In the last paper, we derive an expression to determine the probability of a sensor with a set of heterogeneous neighbors redundant to the desired FoI coverage ratio. We propose a distributed scheduling protocol to put redundant sensors to sleep but maintain k-coverage of FoI in three-dimensional heterogeneous WSNs.
Overview
Partial coverage refers to the relaxation in QoC that requires only part of the FOI to be covered. It is defined as the ratio of the area covered by the sensors to the total area of the field.
Motivation of the Research Work
In most cases, the sensors are placed directly in the FoI to be monitored. In applications where sensors cannot be placed directly in the FoI, the existing literature is not useful for calculating the number of sensors needed to provide the desired coverage and connectivity.
Contributions of the Thesis
For such 3D heterogeneous directional WSNs, we derive the expected value of thek-coverage of 3D FoI. We derive an expression to evaluate the expected degree of sensor redundancy and use it to determine whether a sensor is redundant for a desired FoI coverage ratio.
Organisation of the Thesis
The remainder of this chapter contains state-of-the-art work on coverage and connectivity issues in WSNs. The main components of the physical sensor architecture can be classified into four main units: processing, storage, communication and sensing.
Wireless Sensor Networks Operating Systems
Wireless Sensor Networks Simulators
It has an object-oriented design that allows easy creation and use of the new protocols. Therefore, the network nodes that a given entity represents are determined by the physical position of the nodes.
Wireless Sensor Networks Testbeds
Coverage and Connectivity problems
Type of Coverage
Coverage and Connectivity Problems
Although the work in [6] considers sensor heterogeneity for the coverage and connectivity problem. The low-cost coverage and connectivity problem can be defined as follows: Given a WSN and an FOI, estimate the CSD that provides the desired level of coverage and connectivity.
Introduction
Due to the boundary effects, the sensors near the boundary of the FoI cover a smaller area than the sensors located deep within the FoI. In section 3.3 we arbitrarily derive the expected value of the effective detection area of a sensor, taking into account the boundary effects.
Related Work
Through numerical evaluation and simulation, we validate the analysis and demonstrate the importance of boundary effects and the geometry of the FoI on the estimation of the sensor density. However, the analysis only considers the perimeter and the area of the FoI and not the exact geometry of the FoI.
Estimation of the Effective Sensing Area
- Area of the FoI and the boundary region
- Definition of the effective sensing area
- Effective sensing area near boundary
- Expected value of the effective sensing area
The expected value of the effective sensing area of a sensor in the region Dk,3 is obtained by simply integrating. The expected value of the effective sensing area of a sensor located anywhere in Dk,4 can be obtained by Eq.
Critical Sensor Density for Partial Coverage
The expected FOI coverage ratio is calculated as the ratio of the number of successful tests to the total number of tests performed. It can be noted that the expected FOI coverage ratio is estimated using Eq.
Numerical Results
We create a rectangular boundary over the FoI and calculate the required number of sensors for the given coverage ratio as shown in Fig. It can be seen that the required sensors estimated with our analysis are always lower than that obtained using a rectangular boundary over the FoI.
Conclusion
In most of these studies, sensors are placed directly on the FoI to be monitored. In this work, we consider a deployment scenario in which sensors are randomly deployed outside the FoI to be monitored.
Preliminaries
We estimate the expected values of the effective sensing range and communication range for a sensor located outside the FoI near the boundary. We demonstrate the utility of the analysis in estimating the minimum number of sensors required for a desired level of coverage and connectivity.
Analysis of the k-Coverage with Boundary Deployment
The expected value of the effective sensor area when a sensor extends to Ω can be obtained simply by integrating Eq. The expected value of the effective sensing area for s∈Ω can be obtained simply by integrating Eq.
Analysis of Connectivity with Boundary Deployment
The expected value of the effective communication area when a sensor is in the boundary region Ω can be obtained by simply Eq. The expected value of the effective communication area in this case is obtained by Eq.
Minimum Number of Sensors
Numerical Results
Impact of border region area: First, we calculate the number of sensors required for k-coverage and connectivity as the area of Ω changes. As the area of the border region increases, a greater number of sensors are required to maintain the desired level of coverage and connectivity.
Effect of irregular sensing and communication model
We apply the DoI model and evaluate Lemma 4.1 and Lemma 4.2 numerically under the irregular sensing and communication (ISC) model. This is because the ISC models lead to a reduction in the effective coverage and communication ranges.
Application of the Analysis
Overview of TINet
The output of the sensor is connected to the analog-to-digital converter of the MICAz mod. Due to the limited communication range of the sensors, data collection nodes act as gateway nodes to connect the sensor motes and the base station as shown in Fig. 4.11.
On-Road Experiment
Experimental Results
This indicates that a two-wheeler passed on the left side of the road at time t. The detection of four-wheeled vehicles requires the light to be detected by the sensors on both sides of the road.
Conclusion
This is to verify that the number of sensors required for coverage as calculated from our analysis is correct. The expected values of these were used in estimating the minimum number of sensors required for the desired level of coverage and connectivity.
Introduction
The sensors in a 3D HWSN can be divided into different types based on their sensing range, communication range and/or the probability that they are still alive. We derive an expression to evaluate the expected value of the k-coverage ratio of the 3D FoI.
Related work
They proposed an integrated-concentric-sphere model to analyze both coverage and connectivity in an integrated way. The authors estimated the link probability, node degree and coverage of 3D MANETs assuming random uniform distribution.
Preliminaries
The volume of the communication region of si is nothing but the volume of the communication sphere given by kζik= 43πCi3, where Ci is the communication range. The connection probability m, denoted by γm, is defined as the fraction of deployed sensors in which each sensor is m connected to the network.
Analysis of the k-coverage of the FoI
Validation of the analysis
The simulation results are with a 95% confidence level, although the error bars are not visible in the graphs. Assuming that type 2 sensors are more expensive than type 1 sensors, then instead of placing sensors in a 1:3 ratio, placing them in a 1:1 ratio provides the desired level of coverage with a slightly larger number of sensors. as can be seen from fig.
Numerical Results
Interestingly, the difference in the number of sensors required for a desired coverage ratio k of 0.8 and 0.9 is smaller when only type 2 sensors are used (i.e., n1:n2=0:1) compared to the three cases of others. This is because, as we saw earlier, type 2 sensors have a greater sensitivity range and live fraction.
Analysis of m-connectivity of the 3D HWSN
Validation of the analysis
A Monte Carlo simulation is performed on the simulation results as described in Section 3.4 of Chapter 3.
Numerical Results
This indicates that a higher liveness fraction of the sensors increases the usefulness of sensors for connectivity.
Irregular directional sensing and spherical communication models
We varied the ratio of the number of sensors of each type placed in the 3D FoI (shown as n1 : n2 in the graph). We studied the relationship between 2-coverage and 2-connectivity in terms of the number of sensors in the FoI with the Spherical Sensing and Communication (SSC) model and the ISC model using a 0.05 DoI value.
Application of the Analysis
The algorithm finally returns the number of sensors of each type needed to minimize the network cost and to satisfy the desired k-coverage ratio and m-connectivity. The cost of the network for a given number of sensors of different types is shown in columns 5.
Conclusion
Main Contributions: We derive an expression to quantify the redundancy in the stochastic k-coverage of a point in a 3D FOI. In Section 6.4 we derive the expressions for the probability that a point is redundantly covered and the condition for the redundancy of a sensor in a 3D heterogeneous WSN.
Related work
Motivation: The work in this chapter is motivated by the following limitations noted in the literature. The work in [28, 29] identified whether there are redundant sensors only when the FoI is covered by 1 and the results are not applicable to coverage k.
Preliminaries
If sj is both a sensing neighbor and a communication neighbor of si, then sj is called a sensing and communication neighbor or simply the neighbor of si. Cutting volume: The cutting volume between two spheres centered at p and q with radii r and s, respectively kR(p, r)∩R(q, s)k.
Analysis of the Redundancy of a Sensor for k -coverage
Redundancy in Coverage of a Point
However, for k-coverage of the point, we need to estimate the probability that a point in the detection sphere of si is also covered by at least k neighbors. In general, the probability that q in the detection sphere of si is covered by at least k neighbors can be written as.
Redundancy of a Sensor for k-coverage
Thus, Vk−(kR(si, Si)k −E[ξki]) is the volume of FoI, which is also k-covered without si. Where V0 is the volume of the FoI to be k-covered by the WSN.
Validation of the Analysis
Numerical results for type 1 and k=1 Simulation results for type 1 and k=1 Numerical results for type 2 and k=1 Simulation results for type 2 and k=1. Numerical results for type 1 and k=2 Simulation results for type 1 and k=2 Numerical results for type 2 and k=2 Simulation results for type 2 and k=2.
Sleep Scheduling Protocol for k-coverage
Description of the scheduling protocol
After each round, all sensors become active to participate in the decision phase of the next round. From the information in the neighbor table, each sensor knows the number of neighbors of each type.
Complexity Analysis
Since << N and t×C << N, the space complexity is O(N) which is also near optimal. Since n << N and C << N, the computational complexity is therefore O(N) which is also near optimal.
Performance Evaluation
Next, we studied the effect of FoI volume on the number of active sensors. As expected, without the scheduling protocol, the lifetime of the network is independent of the number of installed sensors, as all sensors remain active.
Practical Considerations
Border effects
Irregular sensing and communication models
We investigated the impact of planning protocol on the number of active sensors in FoI and the k-coverage ratio of FoI with the spherical sensing and communication (SSC) model and ISC model using 0.1 value of DoI, where k = 1.2. This is because the ISC model causes radio irregularity, which reduces the effective area covered by the sensors, while the SSC model ignores this irregularity.
Conclusion
In terms of the coverage ratio (defined in Section 3.1), the partial coverage problem requires that the coverage ratio be no less than a predetermined threshold (less than unity). We propose a scheduling distribution protocol to put redundant sensors to sleep while maintaining partial FOI coverage.
Related work
CCP is a decentralized protocol that configures the network to provide full coverage of the sensor field. Most previous work on the partial coverage problem only applies to homogeneous WSNs and some of them use geographic information in identifying the redundant sensors.
Preliminaries
The degree of redundancy of a type i sensor, denoted by ξi, is defined as the ratio of its sensing area redundantly covered by its neighbors to its total sensing area. Note that this definition is similar to that in [68], except that we use a stronger definition for neighbors, namely SAC neighbors using effective communication range, and only estimate the expected value of the redundancy degree.
Analysis of the Redundancy of a Sensor for Partial Coverage
Redundancy Degree of a Sensor
Now that we can determine the expected value of the sensor range for any sensor. Thus, ηkΨk −(1−E[ξi])kA(si, Si)k is the area of the FoI covered even without the type i sensor.
Validation of the Analysis
The results show that the expected redundancy degree of any sensor increases with the number of neighboring sensors making it a potential candidate to be redundant. 7.3(c) in which both E[ξ1] and E[ξ2] increase sharply with the number of neighbors, because there is a greater number of type 2 sensors among the neighbors compared to the scenario shown in Fig.
Sleep Scheduling Protocol for Partial Coverage
Description of the scheduling protocol
From the information in the neighbor table, each sensor knows the number of neighbors of each type and their status. The first two columns in the table show the number of neighbors of each type, while the third column shows the expected degree of redundancy.
Performance Evaluation
Next, we examine the impact of FoI size on the number of active sensors. 7.8(b) shows that the number of active sensors is the smallest in the proposed protocol, with only type 1 sensors installed.
Conclusion
Wang, “Information coverage in randomly deployed wireless sensor networks,” IEEE Transactions on Wireless Communications, vol. Huang, “On fault-tolerant distributed detection in wireless sensor networks,” IEEE Transactions on Computers , vol.
Illustration of the area coverage in the FoI
Illustration of the target coverage in the FoI
Illustration of the barrier coverage in the FoI
Illustration of a convex polygon shaped FoI with 6 vertices
Illustration of a convex polygon shaped FoI Ψ with 6 vertices
Illustration of the boundary region D of a 6-vertex polygonal FoI being
Illustration of the regions D k,j and effective sensing regions B k,j , for
Illustration of the regions D k,j and effective sensing regions B k,j , for
Parallelogram-shaped FoI
Convex polygon-shaped FoI
Variation in the expected coverage ratio of the FoI for different sensor
Relationship between the sensor density and the perimeter of the FoI
Relationship between the expected coverage ratio and the sensing range
Main components of the architecture of some sensors
A comparison between TinyOS, LiteOS, and Contiki operating system. 12
Results of vehicles counting experiments
Results of vehicle direction detection experiments
Results of vehicle identification experiments
The network cost computed with Algorithm 1
Data stored at a type 1 sensor for 1-coverage of the FoI
Relationship between the number of active sensors and the initial num-
Data stored at a type 1 sensor
Coverage ratio obtained with the protocol
![Figure 3.11 Comparison of the sensor density obtained with Eq. 3.24 and that in [1] for different coverage ratios.](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10497339.0/68.918.181.695.109.341/figure-comparison-sensor-density-obtained-different-coverage-ratios.webp)
