is addressed in [17]. Some works address the coverage and connectivity issue by assuming that there is redundancy in the initial deployment, and the goal is to select a minimal set of active sensors to achieve energy conservation and maintain complete coverage of the sensing field and connectivity of the network. References [4] and [18] address how some sensors can be arranged to go to sleeping modes to extend the network lifetime while maintaining 1-coverage of the sensing field. On the other hand, [19], [20], [21], [22], and [23] consider how these active sensors can be selected to maintain the k-coverage of the sensing field and the connectivity of the network.

The use of mobile sensors has also been discussed in several works. Basu and Redi [24] consider moving nodes to make the network biconnected. When events occur, Butler and Rus [25] discuss how some sensors can be moved to the event locations while still maintaining complete 1-coverage of the sensing field. The authors in [26], [27], [28], and [29] study how sensors can be moved to enhance the coverage of the sensing field by using the Voronoi diagram or attractive/repulsive forces between sensors. In [30], the sensing field is partitioned into grids, and sensors are moved from high-density grids to

low-density ones to achieve more uniform coverage. The work in [31] considers adding several mobile sensors into a stationary sensor network to improve the coverage and connectivity of the original network. As can be seen, the attention of prior works was mainly paid to the use of mobile sensors to improve the topology of an existing network, which is different from the sensor dispatch problem discussed in this paper. Actually, several studies [32], [33], [34] have proposed their design and implementa-tion of mobile sensors. Such mobile platforms are controlled by embedded computers and are mounted with sensors. These studies motivate us to investigate the sensor dispatch problem.

In this paper, we consider more complete solutions to the k-coveragesensor deployment problem by addressing both the placement and dispatch subproblems. In particular, for the sensor placement problem, we allow an arbitrary relationship between sensors’ communication distance rc

and their sensing distance rs. We consider two types of

sensing models: binary and probabilistic. Under the binary sensing model [14], [15], [28], a location can be either monitored or not monitored by a sensor, depending on whether the location is within the sensor’s rsrange. Under

the probabilistic sensing model [12], [23], [35], a location will be monitored by a sensor according to some probability function. We first consider the binary sensing model of sensors and propose two solutions to the placement problem. The first one is based on an intuitive duplication idea, while the second one is based on a more complicated interpolating scheme and thus can save more sensors. Then, we adapt these solutions to the probabilistic sensing model by properly adjusting the sensing distances of sensors. For the sensor dispatch problem, we propose two distributed schemes to let sensors move to the designated locations (computed by the placement result) on their own. The first scheme assumes that sensors have the full knowledge of all target locations in the area of interest. Sensors will compete with each other to move toward their closest locations. The second scheme relaxes the above assumption in a way that sensors can derive other target locations based on several known locations according to the patterns in our placement strategies. Therefore, we can give several locations as seeds in the beginning, and sensors will then extend their range based on the placement pattern in a distributed manner.

In this paper, we consider that the area of interest I may change over time (based on users’ application requirements), so sensors may be dispatched in multiple rounds. Specifically, in each round, when a new I is generated, the sink first calculates the locations to be placed with sensors in I by the proposed placement solutions and announces the complete or partial locations to sensors. Sensors then can automatically move to these designated locations by the proposed dispatch solutions to ensure the k-coverage of I . Because the sink does not know the current statuses and positions of mobile sensors, it cannot determine which sensor should move to which location in a centralized manner. Therefore, distributed dispatch solu-tions are more desirable.

The major contributions of this paper are twofold. First, our schemes allow change of the monitoring region and coverage level of the WSN in an autonomous and distributed manner. This is quite important for those applications where the region of interest may change over time. For example, one can image that a wide area is contaminated by some hazardous material such as the leakage of nuclear or poisonous chemicals. By quickly providing multilevel coverage of these movable regions of pollution, the whole situation can be assessed immediately, and such information can be conveniently used by the rescue team. Second, our deployment solutions are helpful in conditions where the precise initial deployment (for example, by humans) is almost impossible, because the region of interest is very dangerous or even inaccessible to people. By introducing the concept of sensor dispatch, mobile sensors can automatically move to designated locations in an efficient way, and thus, the region of interest can be “self deployed” by these sensors.

The rest of this paper is organized as follows: Section 2 formally defines the sensor placement and dispatch problems. Sections 3 and 4 propose our solutions to these problems. Section 5 presents simulation results to evaluate the proposed schemes. Section 6 concludes this paper.

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We are given a field A, an area of interest I inside A, and a set of mobile sensors S resident in A. For convenience, we assume that I is a rectangular region. Each sensor has a communication distance rcand a sensing distance rs. Sensors

are homogenous, but the relationship of rc and rs can be

arbitrary. For connectivity, we assume that two sensors can communicate with each other if their distance is not larger than rc. For coverage, we consider both the binary and

probabilistic sensing models of sensors. Under the binary sensing model, a location can be monitored by a sensor if it is within the sensor’s sensing region. Thus, a location in A is defined as k-covered if it is within k sensors’ sensing regions, where k is a given parameter. Under the probabilistic sensing model, the detection probability of a sensor will decay with the distance from the sensor to the monitored location. In particular, the detection probability of a location u by a sensor sican be evaluated as [12], [35]

pðu; siÞ ¼ e "dðu;siÞ_; if dðu; s iÞ  rs; 0; otherwise;  ð1Þ where " is a parameter indicating the physical character-istics of the sensor, and dðu; siÞ is the distance between u

and si. Thus, a location in A is considered as k-covered if the

probability that there are at least k sensors that can detect this location is not smaller than a predefined threshold pth,

where 0 < pth< 1. With the above definitions, an area in A

is considered as k-covered if every location inside that area is k-covered. We assume that sensors can be aware of their own positions, which can be obtained by the Global Positioning System (GPS) [36] or other localization techni-ques [37], [38].

Given an integer k, the k-coverage sensor deployment problem can be divided into two subproblems: the

k-coverage sensor placement problem and the distributed sensor dispatch problem. The objective of the placement problem is to determine the minimum number of sensors required and their locations in the area of interest I to guarantee that I is k-covered and that the network is connected. Considering that mobile sensors are arbitrarily placed inside A and that there are sufficient sensors, the dispatch problem asks how sensors can be moved to designated locations (according to the result computed by the placement strategy) in a distributed manner such that the total energy consumption of sensors due to movement is minimized, that is, minP_i2Semove

i  di, where emovei is the

energy cost for sensor i to move in one unit distance, and di

is the total distance that sensor i has traveled. Note that here, we assume that a sensor will move at a constant speed and will incur a constant rate of energy drain during its motion [30], [39]. However, the energy model may be defined in a different way from this one.

3

k-Coverage

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In this section, we deal with the k-coverage sensor placement problem. We first consider the binary sensing model of sensors and propose two placement solutions. The first solution is based on a naive duplication idea, while the second solution is inspired by a more complicated interpolating concept. Then, we discuss how these placement schemes can be adapted to the probabilistic sensing model.

3.1 The Naive Duplicate Placement Scheme

One intuitive idea to achieve a k-coverage placement is to use a good sensor placement method to determine the locations of sensors to ensure 1-coverage and connectivity in I and then duplicate k sensors on each designated location. For the 1-coverage placement, we adopt the method proposed in [15], which has been proved to be able to use the minimum number of sensors to achieve 1-coverage and connectivity [40]. In this 1-1-coverage place-ment, sensors are placed row by row, where each row of sensors will guarantee continuous coverage and connectiv-ity, while adjacent rows will guarantee continuous coverage of the whole area. According to the relationship of rcand rs,

we separate the discussion into two cases, as shown in Fig. 1. When rc<

ffiffiffi 3 p

rs, sensors on each row are separated

by a distance of rc, so the connectivity of sensors in each

row can be guaranteed. Since rc<

ffiffiffi 3 p

rs, each row of sensors

can cover a beltlike area of width 2, where  ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 s14r2c

q

. Adjacent rows will be separated vertically by a distance of rsþ  and will be shifted horizontally by a distance ofr₂c.

This guarantees the coverage of the whole area. When rc ffiffiffi3

p

rs, the aforementioned placement will use too many

sensors, so a common regular placement of triangular lattice [41] should be adopted, where adjacent sensors will be regularly separated by a distance ofpffiffiffi3rs.

After determining the 1-coverage placement, we can duplicate k sensors on each location to ensure k-coverage of the whole area. Note that in the case of rc<

ffiffiffi 3 p

distance between sensors on adjacent rows is larger than rc,

it is necessary to add some extra columns of sensors, where sensors on each column are separated by a distance not larger than rc, to connect adjacent rows.

3.2 The Interpolating Placement Scheme

The previous duplicate scheme may result in some subregions in I that have coverage levels much higher than k. Consequently, the following interpolating placement scheme will try to balance the coverage levels of subregions. Observe that in Fig. 1a, a large amount of subregions in a row are actually more than 1-covered. Thus, we can “reuse” these subregions when generating a multilevel coverage placement. Based on this observation, the interpolating placement scheme will first find out those insufficiently covered subregions and then place the least number of sensors to cover these regions. Note that these newly added

sensors should remain connected with the formerly placed sensors. According to the relationship of rc and rs, we

separate the discussion into three cases. The case of rc

ffiffi

3 p

2 rs. In Fig. 1a, we can observe

that the insufficiently covered subregions (that is, only 1-covered regions) are located between adjacent rows (marked by gray). If we add an extra row of sensors between each pair of adjacent rows in Fig. 1a, as Fig. 2a shows, the coverage level of the sensing field will directly become three. Here, each extra row is placed above the previous row by a distance of rs, and neighboring sensors in

each extra row are still separated by a distance of rc. Note

that in Fig. 2a, some sensors may be placed outside the area of interest I . This may lead to the failure of the interpolating scheme to calculate a feasible solution when I ¼ A. To solve this problem, we can place these outside sensors on the boundary of I, as shown in Fig. 2b. In this case, 3-coverage of I can still be achieved, because sensors are placed more compactly.

In the case of rc

ffiffi

3 p

2 rs, since the distance between

sensors on adjacent rows is rs (which is larger than rc),

we have to add at least one column of sensors, each separated by a distance not larger than rc, to connect

adjacent rows.

To summarize, the previous duplicate scheme uses 3x rows of sensors to ensure 3-coverage of a beltlike area of width ðx  1Þrsþ ðx þ 1Þ, while this interpolating scheme

uses only 2x þ 1 rows of sensors to ensure 3-coverage of the same region. In general, for k > 3, we can apply k

3

 

times of the above 3-coverage placement and apply ðk mod 3Þ times of the 1-coverage placement to achieve k-coverage in I . Therefore, while the duplicate placement requires kx rows of sensors to cover a region, this interpolating placement requires only k

3   ð2x þ 1Þ þ ðk mod 3Þ  x   rows of sensors. The case of pffiffi3 2 rs< rc 2þpffiffi3

3 rs. In this case, if the

desired coverage level k is two, we can directly apply the

WANG AND TSENG: DISTRIBUTED DEPLOYMENT SCHEMES FOR MOBILE WIRELESS SENSOR NETWORKS TO ENSURE MULTILEVEL... 1283

Fig. 1. The 1-coverage sensor placement method proposed in [15]. (a) The case of rc<

ffiffiffi 3 p rs. (b) The case of rc ffiffiffi 3 p rs.

Fig. 2. The interpolating placement scheme in the case of rc

ffiffi

3 p

same placement in the previous case. The result is shown in Fig. 3a. However, because the sensing distance rsis relatively smaller (as opposed to the case of rc

ffiffi

3 p

2 rs),

there are some subregions that are only 2-covered but not 3-covered (marked by gray in Fig. 3a). Therefore, if the desired k is three, we need to add one extra row of sensors (marked as new’ i) between each new row i and old row i, as Fig. 3b shows. Note that these extra rows are shifted horizontally by a distance ofrc

2 from the previous rows and

neighboring sensors are separated regularly by a distance of 2rc. Also, note that each new’ row i can connect with its

adjacent new row i and old row i, as shown in Fig. 3c. In particular, because jsnsaj ¼ jsnsbj ¼ jsnscj ¼ jsnsdj ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2rs  2 þ 1 2rc  2 s <1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ffiffiffi 3 p rc  2 þr2 c s < rc;

the sensor sn in a new’ row i can communicate with its

four neighbors sa, sb, sc, and sd in the adjacent new and

old rows.

In the case of pffiffi3

2 rs< rc< rs, because the distance

between sensors on adjacent rows may be larger than rc,

we have to add extra sensors between them to maintain the network connectivity. There are two cases to be discussed. When k ¼ 2, we need to add at least one column of sensors between every two adjacent rows to connect them. When

k 3, because a new’ row has already connected with its adjacent new and old rows, we only have to add these extra columns of sensors between each old row i and new row i þ 1 to maintain the network connectivity.

To summarize, the previous duplicate scheme uses 3xrows of sensors to ensure 3-coverage of a beltlike area of width ðx  1Þrsþ ðx þ 1Þ, while this interpolating scheme

can use only 2:5x þ 1 rows of sensors to ensure 3-coverage of the same region (the third addition of rows only needs about 0:5xextra sensors). In general, for k > 3, we can also apply k

3

  times of the above 3-coverage placement and apply ðk mod 3Þ times of the 1-coverage placement to achieve k-coverage in I. Therefore, while the duplicate placement requires kx rows of sensors to cover a region, this interpolating placement only requires k 3   ð2:5x þ 1Þ þ ðk mod 3Þ  x   rows of sensors. The case of rc>2þ ffiffi 3 p

3 rs. In the previous case, when rc

increases, the areas of these only 2-covered regions in Fig. 3a also increase. To achieve the 3-coverage placement using fewer sensors, each sensor sn in a new’ row should

completely cover two only 2-covered regions (marked by gray), as shown in Fig. 3d. In this case, we should make jxsnj  rs, so we can obtain jxsnj ¼ jxyj þ jysnj ¼ rc ffiffiffi 3 p 2 rs  þ1 2rc rs ) rc 2þpffiffiffi3 3 rs:

Fig. 3. The interpolating placement scheme in the case of pffiffi3

2rs< rc2þ

ffiffi

3 p

3 rs. (a) The placement for k¼ 2. (b) The placement for k ¼ 3.

Clearly, when rc>2þ

ffiffi

3 p

3 rs, sensor sn can no longer cover

the nearest two 2-covered regions. Thus, we need to add one extra sensor in the new’ row to cover every 2-covered region. In this case, if the duplicate scheme uses 3x rows of sensors to ensure 3-coverage of a beltlike area of width ðx  1Þrsþ ðx þ 1Þ, this interpolating scheme should use

3xþ 1 rows to achieve the same goal. Since the interpolat-ing placement will not save sensors compared to the duplicate placement, we adopt the duplicate scheme in the case of rc>2þ

ffiffi

3 p 3 rs.

3.3 Adapting to the Probabilistic Sensing Model In this section, we discuss how the previous two placement schemes can be adapted to the probabilistic sensing model, where the detection probability of a sensor to any location follows that specified in (1). To simplify the presentation, we call the probability that a location u can be detected by at least k sensors as the k-covered probability of location u. To adapt our placement schemes, we first find the minimum k-covered probability pmin in our placement.

Then, we calculate a pseudo sensing distance rp

s according

to pmin and pth and replace the original sensing distance rs

by rp

s in the placement to guarantee that every location

inside I is still k-covered under the probabilistic sensing model. In this section, we assume that I  A and the desired coverage level k  3.

3.3.1 Adaptation of the Duplicate Placement Scheme Observing in Fig. 1, there must be a location u covered by only one sensor with a distance approximate to rs. Such a

location u is very close to the sensing boundary of the sensor placed at location a but not inside the sensing ranges of sensors placed at locations b and c. Thus, we can derive the detection probability of location u by the sensor sa

located at a as pðu; saÞ ¼ e"dðu;saÞ e"rs. Because the

duplicate scheme places k sensors on each location specified in Fig. 1, location u will have the minimum k-covered probability pmin. In particular, location u will be

detected by a set Sa of k sensors placed at location a with

the probability

pmin¼ pðu; SaÞ ¼

Y

si2Sa

pðu; siÞ  ek"rs:

Therefore, the duplicate scheme can guarantee a k-covered probability of at least ek"rs _{in any location of the area of}

interest I . On the other hand, if we want to guarantee that every location inside I has a k-covered probability not smaller than the given threshold pth, we can calculate the

pseudo sensing distance rp sby

ek"rps _{ p}

th) rps

 ln pth

k" :

With the above argument, if we replace rs by rps when

executing the duplicate scheme, we can guarantee that I is still k-covered under the probabilistic sensing model. 3.3.2 Adaptation of the Interpolating Placement Scheme According to the relationship of rc and rs, we separate the

discussion into three cases.

The case of rc

ffiffi

3 p

2 rs. We first consider the case of k ¼ 3.

Observing in Fig. 2a, there are some subregions covered by exactly three sensors (marked by gray). Among these regions, there will be a location u with a minimum 3-covered probability. In particular, such a location u will be covered by sensors sa, sb, and sc located at a, b, and c,

respectively. Since dðu; saÞ ¼ rs, we have pðu; saÞ ¼ e"rs. In

addition, because dðu; sbÞ ¼ dðu; scÞ < ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2rc  2 þ 1 2rs  2 s 1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi_ffiffiffi 3 p 2 rs  2 þr2 s s ¼ ffiffiffi 7 p 4 rs; we can obtain pðu; sbÞ ¼ pðu; scÞ > e

ffiffi

7 p

4"rs_{. Thus, the 3-covered}

probability of location u is

pabc¼ pðu; saÞ  pðu; sbÞ  pðu; scÞ > e

2þpffiffi7 2 "rs_:

In the interpolating scheme, when k  3 is a multiple of three, we will placek

3 sensors on each location specified in

Fig. 2a. Therefore, we can obtain pmin¼ ðpabcÞ k 3_{> e}2þ ffiffi 7 p 6 k"rs_{: ð2Þ}

When k is not a multiple of three, we will add extra ðk mod 3Þ sensors on each location in the old rows in Fig. 2a. Thus, we have pmin¼ ðpabcÞ k 3 pðu; s cÞ ð Þðk mod 3Þ: ð3Þ By combining (2) and (3), we can derive that

pmin> e 2þpffiffi7 6 kþ ffiffi 7 p 4ðk mod 3Þ   "rs_{: ð4Þ}

To calculate the pseudo sensing distance rp

s, we can make e 2þ ffiffi7 p 6 kþ ffiffi 7 p 4ðk mod 3Þ   "rps _{ p} th ) rps  ln pth 2þpffiffi7 6 kþ ffiffi 7 p 4 ðk mod 3Þ  " : The case of pffiffi3 2 rs< rc 2þpffiffi3

3 rs. Again, we first

con-sider the case of k ¼ 3. Observing in Fig. 3b, there are some subregions covered by exactly three sensors (marked by gray). Among these regions, there will be a location u that has the minimum 3-covered probability. In particular, such a location u is covered by sensors sa, sb,

and sc at locations a, b, and c, respectively. Because

dðu; saÞ ¼ dðu; scÞ ¼1₂rs, we have pðu; saÞ ¼ pðu; scÞ ¼ e

1 2"rs_.

Moreover, since dðu; sbÞ ¼1₂rc2þ

ffiffi 3 p 6 rs, we can obtain pðu; sbÞ  e 2þpffiffi3

6 "rs_{. Thus, the 3-covered probability of}

location u will be

pabc¼ pðu; saÞ  pðu; sbÞ  pðu; scÞ  e

8þpffiffi3 6 "rs_:

Similar to (4), when k  3, we can derive the minimum k-coveredprobability pmin as

ðpabcÞ k 3_{ pðu; s} cÞ ð Þðk mod 3Þ e 8þ ffiffi3 p 18kþ 1 2ðk mod 3Þ   "rs_:

Again, the pseudo sensing distance rp scan be derived as e 8þ ffiffi 3 p 18 kþ 1 2ðk mod 3Þ   "rps _{ p} th ) rp s  ln pth 8þpffiffi3 18 kþ 1 2ðk mod 3Þ  " : The case of rc>2þ ffiffi 3 p

3 rs. In this case, since the duplicate

scheme is adopted, we can obtain pmin ek"rs and

rp_s ln pth

k" .

Table 1 summarizes the approximate threshold values of the minimum k-covered probability pmin and the pseudo

sensing distance rp

sin the interpolating scheme.

4

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D

S

After determining the locations to be placed with sensors, the next issue is how we can move existing sensors in the field A to the designated locations in I such that the energy consumption of sensors due to movement can be minimized. Since we cannot obtain the current statuses and positions of sensors, it is impossible to compute an optimal solution to dispatch sensors in a centralized manner. Thus, we propose two distributed dispatch schemes in this section.

4.1 The Competition-Based Dispatch Scheme In this scheme, when an area of interest I is determined, the sink will first calculate a set of locations L ¼ fðx1; y1; n1Þ; ðx2; y2; n2Þ;    ; ðxm; ym; nmÞg to be placed

with sensors in I according to our placement schemes in Section 3. Here, each element ðxj; yj; njÞ, j ¼ 1 . . . m,

indi-cates that nj sensors need to be placed on location ðxj; yjÞ.

The sink then broadcasts L to all sensors.

On receiving L from the sink, sensors will compete with each other to move toward these locations. In particular, each sensor si will construct a table OCC½1 . . . m such that

e v e r y e n t r y OCC½j ¼ fðsj1; dj1Þ; ðsj2; dj2Þ; . . . ; ðsj; djÞg,

 nj, contains the set of sensors that have already moved

into or are still on their way moving toward location ðxj; yjÞ

and their corresponding distances to ðxj; yjÞ. Specifically,

each record ðsj; djÞ,  ¼ 1 . . . , indicates that sensor sjhas

chosen to cover location ðxj; yjÞ, and its current estimated

distance to ðxj; yjÞ is dj. When dj¼ 0, it means that sensor

sjhas already arrived at ðxj; yjÞ. Initially, OCC½j ¼ ; for all

j¼ 1 . . . m. To simplify the presentation, we say that a location ðxj; yjÞ is covered if a sufficient number njof sensors

have committed to move toward ðxj; yjÞ (that is,

jOCC½j j ¼ nj); otherwise, ðxj; yjÞ is uncovered. A sensor si

is engaged if it has chosen to move to or has already moved into any location in L; otherwise, it is free or terminated. The initial state of each sensor is free. A free sensor will try to

become engaged and move toward a destination. When the free sensor finds that there is no location that it can cover, it will enter the terminated state. Fig. 4 illustrates the state transition diagram of a sensor.

When the state of a sensor si is free, it will check its

OCC½1 . . . m table to select a location in L as its destination. The selection is given as follows:

1. The first priority is to consider uncovered locations. Specifically, if there is a location ðxj; yjÞ such that

jOCC½j j < nj;ðxj; yjÞ will be considered first. If

multiple locations are qualified, the location ðxj; yjÞ

such that dðsi;ðxj; yjÞÞ is minimized will be selected,

where dðsi;ðxj; yjÞÞ is the distance between si’s

current position to ðxj; yjÞ. In this case, si will add

a record ðsi; dðsi;ðxj; yjÞÞÞ in its OCC½j entry and

enter the engaged state.

2. If all locations in L are already covered (that is, jOCC½j j ¼ nj, 8j ¼ 1 . . . m), si selects a location

ðxj; yjÞ such that there is a record ðsk; dkÞ 2 OCC½j

and emove

i  dðsi;ðxj; yjÞÞ < emovek  dk. If multiple

locations are qualified, the location ðxj; yjÞ such

that emove

k  dk emovei  dðsi;ðxj; yjÞÞ is maximized

will be selected. In this case, si will replace the

original record ðsk; dkÞ 2 OCC½j by the new record

ðsi; dðsi;ðxj; yjÞÞÞ in its OCC½j entry and enter the

engaged state. Here, both sensors si and sk are

competing for the same location ðxj; yjÞ. Because si

can consume less energy to move to ðxj; yjÞ, we

should replace sk’s mission by sito reduce the total

moving energy. Note that sensor sk will realize that

it loses the competition when it receives an update message originated from si later.

When sensor sibecomes engaged, it begins moving toward

its destination. Otherwise, siwill enter the terminated state,

because it does not need to cover any location.

TABLE 1

Approximate Threshold Values of pmin and rps in the Interpolating Placement Scheme

Fig. 4. The state transition diagram of each sensor siin the

For maintenance purposes, each sensor si will

periodi-cally perform the following actions:

1. Update the content of its OCC½1 . . . m table. Speci-fically, for each ðsj; djÞ 2 OCC½j , j ¼ 1 . . . m, we

decrease dj by the expected moving distance of sj

during the last period of time, unless dj¼ 0.

2. Broadcast si’s current status to its one-hop neighbors,

including its ID, its moving energy cost emove i , its

OCC½1 . . . m table, and its current position and state. The above actions can be controlled by setting two timers Tupdate OCC and Tbroadcast. Note that the update of the

OCC½1 . . . m table is based on the assumption that sensors all move in the same constant speed. If this assumption is not valid, dj is only an estimated distance for sensor sj to

location ðxj; yjÞ. In this case, we can make an extension by

including each sensor’s moving speed in its broadcast message.

When a sensor si receives an update message from

another sensor sk, two actions will be taken:

1. First, si has to update its OCC½1 . . . m table as

follows: Let us denote by OCCi½1 . . . m and

OCCk½1 . . . m the tables of si and sk, respectively.

For each j ¼ 1 . . . m, we calculate the union Uj¼ OCCi½j [ OCCk½j . If jUjj  nj, we will replace

OCCi½j by Uj. Otherwise, it means that there are too

many sensors scheduled to cover ðxj; yjÞ, in which

case we will truncate those records ðsk; dkÞ in Ujthat

have more moving energy (that is, a large value of emove

k  dk) until the size jUjj ¼ nj. Then, we replace

OCCi½j by the truncated Uj. Note that the above

merge of two sets may lead to a special case that si

was in the original OCCi½j entry but is not in the

new OCCi½j entry. In this case, it means that sihas

been replaced by some other sensors with a lower moving energy to ðxj; yjÞ. If so, sensor si should

change its state from engaged to free and then reselect another destination.

2. After the above merge, if si remains engaged, say,

with ðxj; yjÞ being its destination, we will conduct

the following optimization. We will check if emove_i  d sð i;ðxl; ylÞÞ þ emovek  d s k;ðxj; yjÞ

< emove_i  d si;ðxj; yjÞ

  þ emove

k  d sð k;ðxl; ylÞÞ;

where ðxl; ylÞ is the current destination of sk. If so, it

means that the total moving energy of si and skcan

be reduced if we exchange their destinations. In this case, siwill communicate with skfor this trade. Once

the trade is confirmed, si will replace the records

ðsi; diÞ and ðsk; dkÞ in OCCi½j and OCCi½l by the new

records ðsk; dðsk;ðxj; yjÞÞÞ and ðsi; dðsi;ðxl; ylÞÞÞ,

re-spectively. Note that sk will also update its OCCk½j

and OCCk½l entries with the same records.

In the above steps, if any entry in the OCCi½1 . . . m table has

been changed, si will broadcast the modified content to its

direct neighbors.

When a sensor si is in the engaged state, it will keep

moving toward its destination ðxj; yjÞ. When si arrives at

ðxj; yjÞ, it will change its state to terminated and begin its

monitoring job at the designated location. Meanwhile, it still executes the maintenance actions until the sink commands it to stop. Since the sink will eventually observe that I is k-covered(by receiving the sensing reports from sensors), it can notify all sensors to exit from the dispatch algorithm. Fig. 5 summarizes the main steps of the competition-based scheme. Theorem 1 shows that the competition-based scheme can guarantee I to be k-covered if there are sufficient sensors.

Theorem 1. Given an area I A, the competition-based dispatch scheme guarantees that I will be eventually k-coveredif there are sufficient mobile sensors inside A. Proof.Since the proposed placement schemes in Section 3

can compute a set of locations L inside I to be placed with sensors to ensure that I is k-covered, we only have to show that every location ðxj; yjÞ 2 L will

eventually be covered by nj sensors. Observe that in

the competition-based scheme, it is guaranteed that an engaged sensor si will eventually arrive at location

ðxj; yjÞ if the record ðsi; diÞ remains in si’s OCC½j entry.

However, if the record ðsi; diÞ is removed during si’s

movement toward ðxj; yjÞ, it means that either another

sensor sktrades its current destination ðxl; ylÞ with sior si

loses the competition. In the former case, the locations ðxj; yjÞ and ðxl; ylÞ will be covered by sk and si,

respectively. In the latter case, it means that ðxj; yjÞ has

already been committed by more than njsensors, so it is

safe for sensor si to give up the location ðxj; yjÞ. In this

case, sihas to reselect another destination. If sifinds that

jOCC½j j ¼ njfor all j ¼ 1 . . . m, then every location in L

has been committed by sufficient sensors, so all locations will be eventually covered by nj sensors. Therefore, the

competition-based dispatch scheme guarantees that I will be eventually k-covered if there are sufficient mobile sensors. tu Remark 1.Theorem 1 also shows that the competition-based scheme can converge when there are sufficient sensors. However, when the number of sensors is not sufficient to cover I , the competition-based scheme still guarantees that each sensor can eventually find a location to cover. In this case, if the sink knows in advance the total number of mobile sensors, it can also notify all sensors to exit from the dispatch algorithm earlier. If this assumption is not valid, a time-out mechanism should be applied to guarantee the convergence of this dispatch scheme. In this case, the sink

WANG AND TSENG: DISTRIBUTED DEPLOYMENT SCHEMES FOR MOBILE WIRELESS SENSOR NETWORKS TO ENSURE MULTILEVEL... 1287

can maintain a timer to decide when to terminate the dispatch algorithm.

Remark 2. There is a hidden assumption that the initial deployment of the network is connected, so sensors can receive the target locations L from the sink safely. For those sensors isolated from the initial network, they can only receive L when other sensors with L move close to them (by step 4). However, to alleviate the worst situation that some sensors may be always isolated from other sensors, we can enforce sensors to roam around randomly from time to time to increase the probability of information exchange.

Remark 3. Most message exchanges in the competition-based scheme rely on broadcast mechanism (steps 1 and 4). Since sensors will periodically broadcast their statuses and OCC tables, this scheme can tolerate the slight loss of messages. Thus, no extra acknowledgment mechanism is required to ensure proper operations of the competition-based scheme. In addition, to ensure that sensors correctly update their OCC tables, a time-stamp or a sequence number is needed in each message to distinguish new from old messages.

Remark 4. In the competition-based scheme, sensors will find out and move to their destinations on their own, without any interaction with the sink. The sink only announces available target locations in the begin-ning. Thus, the competition-based scheme is essentially distributed.

4.2 The Pattern-Based Dispatch Scheme

The previous competition-based scheme assumes that every sensor has full knowledge of all target locations inside I . This requires the sink to execute the placement scheme for I and then to broadcast all target locations to every sensor. Consequently, in this section, we propose a pattern-based dispatch scheme, which allows sensors to derive the target locations on their own, thus relaxing the above limitation.

Observe that our placement schemes in Section 3 actually place sensors with some regular patterns. Specifically, in the duplicate placement scheme, sensors will be placed in a hexagonlike fashion. Thus, each sensor at the location ðx; yÞ can derive its potential six neighbors’ positions according to Table 2. When the interpolating placement scheme is adopted, the pattern will be changed according to the relationship of rc and rs:

1. rc

ffiffi

3 p

2 rs. Recall the placement in Fig. 2a. There are

two patterns A and B, which will be repeated in each

old row and new row, as shown in Fig. 6a. Therefore, a sensor silocated at ðx; yÞ can derive its five neighbors’

positions according to its pattern. Moreover, si can

also derive the patterns of its neighbors, depending on its own pattern (indicated by the letters inside circles in Fig. 6a).

2. pffiffi3

2 rs< rc 2þpffiffi3

3 rs. In this case, if the desired

coverage level k is two, we can directly apply patterns A and B in the previous case. However, when k  3, there is an extra row (marked as new’) between each new and old rows in Fig. 3b. This will result in four placement patterns C, D, E, and F, as Fig. 6b shows, depending on a sensor’s position and its row number. Thus, a sensor silocated at ðx; yÞ can

derive its six neighbors’ positions based on its pattern. In addition, si can also derive the patterns

of its neighbors according to its own pattern (indicated by the letters inside circles in Fig. 6b). Note that we do not derive the patterns for sensors at the extra new’ rows (although this is feasible, deriving these patterns will complicate the problem a lot). That is why sensors marked by double circles are not assigned with any pattern letter.

3. rc>2þ

ffiffi

3 p

3 rs. In this case, since the duplicate

place-ment scheme is adopted, a sensor can compute its neighbors’ positions according to Table 2.

To summarize, the above observations allow a sensor to derive its direct neighbors (within the rs range) and the

patterns that they will use. This property allows us to expand from a partial deployment to a full deployment of sensors in I . Note that since the values of rc and rs are

known, each sensor can maintain a small table to record the related positions of its neighbors in each pattern. Thus, the calculation of neighbors’ positions can be translated to a simple table lookup procedure.

With the above property, the pattern-based dispatch scheme works as follows: Each sensor initially keeps a set of seed locations L0¼ fðx1; y1; n1; 1Þ; ðx2; y2; n2; 2Þ;    ;

ðx; y; n; Þg, which is a partial list of locations to be

placed with sensors in I, where jis the pattern used by the

sensor at location ðxj; yjÞ. Clearly, L0can be considered as a

subset of L. Note that these seed locations should be sparsely distributed over I so that sensors may not crowd into only few locations in the beginning. Each sensor then executes the competition-based scheme to contend for their closest locations in L0. However, the original steps 3 and 5 in the competition-based scheme should be modified as follows:

. Step 3’: A free sensor siwill try to select a location in

L0 as its destination. If si cannot find any available

location from its current OCC½ table, it will calculate some new locations based on the known locations and their patterns in the OCC½ table. Then, siwill try to select a destination among these

newly derived locations. However, if si cannot

calculate any new location from its current L0(which means that L0¼ L), siwill enter the terminated state,

since it does not need to cover any location. . Step 5’: When an engaged sensor si arrives at its

destination, it will derive some new locations from

TABLE 2

Coordinates of the Six Neighbors of a Sensor Located atðx; yÞ in the Duplicate Placement Scheme

its current L0and add the corresponding new entries in its OCC½ table.

Corollary 1. Given an area I A, the pattern-based dispatch scheme guarantees that I can be k-covered if there are sufficient mobile sensors inside A.

Proof. From Theorem 1, we know that the competition-based dispatch scheme can ensure that I is k-covered if there are sufficient sensors. Since the pattern-based scheme works similarly to the competition-based one, we only need to show that the complete information of L can be eventually known by all sensors. Observing in the pattern-based scheme, since a sensor can either derive new locations by itself (according to steps 3’ and 5’) or learn new locations from other sensors (by step 4 in the competition-based scheme), the complete information of L can be propagated throughout the whole network. Therefore, the pattern-based scheme also guarantees I to be k-covered when there are sufficient mobile sensors. tu

5

E

R

In this section, we present some experimental results to evaluate the performances of the proposed schemes. The

evaluation includes three parts. First, we measure the numbers of sensors required by different placement schemes discussed in Section 3. Second, we verify the effectiveness of our sensor dispatch schemes proposed in Section 4. Finally, we study the effect of seed locations on the pattern-based dispatch scheme.

5.1 Evaluations of the Sensor Placement Schemes The first experiment measures the numbers of sensors required by different placement schemes. We design an area of interest I as a 1,000 m  1,000 m square region to be placed with sensors. The communicate distance rc is set to

10 m, which is approximate to that specified in the IEEE 802.15.4 Standard [42] in an indoor environment. To reflect the relationships of rc<

ffiffi 3 p 2 rs, rc ffiffi 3 p 2 rs (boundary case),pffiffi3 2 rs< rc< 2þpffiffi3 3 rs, rc 2þpffiffi3

3 rs(boundary case), and

rc>2þ

ffiffi

3 p

3 rs, we set the sensing distance rsto 15, 11.55, 10,

8.04, and 6 m, respectively. We mainly compare the results of the duplicate and interpolating placement schemes discussed in Section 3. For baseline reference, we also calculate the theoretical lower bound of the number of sensors required by _rjI j2

s

l m

 k, where jI j is the area of I

WANG AND TSENG: DISTRIBUTED DEPLOYMENT SCHEMES FOR MOBILE WIRELESS SENSOR NETWORKS TO ENSURE MULTILEVEL... 1289

Fig. 6. The repeated patterns in the interpolating placement scheme. (a) The case of rc

ffiffi 3 p 2 rs. (b) The case of ffiffi 3 p 2 rs< rc 2þpffiffi3

3 rswhen the desired

(that is, 106_m2 _{in this experiment). Note that the above}

lower bound can never be achieved, because it does not consider the connectivity and coverage overlapping between sensors.

Fig. 7 illustrates the numbers of sensors required when the desired coverage level k increases from two to seven. When k ¼ 2, the interpolating scheme requires slightly more sensors compared with the duplicate scheme, because the former needs an extra row of sensors to ensure 2-coverage of I’s boundary. However, when k  3, the interpolating scheme can save approximately 19.4 percent  32.5 percent and 10.1 percent  16.8 percent of sensors as opposed to the duplicate scheme in the case of rc

ffiffi 3 p 2 rs andpffiffi3 2 rs< rc 2þpffiffi3 3 rs, respectively. When rc> 2þpffiffi3 3 rs, the

interpolating scheme works the same as the duplicate scheme, so they require the same number of sensors. Note that when rcbecomes larger, our placement schemes will be

dominated by the value of rs, so the numbers of sensors

required by the duplicate and interpolating schemes are closer to the theoretical lower bound as rc increases.

5.2 Performances of the Sensor Dispatch Schemes In the second experiment, we estimate the total moving energy and average moving distance of sensors when different dispatch schemes are adopted. We design a field A as a 600 m  600 m square region. The area of interest I is a 300 m  300 m square region located at the center of A. Three scenarios, namely, hollow, right, and central, are considered. In the hollow scenario, sensors are randomly distributed inside the region of A  I. In the right scenario, sensors are arbitrarily placed inside a 150 m  600 m rectangle region located at the right side of A  I . In the central scenario, sensors are initially concentrated inside a 100 m  100 m square region located at the center of I . With the setting of ðrc; rsÞ ¼ ð34:7 m; 20:0 mÞ;

ð24:1 m;13:9 mÞ; ð19:3 m;11:1 mÞ; ð16:7 m;9:62 mÞ; ð14:9 m; 8:6 mÞ;

ð13:4 m;7:71 mÞ; and ð12:5 m; 7:16 mÞ, we can obtain 100, 200, 300, 400, 500, 600, and 700 locations to be placed with sensors inside I , respectively, according to the interpolating placement scheme (in the case of rc>2þ

ffiffi

3 p

3 rs). We set the

desired coverage level k ¼ 3 so that there will be 300, 600, 900, 1,200, 1,500, 1,800, and 2,100 sensors needed to be dispatched to I. The moving speed of each sensor is set to 1 m/s. The moving energy cost emove

i of a sensor i is

randomly selected as [0.8 J, 1.2 J] per meter. For our sensor dispatch schemes, the two timers Tupdate OCC and

Tbroadcastare set to 5 s. In the pattern-based dispatch scheme,

we randomly select 10 percent, 20 percent, and 30 percent of target locations inside I as the seed locations. For comparison purposes, we design a greedy dispatch scheme, where sensors are assumed to know all target locations inside I, and they will simply move toward their closest locations without exchanging any information with other sensors. In this case, a sensor can realize that its destination has been occupied by sufficient sensors only when the sensor moves close to its destination (that is, not larger than the communication distance rc). For baseline reference, we

also design a centralized dispatch scheme. In this scheme, we assume that the sink knows the positions and statuses of all sensors and thus can calculate an optimal dispatch.

Fig. 8 shows the total moving energy and average moving distance of sensors under the greedy, competition-based, and centralized dispatch schemes. As can be seen, when the number of sensors increases, the average moving distances of the greedy and competition-based schemes also increase. This is because each sensor has to compete with more other sensors and thus increases its moving distance. Nevertheless, the greedy scheme will lead sensors to move much longer distances (and thus consumes more energy) compared with the competition-based scheme. This is because sensors just blindly move toward their nearest locations without exchanging necessary information to avoid moving to the same locations. In the hollow and right scenarios, the situation becomes worse as the number

Fig. 7. Comparison on the numbers of sensors required under different coverage levels k. (a) rc<

ffiffi 3 p 2rs. (b) rc ffiffi 3 p 2 rs. (c) ffiffi 3 p 2rs< rc<2þ ffiffi 3 p 3 rs. (d) rc2þ ffiffi 3 p 3 rs. (e) rc>2þ ffiffi 3 p 3 rs.

of sensors increases, since the number of unnecessary contests also increases in the greedy scheme. In the central scenario, the average moving distance of the greedy scheme is always kept very high (as compared with the other two dispatch schemes), because sensors are initially concen-trated in a small region. Thus, in Fig. 8, we can observe that simply taking a greedy strategy to dispatch sensors will make them exhaust much energy, thereby greatly short-ening the network lifetime. On the other hand, by properly exchanging and maintaining necessary information of sensors, our competition-based scheme can consume slightly more energy compared with the centralized scheme (especially in the hollow and right scenarios). Note that in the central scenario, since sensors have similar initial positions, there will be more sensors that compete for the same destinations. Thus, the competition-based scheme will cause sensors to move longer distances compared with the centralized scheme.

Fig. 9 illustrates the total moving energy and average moving distance of sensors under the pattern-based and

based dispatch schemes. The competition-based scheme outperforms the pattern-competition-based scheme, because sensors have full knowledge of target locations. In the pattern-based scheme, the average moving distance will arise as the number of sensors increases. This is because sensors have to compete for those few known locations in the beginning, thus increasing their moving distances. However, the average moving distance (and the total moving energy) of the pattern-based scheme can decrease when there are more target locations selected as seeds.

5.3 Effect of Seed Locations on the Pattern-Based Dispatch Scheme

The third experiment evaluates the effect of seed locations on the average moving energy of sensors in the pattern-based dispatch scheme. In this experiment, we set the number of sensors as 600 and 1,500 and randomly select 5 percent to 70 percent of target locations inside I as the seed locations.

WANG AND TSENG: DISTRIBUTED DEPLOYMENT SCHEMES FOR MOBILE WIRELESS SENSOR NETWORKS TO ENSURE MULTILEVEL... 1291

Fig. 8. Comparison on the total moving energy and average moving distance of sensors under the greedy, competition-based, and centralized dispatch schemes. (a) Hollow scenario. (b) Right scenario. (c) Central scenario.

Fig. 10 shows the effect of seed locations. As can be seen, the average moving energy of sensors can be reduced when the number of seed locations increases. When the percen-tage of seed locations arrives at 100 percent, the pattern-based scheme will work the same as the competition-pattern-based scheme. In Fig. 10a, we can observe that in the hollow scenario, the difference between the average moving

energies of the pattern-based scheme and the competition-based scheme can be smaller than 10 J when there are more than 40 percent  45 percent of target locations selected as seeds. In the right scenario (that is, Fig. 10b), when the number of sensors is 600 (respectively, 1,500), such a difference can be achieved if there are more than 15 percent  20 percent (respectively, 35 percent  40 percent) of

Fig. 10. Effect of seed locations on the average moving energy of sensors in the pattern-based dispatch scheme. (a) Hollow scenario. (b) Right scenario. (c) Central scenario.

Fig. 9. Comparison on the total moving energy and average moving distance of sensors under the pattern-based and competition-based dispatch schemes. (a) Hollow scenario. (b) Right scenario. (c) Central scenario.

target locations selected as seeds. On the other hand, in the central scenario (that is, Fig. 10c), such a difference can be achieved if we select at least 45 percent  50 percent of seed locations. To summarize, in Fig. 10, we can observe that the performance of the pattern-based scheme can be signifi-cantly improved by selecting 40 percent  50 percent of target locations as seeds.

6

C

F

W

In this paper, we have proposed systematical solutions to the k-coverage sensor placement problem and distributed sensor dispatch problem. Our placement solutions allow an arbitrary relationship of sensors’ communication distance and their sensing distance and can work properly under both binary and probabilistic sensing models. It is verified that the interpolating placement scheme requires fewer sensors to ensure k-coverage of the sensing field and connectivity of the network as compared with the duplicate placement scheme. Our dispatch solutions are based on the competitive nature of a distributed network. Simulation results have shown that the competition-based dispatch scheme performs better than the greedy and pattern-based dispatch schemes. However, by selecting sufficient seed locations, the pattern-based scheme can work as efficiently as the competition-based scheme.

As to future work, sensor deployment in arbitrary-shaped regions for multilevel coverage deserves further study. When the area of interest I is of an arbitrary shape, one potential approach is to form a rectangle region that can fully cover I . Then, we can apply our solution to this rectangle and remove those sensors that are outside the area of interest. Another way is to approximate I by multiple smaller rectangles. In our model, sensors’ energy drain is at a constant speed when moving around. More sophisticated energy consumption models of mobile sensors can be defined, and this deserves further investigation. For example, a start-up energy cost may be incurred when first moving a sensor, and a cost may be incurred to enforce a sensor to turn around. In addition, variable moving speeds can be considered too.

A

Y.-C. Tseng’s research is cosponsored by Taiwan MoE ATU Program, by NSC Grants 93-2752-E-007-001-PAE, 96-2623-7-009-002-ET, 95-2221-E-009-058-MY3, 95-2221-E-009-060-MY3, 95-2219-E-009-007, 95-2218-E-009-209, and 94-2219-E-007-009,by Realtek Semiconductor Corp., by MOEA under Grant 94-EC-17-A-04-S1-044, by ITRI, Taiwan, by Microsoft Corp., and by Intel Corp.

R

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You-Chiun Wang received the BEng degree in computer science and information engineering from the National Chung Cheng University in 2001 and the MEng degree in computer science and information engineering and the PhD degree in computer science from the National Chiao Tung University, Hsinchu, Taiwan, Re-public of China, in 2003 and October 2006, respectively. He is currently a postdoctoral research associate in the Department of Com-puter Science, National Chiao Tung University. His research interests include wireless network and mobile computing, communication proto-cols, and wireless sensor networks. He is a member of the IEEE.

Yu-Chee Tseng received the PhD degree in computer and information science from the Ohio State University in January 1994. Since 2000, he has been a professor in the Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, Republic of China, where he has also been the chairman since 2005. Since 2006, he has also been an adjunct chair professor at the Chung Yuan Christian University. He has been an associate editor for Telecommunication Systems and the IEEE Transactions on Vehicular Technology since 2005 and the IEEE Transactions on Mobile Comput-ing since 2006. His research interests include mobile computComput-ing, wireless communication, network security, and parallel and distributed computing. He is a senior member of the IEEE. He received the Outstanding Research Awards from the National Science Council, Taiwan, in 2001-2002 and 2003-2005, the Best Paper Award in the 32nd International Conference on Parallel Processing (ICPP 2003), the Elite IT Award in 2004, and the Distinguished Alumnus Award from the Ohio State University in 2005.

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