Sensor Network Architectures for Monitoring Underwater ... - IEEE Xplore

.

Failure Impact on Coverage in Linear Wireless Sensor Networks Nader Mohamed1, Jameela Al-Jaroodi2, Imad Jawhar1, and Sanja Lazarova-Molnar1 1

The College of Information Technology, UAE University, Al Ain, UAE 2 Middleware Technologies Lab., Bahrain [email protected] ; [email protected]; [email protected] ; [email protected] Abstract – Wireless Sensor networks (WSN) are used to monitor long linear structures such as pipelines, rivers, railroads, international borders, and high power transmission cables. In this case a special type of WSN called linear wireless sensor network (LSN) is used. One of the main challenges of using LSN is the reliability of the connections across the nodes. Faults in a few contiguous nodes may cause the creation of holes (segments where nodes on either end of them cannot reach each other), which will result in dividing the network into multiple disconnected segments. As a result, sensor nodes that are located between holes may not be able to deliver their sensed information, which negatively affects network’s sensing coverage. In this paper, we provide analysis of the different types of node faults in LSN and study their negative impact on the sensing coverage. We develop an analytical model to estimate the impact of faults on coverage in LSNs. We verify the correctness of the developed model through a number of simulation experiments to compare both calculated and simulated results under various network and fault scenarios.

Keywords–Linear Wireless Sensor Networks, Linear Structure Monitoring, Fault Tolerance, Modeling, Sensing Coverage.

I. INTRODUCTION The advent of communication and computer technologies has resulted in many innovations such as the development of low cost, low power, easily deployable and selforganized wireless sensors. This technology opens great opportunities for a wide array of monitoring applications such as environmental, industrial, and security applications. Some of the applications involve monitoring linear structures that could extend for hundreds of kilometers in harsh or uninhabited environments. The WSN used for monitoring this type of infrastructures are called Linear wireless Sensor Networks (LSN). Typical applications of LSN include monitoring water, oil, and gas pipelines; rivers; railways; international borders; and high power transmission cables [1]. Each sensor node is equipped with the necessary sensing elements, a battery, a wireless transceiver, a lowcapability processor, a small memory, and a small storage unit. The sensors are lined through the structure to provide three main functions: sensing, information relay and information filtering. The sensing function is to observe any interesting changes in or around the monitored structure.

The information relay helps forward the observed data to the main station using multi-hop communication. The filtering function filters out unwanted data and aggregates multiple pieces of sensed data into smaller messages. This optimizes communication, processing, and routing as well as the power needs thus extending the life of the LSN. WSNs are generally designed to have good coverage [2][3][4]. However, the special way LSNs are designed result in a major challenge of losing connectivity in the network in the presence of multiple node faults [5]. This is due to faults in neighboring and consecutive nodes. Nodes can fail due to battery exhaustion, hardware failures, and natural or intentional damages. These consecutive faulty nodes form holes, which may cause the LSN to be divided into multiple disconnected segments. Some of these segments will become isolated thus they cannot transfer their sensed data to the main station. As a result the isolated segments will not provide any sensing coverage. In this paper, we study the types of faults in LSN and the impact of these faults on the sensing coverage. We develop an analytical model to estimate coverage in LSNs in the presence of node faults. We verify the correctness of the developed model by conducting a number of simulation experiments to compare both calculated and simulated results under different network configurations and fault scenarios. This analytical model can be used to analyze LSNs such as the one used for monitoring underwater pipelines [6]. Underwater pipelines extend for hundreds of kilometers at depths reaching hundreds of meters and subjected to high pressure [7]. At such depths, there is a high need for reliable LSNs as it is really difficult to perform any simple maintenance activities. The rest of the paper is organized as follows: Section II provides background information about LSN. Section III discusses the different types of faults in LSN and their impact on the sensing coverage. Section IV develops an analytical model to estimate the coverage in the presence of node faults. Section V provides experimental validations of the model. Section VI discusses the related work and Section VII concludes the paper.

.

II. BACKGROUND Wireless sensor nodes can be installed on a linear structure to observe the status of the structure and its surrounding environment. Sensing nodes usually have limited transmission compatibilities where each node can communicate with only a few neighboring nodes [8]. Nodes collaborate among themselves in both sensing and communication functions. Multi-hop communication is used to transfer the sensed and control data across the linear structure and to/from the main control station. Wireless networks can solve some of the reliability problems of current wired networks technologies that are used to monitor linear structures [9]. For example, WSNs can still function even when some nodes are disabled. Faults in sensor nodes can be easily tolerated using other available nodes to cover the faulty ones. Using dense WSNs with a high number of nodes and/or using wide wireless transmission ranges, the network can maintain connectivity and the sensed and control data can be transmitted through the network to its destination even with the existence of some node faults. For example, each node in Figure 1 can communicate with two nodes to the left and two nodes to the right. If for example nodes 3 and 5 are damaged, node 4 can still send its sensed data through nodes 2 or 6. The maximum number of neighboring nodes that each node can communicate with each side can be defined as a Maximum Jump Factor (MJF). For example, MJF in Figure 1 is 2, thus Node 4 can communicate with a maximum of two nodes on each side.

1

2

3

4

5

6

7

8

1

Figure 1. Reliability in a dense LSN.

Each senor node on a linear structure is usually equipped with a transceiver, a processor, a battery, memory, and small storage in addition to one or more sensing elements. Power consumption is critical to the life span of LSNs. Linear structures need to be monitored throughout their life span which could extend to tens of years. Therefore the associated LSNs should also be long lived. Unlike wired networks where the power is not at all a constraint as the wires deliver power to the different sensor nodes, LSN designers have to consider power as one of the main constraints in the wireless system. Power in a sensing node is consumed by every element on it. A transceiver consumes power waiting for a signal and when transmitting or receiving data. Sensing elements also consume power and

the processor as well. Careful scheduling of these resources is needed to optimize power consumption. Although increasing the transmission range can provide better communication reliability, the nodes will consume more energy. A dynamic configuration for the wireless transmission range can provide better power management. An example of this configuration is in Figure 2. In this network, nodes 3 and 5 have failed. Therefore, the wireless range for node 4 is increased to reach nodes 2 and 6 while other nodes use a smaller transmission range to reduce the power consumption. The sensed data is transferred through the line to the main station in either direction or both if both directions are connected to the main station. Connecting both directions to the main station will double the communication reliability [7][10].

1

2

3

4

5

6

7

8

Figure 2. Automatic wireless range configuration.

III. FAULTS AND COVERAGE IN LSN Sensor nodes are usually initially distributed to cover the whole linear structure in terms of both sensing and communication coverage. A node senses interesting events and this observation is reported to the main station using multi-hop communication. Sensors in LSN nodes can have different sensing range capabilities. In a uniform LSN where nodes are distributed at uniform distances, let us define the distance between two neighboring nodes i and i+1 as one distance unit. Then a LSN with healthy nodes can provide 100% sensing coverage for the monitored linear structures if the Node Sensing Rang (NSR) is one distance unit. This coverage is reduced if there are some faulty nodes. However, if NSR is larger than d (one distance unit), then some node faults can be easily tolerated without reducing the percentage of the sensing coverage. For example, if NSR is 2 distance units. This means that the area between two neighboring nodes i and i+1 is monitored twice by both nodes. In this case, this area will be still under monitoring even if node i or node i+1 are faulty. LSN is usually designed to provide a full sensing coverage. However, after some time, there will be some faults among the nodes. Let us consider that we have a onesegment network with homogeneous nodes. Let us also assume that there is a uniform distance between each two nodes. In addition, nodes have a specific MJF. Let us define a term Hole (H) as the number of contiguous faulty nodes in

.

the LSN. Each hole can be of size of one or more nodes. For example, in Figure 3, we have two holes: H1 and H2. The first one is with size 1 where only node 2 is faulty while the second hole, H2, is of size 3 where nodes 5, 6, and 7 are faulty. We use Z(H1) = 1 and Z(H2) = 3 where Z is the size function of a hole. In addition, we can use R(Hi) = [Fi : Li] to specify the ID of first faulty node, Fi, and the ID of last faulty node, Li, in Hi. Thus we have Z(Hi) = Li – Fi + 1.

continue to function. This one DH will divide the LSN into two segments: one on the left side of the DH and the other is on the right side. As the size of the DH is larger or equal to MJF then this DH will disable information exchange between both segments as shown in Figure 4. In this case, all healthy nodes on the left side of the DH will use a rightto-left forwarding direction while all healthy nodes on the right-side will use a left-to-right forwarding direction to communicate with the main station. Forwarding Direction

Forwarding Direction 1

2 Z(H1 )= 1

3

4

5 6 Z(H2 )= 3

7

8

Figure 3. Two holes in the LSN. A special type of hole is a Disconnecting Hole (DH), which disconnects the network into two segments that cannot directly communicate with each other using an extended wireless range. In other words, the size of a DH is larger than or equal to the MJF used for the nodes in the LSN, Z(DH) ≥ MJF. For example if the MJF of the LSN in Figure 3 is 2, then H2 is DH while H1 is not. This is because Z(H2) = 3 which is larger than the MJF while Z(H1) = 1 which is less than the MJF. There are different types of faults in a one-segment LSN with homogenous nodes distributed uniformly over the linear structure. Assume that both ends of the LSN are connected to the main station. The faults have different impacts on the communication and sensing coverage. For example, if there are multiple holes that are all not disconnecting holes, then the LSN will function normally. Although there will be some holes with sizes smaller than MJF, any sensed information can be transferred to the main station through the left or right side of the network. Any hole can be jumped over by extending the wireless range of the node that forwards the sensed data to the MJF to reach the next functioning node. The sensing coverage in each hole may or may not be affected. This depends on the size of the hole and NSR. Let U(Hi) be the size of the uncovered sensing area in Hi: 0  U (Hi )   Z ( H )  ( NSR  1) i 

Z ( H i ) NSR ........(1) Otherwise

For example, if Z(Hi) is 3 and NSR is 4, then U(Hi) is 0. In another, if Z(Hi) is 6 and NSR is 3, then U(Hi) is 4. If there are n nodes and k holes in a LSN, then the sensing coverage percentage, C, is: k

C 

n  U ( H i ) i 1

n

............................................(2)

In another fault case, there are multiple holes; only one of them is a disconnecting hole. In this case the LSN will

3

2

1

5

4

7

6

Z(DH1) = 2

8

Figure 4. LSN with MJF=2. LSN is divided into two segments by a DH. Each one will communicate in a different direction.

The sensing coverage of LSN can be calculated using Equations (1) and (2) as in Fault Type 1. In the example shown in Figure 5, the size of DH is 3, while NSR is 4, then the healthy nodes 6 and 10 cover the whole area of DH. In another example (see Figure 6) the size of DH is 5 while NSR is 4. In this case, there are 2 distance units that are not covered by both healthy nodes 6 and 12.

1

2

3

4

5

6

7 8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

Figure 5. LSN with MJF = 2. Z(DH)=3 and NSR = 4. The whole DH is covered.

1

2

3

4

5

6

7 8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

Figure 6. LSN with MJF = 2. Z(DH)=5, and NSR=4. The whole DH is not covered.

In another fault case, there are multiple holes; only two of them are disconnecting holes. In this case, the LSN will be divided into three segments. Let the DHs be DH1 and DH2. The first segment is before DH1, the second segment is between DH1 and DH2, and the third segment is after DH2 as shown in Figure 7. In this figure, DH1 is from node 5 to node 6 while DH2 is from node 11 to node 13. The first segment covers nodes 1 thru 4, the second covers nodes 7 thru 10, and the third covers nodes 14 thru 17. All nodes in the first segment can communicate with the main station in the right-to-left direction while all nodes in the third segment can communicate with the main station in the leftto-right direction. However, healthy nodes in the second segment cannot communicate with the main station at all.

.

Z(DH1)= 2 1

2

3

4

5

6

7

Z(DH2)=3 8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

Figure 7. LSN with MJF=2. There are two DHs: DH1 and DH2. The segment between DH1 and DH2 is not connected.

In another case, there are multiple holes with more than two disconnecting holes. In this case, let us assume that there are k DHs: DH1 thru DHk. This means that the LSN will be divided into k+1 segments. With the existence of k DHs, all nodes starting from the first node in DH1 thru the last in DHk will not be able to communicate with the main station. As a result, the areas from DH1 to DHk will be uncovered. The effect of this type of fault is similar to having a large DH, DH1,k that expand from the first node in DH1 to the last node in DHk. Equations (1) and (2) can be used to find uncovered areas as well as the coverage percentage due to this large DH. IV. COVERAGE MODELING In this section, a sensing coverage analytical model is developed for linear wireless sensor networks with the presence of node faults. To understand the impact of faults in the LSN, we will start with simple faults of two disconnecting holes then we will cover the general case with multiple disconnecting holes. Two disconnecting holes in a LSN can have different impact levels on the coverage. This depends on their locations in the LSN. The worst case is when both holes are located very far from each other at the opposite ends of the LSN. In this case the whole network will be disconnected from the main station and all nodes in the network will not be able to send their sensed information. The best case is when both holes are located very close to each other at any location. In this case, only the area from the first hole to second hole will be uncovered while all other parts will be connected to the main station. The average case that can be generally used for evaluation is shown in Figure 7. The result of this case is like dividing the LSN into three equal seized segments. The first hole is between the first and second segment while the second hole is between the second and third segment. Both first and third segments will be connected to the main station and covered while the second segment will not be connected and uncovered. For a network with two small disconnected holes, the coverage will be reduced to around two-thirds of the full coverage. Similar to the two-hole case, the occurrence of multiple disconnecting holes in a LSN can have different impact levels on the coverage. This depends on their locations. The worst case is when two of the disconnecting holes are very far from each other at the opposite ends of the LSN. In this case the whole network will be disconnected from the main

station and all nodes in the network will not be able to send their sense information. In contrast, the best case is when all holes are located very close to each other. In this case, only the area from the first disconnecting hole to the last disconnecting hole will be uncovered while all other parts will be connected to the main station and covered. The average case is like dividing the network into (k+1) equal sized segments where there are k disconnecting holes. Each disconnecting hole disconnects two neighboring segments. In this case, only the first and the last segment will be connected to the main station and their areas are covered while all other segments are not connected and their areas are not covered. Thus the coverage will be reduced to 2/(k+1) of the full coverage. Let the network size be n and the expected coverage with zero holes, EC0, be 100 percent, then if there are k small disconnected holes, then the expected coverage ECk will be reduced to:

EC K 

2 .................................................3 k 1

If there are k small disconnecting holes, the LSN will be divided into two kinds of expected percentages: expected Connected Area (CAk) and expected Disconnecting Area (DAk). The Connected Area contains the connected parts on both ends of the LSN while the Disconnected Area is the disconnecting part that contains all disconnecting holes and the segments of the network between those holes. We have:

CAk  DAk  1....................................................(4) To find the values of CAk and DAk, we use Equation (3) which provides expected coverage percentage and also represents the percentage of the expected connected area: CAk 

2 .......................................................(5) k 1

DAk  1 

2 k 1  .......................................(6) k 1 k 1

Now, Equation (3) does not include uncovered subareas due to holes that are not disconnecting holes (holes) in the connected area. Although, these will not have high impact on the coverage, we can include them for better estimation. All holes with sizes 1 to MJF-1 are holes. Let NHi be the number of holes of size i in the whole LSN. Based on Equation (5), if we have k disconnecting holes, the expected connected area percentage will be CAk. This means that the number of holes with sizes i in the connected area is NHi.CAk. From Equation (1), the uncovered area Ui from a hole with size i is: 0  Ui   i   NSR  1

i  NSR .......................(7) Otherwise

.

Now, the expected total of uncovered area from all holes with sizes i that are located in the connected area is NHi.CAk.Ui. From this equation we can find the expected total of all holes located in the connected area, UCA,k: U CA,k 

MJF 1`

 NH i 1

i

 CAk  U i ...............................(8)

We can use this equation to adjust Equation (3) to include uncovered areas due to not only the disconnecting holes but also due to holes located in the connected area: ECk 

U 2  CA,k ..........................................(9) k 1 n

We have: NH i  (1  f ) 2  f i  (n  i)..............................(15)

Here, as the LSN size increases the chance to have more holes in the LSN also increases. A realistic value of f is generally very low as the probability to have holes with sizes larger than a certain number in a LSN is very small. For example if there 1000 nodes with 20% node fault rates, based on Equation (15), the expected number of holes with size 11 is very small: 1.31x10-5. Therefore, we can consider that we have a variable v that represents the maximum size of possible holes. The total expected number of holes in the network is: TH 

TH  1  f

MJF 1

EC k 

2  k 1

i 1

n

EC k 

2  k 1

2

  2  EC k  1 k 1   

 NH i 1

i

MJF 1 i 1

k 

v

 NH ......................................................(18)

i  MJF

i

2   f i  n  i ...............................(19) v

i  MJF

......................(11)

 U i   ....................(12)  n  

 NH

v

The total expected number of disconnecting holes is:

k  1  f

U i 

nk  1

2   f i  n  i .............................(17) i 1

..............(10)

We replace CAk with Equation (5), we get: MJF 1

i

i 1

We replace UCA,K with Equation (8), we get:

 NH i  CAk  U i 

v

 NH ....................................................(16)

i

Equations (3) and (12) show direct links between the number of disconnecting holes and the expected coverage. In this section, we will also find the expected number of holes. Given a LSN with n uniformly distributed nodes and a specific MJF, each node has a chance to independently fail with probability f within a certain period T. T can be the time to a periodic full maintenance or the time that the LSN is needed to live. There is a need to find the expected number of holes that will occur and their sizes within the time T. Let us first find the probability equation when a healthy node in the LSN has a hole directly in front of it with exactly size i. We name this equation Wf,i: i

W f ,i  (1  f ) 2  f ...........................................(13)

Here, as f increases, the chance to have a healthy node with a hole in front of it with size i also increases. As there are n nodes in the LSN and all nodes other than the last i node, which has no chance to have a hole in front of it, have the same chance to have a hole in front of them, then the number of holes in the LSN with size i is: NH i  W f ,i  n  i ...........................................(14)

Generally, the value of variable v is enough to be 10 for most cases. However, this number can be increased for more accurate results. As the majority of holes will be small, we can use NHi from Equation (15) and k from Equation (19) in Equation (12) to find the expected coverage percentage with the presence of faults as:  1  f  2  EC  1 k 1  

2   f i  n  i  U i   MJF 1 i 1

n

....(20)   

where we can get k from Equation (19) and Ui from Equation (7). Equation 20 is valid if k is equal to or larger than 1. Otherwise if k is less than 1, this means there is no hole and the coverage stays at high level. V. VALIDATIONS AND ALNYSIS A set of simulation experiments was conducted to validate the analytical model developed in the previous section. The experiments compare the calculated and simulated coverage of LSNs. Each LSN will be initially deployed to provide full coverage. However, after some time, some faults will occur in some nodes thus reducing the coverage in the LSN. In this case the LSN needs maintenance to regain full coverage again. The simulations were developed using Java, where experimental situations were created with 10,000 LSNs that were generated randomly to have different types of faults

.

for each situation. The results are the averages measured from all these faulty LSNs. The first experiment validates the expected coverage result of LSN with two disconnecting holes, a simulation experiment was conducted for different LSN sizes to allow us to compare the calculated and simulated results. The simulation was developed using 10,000 faulty LSNs each with two disconnecting holes at randomly generated locations. The size of both disconnecting holes was 2 while MJF was also 2. The results were the averages measured from all these faulty LSNs. The results of both calculated and simulated coverage are shown in Figure 8. As we can see the results are matched for all LSN sizes. This also shows that the expected coverage percentage is reduced to around 66.7% of the full coverage.

Figure 9. Expected coverage percentage for different sizes of LSNs with four disconnecting holes.

Figure 10. Expected coverage percentage for 1000-node LSN. Figure 8. Expected coverage percentage for different sizes of LSNs with two disconnecting holes.

To validate Equation (3) for the expected coverage with k disconnected holes, simulation experiments were conducted to compare the calculated and simulated results. The first experiment was conducted for different LSN sizes with 4 disconnecting holes. The experimental situations were created with 10,000 faulty LSNs each with four disconnecting holes at randomly generated. The size of the disconnecting holes was 2 while MJF was also 2. The results were the averages measured from all these faulty LSNs. The results of both calculated and simulated coverage are shown in Figure 9. As we can see the results are matched for all LSN sizes. This also shows that the expected coverage percentage is reduced to around 40% of the full coverage. The second experiment was conducted to find the expected coverage percentage for a LSN with 1000 nodes under different numbers of disconnecting holes. The results are shown in Figure 10, where we have the simulated results and the calculated results calculated in Equation (3). As we can see both simulated and calculated results are very similar, which validates Equation (3). The results also show that as the number of disconnecting holes increases the expected coverage of the LSN decreases.

The third experiment was conducted to validate the number of holes equation, Equation (15). Here, as the LSN size increases the chance to have more holes in the LSN also increases. Figure 11 shows the calculated and simulated numbers of holes in a 1000-node LSN with a node fault rate of 20%. As we can see the holes sizes are small even with high node fault rates. In this example, all holes are mostly of sizes less than 5 nodes.

Figure 11. The Number of Calculated and Simulated Holes in 1000-node LSN with 20% Node Fault Rate.

.

To verify the developed expected coverage equation, Equation (20), a set of two experiments was conducted. These experiments were developed to compare the results of the equation with the simulation results. The first experiment compares the coverage under different node fault rates. The network size used is 5000 nodes, MJF is 2, and NSR is 2. Both calculated and simulated cases were conducted for different node fault rates starting from 5% to 20%. This large range was selected to ensure some occurrence of disconnecting holes. The results are shown in Figure 12.

Figure 12. Coverage Under Different Node Fault Rates. No. of Nodes = 5000, MJF=2, and NSR=2.

The second experiment compares the coverage under different MJF values. Here, networks with sizes 5000 nodes were used with the node fault rate at 30%. This high fault rate was selected to make sure several disconnecting holes would occur. The experiment was conducted for MJF values from 2 thru 5, while NSR was kept as 2. Both calculated and simulated results are very similar as shown in Figure 13. As we can notice as MJF increases the reliability and the coverage are significantly enhanced. The coverage is enhanced more than 3 times by increasing MJF from 4 to 5.

VI. RELATED WORK Different aspects of LSN have been investigated recently by researchers. We surveyed the applications, issues and classifications of LSN in [1][5]. In addition, we developed a number of efficient routing protocols [11] and a distributed topology discovery algorithm [12] for LSN. Zimmerling et al. studied energy-efficient and localized power-aware routing in LSN [13][14]. Noori and Ardakani proposed an analysis to characterize the traffic load distribution over a randomly deployed LSN [15]. Liu et al. provided an algorithm for an energy-balanced data gathering for LSN [16]. Li provided an energy-efficient node replacement schemes in LSN to balance network load and extend network lifetime [17]. Finally, Martin and Paterson developed a lightweight key redistribution mechanism for LSN [18]. The coverage problem was one of the important issues of WSN that recently got high attention [2][3][4]. Some of the research was dedicated for developing approaches that can achieve high coverage [19][20][21][22][23][24], while other work was dedicated for developing analytical models and optimization techniques for high WSN coverage [25][26][27][28][29][30]. However, all of these efforts covered randomly deployed two and three-dimensional WSN. LSNs represent a special case of WSN that has its own unique characteristics and coverage problems. None of the mentioned work studied the coverage problem in LSN, which is important for some critical infrastructure applications such as pipeline, long power line, river, and highway monitoring. VII. CONCLUSION There are different types of node faults in LSNs. Some types of faults may significantly reduce the sensing coverage, while some have very limited effects. We developed an analytical model that can provide estimations for failure impact on coverage in LSNs. The model was validated with a number of simulation experiments that have shown clear correspondence between the theoretical model and the experimental results. The developed model can be applied for designing and maintaining LSNs used for applications to monitor critical linear infrastructures. ACKNOWLEDGMENT This work is supported in part by UAEU Research grant # 3IT008.

Figure 13. Coverage under different MJF values. No. of Nodes = 5000, NSR = 2, and Fault Rate = 30%.

.

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

I. Jawhar, N. Mohamed, and D. P. Agrawal, “Linear Wireless Sensor Networks: Classification and Applications,” in The Journal of Network and Computer Applications, Elsevier, Vol. 34, No. 5, pp. 1671-1682, September 2011. J. Li, L.L. Andrew, C.H. Foh, M. Zukerman, and H.H. Chen, “Connectivity, coverage and placement in wireless sensor networks,” Sensors, 9(10):7664-7693, 2009. G. Fan and J. ShiYao, “Coverage problem in wireless sensor network: a survey,” Journal of Networks, 5(9):1033-1040, 2010. W.A.N.G. Yan-Li and A. N. Shi-qan, “Research on the Coverage of Wireless Sensor Network,” Journal of Transcluction Technology, 2, 025, 2005. I. Jawhar and N. Mohamed, “A Hierarchical and Topological Classification of Linear Sensor Networks", in Proc. of The Eighth Annual Wireless Telecommunications Symposium (WTS 2009), IEEE Communication Society, pp. 72-79, 22-24 April 2009. N. Mohamed, I. Jawhar, J. Al-Jaroodi, and L. Zhang, “Monitoring Underwater Pipelines Using Sensor Networks,” in The 12th IEEE International Conference on High Performance Computing and Communications (HPCC-2010), Melbourne, Australia, pp. 346-353, September 1-3, 2010. N. Mohamed, I. Jawhar, J. Al-Jaroodi, L. Zhang, “Sensor Network Architectures for Monitoring Underwater Pipelines,” in Sensors - The Special Issue on Underwater Sensor Nodes and Underwater Sensor Networks, Vol. 11, No. 11, pp. 10738-10764, November 2011. F. Davoli, M. Marchese, and M. Mongelli, “Non-linear coding and decoding strategies exploiting spatial correlation in wireless sensor networks,” IET Communications, Vol. 6, No. 14, 2198-2207, 2012. I. Jawhar, N. Mohamed, M. Mohamed, and M. Aziz, “A Routing Protocol and Addressing Scheme for Oil, Gas, and Water Pipeline Monitoring Using Wireless Sensor Networks,” in Proc. of The Fifth IEEE/IFIP International Conference on Wireless and Optical Communications Networks (WOCN2008), IEEE, May 2008. N. Mohamed and I. Jawhar, “A Fault-Tolerant Wired/Wireless Sensor Network Architecture for Monitoring Pipeline Infrastructures,” in Proc. of The Second International Conference on Sensor Technologies and Applications (SENSORCOMM 2008), IEEE Computer Society Press, pp. 179-184, August 2008. I. Jawhar, N. Mohamed, K. Shuaib, and N. Kesserwan, “An Efficient Framework and Networking Protocol for Linear Wireless Sensor Networks,” The Ad Hoc & Sensor Wireless Networks Journal, Old City Publishing, London, UK, Special Issue on Wireless Sensor and Actor Networks, Vol. 7, No. 12, pp. 3-21, 2009. I. Jawhar, N. Mohamed, and L. Zhang, “A Distributed Topology Discovery Algorithm for Linear Sensor Networks,” In Proc. of IEEE International Conference on Communications in China, IEEE, Beijing, China, August 1518, 2012. M. Zimmerling, W. Dargie, and J.M. Reason. “Energyefficient routing in linear wireless sensor networks,” IEEE International Conference on Mobile Adhoc and Sensor Systems (MASS), 2007.

[14] M. Zimmerling, W. Dargie, and J. M. Reason. “Localized

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

power-aware routing in linear wireless sensor networks,” Proc. of the 2nd ACM international conference on Contextawareness for self-managing systems, ACM, 2008. M. Noori and M. Ardakani. “Characterizing the traffic distribution in linear wireless sensor networks,” Communications Letters, IEEE, Vol. 12(8): 554-556, 2008. AF Liu, et al. “An energy-balanced data gathering algorithm for linear wireless sensor networks,” International Journal of Wireless Information Networks, Vol. 17(1): 42-53, 2010. H. Li and X. Shunjie, “Energy-Efficient Node Placement in Linear Wireless Sensor Networks,” 2010 International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), Vol. 2. IEEE, 2010. K. Martin and M. Paterson, “Ultra-lightweight key predistribution in wireless sensor networks for monitoring linear infrastructure,” Information Security Theory and Practice. Smart Devices, Pervasive Systems, and Ubiquitous Networks, pp. 143-152, 2009. H.M. Ammari and S. K. Das, “Integrated coverage and connectivity in wireless sensor networks: A two-dimensional percolation problem,” IEEE Transactions on Computers, 57(10): 1423-1434, 2008. N. Boudriga, M. Hamdi, and S. Iyengar, “Coverage Assessment and Target Tracking in 3D Domains,” Sensors, 11(10):9904-9927, 2011. N.A.A. Aziz, K. A. Aziz, and W.Z.W. Ismail, “Coverage strategies for wireless sensor networks," World Academy of Science, Engineering and Technology 50 (2009): 145-150. G. Fan, R. Wang, H. Huang, L. Sun, and C. Sha, “Coverageguaranteed sensor node deployment strategies for wireless sensor networks,” Sensors, 10(3), 2064-2087, 2010. V. Zalyubovskiy, A. Erzin, S. Astrakov, and H. Choo, “Energy-efficient area coverage by sensors with adjustable ranges,” Sensors, 9(4), 2446-2460, 2009. M. Cardei and J. Wu “Energy-efficient coverage problems in wireless ad-hoc sensor networks,” Computer Communications, Vol. 29, No. 4, pp. 413-420, 2006. V. Coskun, “Relocating sensor nodes to maximize cumulative connected coverage in wireless sensor networks,” Sensors, 8(4), 2792-2817, 2008. S.J. Habib, “Modeling and Simulating Coverage in Sensor Networks,” Computer Communications, 30(5): 1029-1035, March 2007. S. Pashazadeh and M. Sharifi, “A geometric modelling approach to determining the best sensing coverage for 3dimensional acoustic target tracking in wireless sensor networks,” Sensors, 9(9):6764-6794, 2009. N.A.B.A. Aziz, A.W. Mohemmed, and M.Y. Alias, “A wireless sensor network coverage optimization algorithm based on particle swarm optimization and Voronoi diagram,” In International Conference on Networking, Sensing and Control (ICNSC'09), pp. 602-607, IEEE, March 2009. J. Wang, and N. Zhong, “Minimum-cost sensor arrangement for achieving wanted coverage lifetime,” International Journal of Sensor Networks, 3(3), 165-174, 2008. H. M. Ammari and S.K. Das, “A Study of k-coverage and measures of connectivity in 3D wireless sensor networks,” IEEE Transactions on Computers, 59(2):243-257, 2010.