to the best of our knowledge.
Major Contributions: We derive an expression to quantify the redundancy in stochastic k-coverage of a point in a 3D FoI. We extend the analysis to derive an expression to determine the probability of a sensor, with a set of neighbours of different types, being redundant fork-coverage of the FoI. We propose a distributed scheduling protocol to put the redundant sensors to sleep yet maintaining the desired level of coverage in the FoI. This protocol does not require the sensor to have any information about its geographical location/relative position to discover its redundancy.
The rest of the chapter is organised as follows: In the next section, we briefly discuss the literature on the scheduling protocols for 3D WSNs which also addresses the coverage problem. In Section 6.3 we define the network model, the terms and the notation used. In Section 6.4 we derive the expressions for the probability of a point being redundantly covered and the condition for the redundancy of a sensor in a 3D heterogeneous WSN. We also validate the expressions with numerical evaluation and simulation results. Section 6.5 discusses the proposed simple scheduling protocol which can help a sensor determine if it is redundant based on the information about its neighbours and schedule its activity. Simulation results to demonstrate the benefit of sleep scheduling on the lifetime of a WSN are presented for different network scenarios.
A few practical considerations for the proposed work are discussed in Section 6.6 and the chapter is concluded in Section 6.7.
of the Reuleaux tetrahedron, where each point in a 3D FoI is k-covered. The basic approach is to divide the sensing region of a sensor into twelve equal-sized sectors and if each sector consists of another sensor then it is redundant. The proposed protocol guarantees that the sensing region of each sensor is k-covered. Huang et al. [3] formulated the coverage problem as a decision problem, where the goal is to determine whether each point in a FoI is covered by at least k sensors. The basic idea is to reduce the geometric problem from a 3D space to a 2D space by observing that the FoI is divided into number of regions by the sensing spheres and that the level of coverage of a region can be derived from the spherical segments comprising the same. Furthermore, each spherical segment must be bounded by a number of circular segments, and the level of coverage of a spherical segment can be derived from those circular segments that surround the spherical segment. This transforms the 2D problem into a one-dimensional (1D) problem which implies that it is sufficient to determine the coverage of the circular segment. The authors also proposed a distributed energy-conserving protocol that can reduce the number of sensors in active state and still maintain sufficient coverage eliminating the redundant sensors.
The authors in [29] derived a distributed algorithm to choose a subset of working sensors for full coverage. The authors proposed a backup scheme, where each sensor has a designated substitute set from the sleeping set of sensors. Xiao et al. in [28]
proposed an immune-ant colony coverage control algorithm for energy efficient oper- ation of a 3D WSN. An artificial immune algorithm is used to improve ant colony algorithm to avoid the possibility of a local optimal solution. A deployment strategy was also proposed for the placement of sensors in a 3D FoI. Xiaole et al. [69] stud- ied the problem of constructing connected and full covered optimal 3D WSNs. The authors designed a set of regular patterns for k-connectivity and full coverage, where k = 14,6.
Motivation: The work in this chapter is motivated by the following limitations observed in the literature. The work in [2] derives the necessary conditions to deter- mine if a sensor is redundant but assumed that each sensor has location information.
The use of technology for geolocation is not feasible for low cost and low power 3D WSNs. Without any geographical information, it is usually hard to check if a sen- sor is redundant. Similar limitations also apply to the work in [3, 28, 29] and to the best of our knowledge, none of the previous works can be applied if the sensors do not have their location information. The work in [28, 29] identified if there are redundant sensors only when the FoI is 1-covered and the results are not applicable for k-coverage. 1-coverage of the FoI is not sufficient in certain WSN applications such as military applications where a high degree of reliability is necessary. All the work in the literature so far assumed that the sensors are homogeneous. Though the work in [6] considered the heterogeneity of sensors for the connectivity problem, the results are approximate since, only the sensors with smallest range are considered for the analysis. The assumption of homogeneity is usually hard to maintain in large scale WSNs and there is no work that explicitly addresses the coverage problem in heterogeneous 3D WSNs.
In summary, there is no work in the literature on coverage-preserving scheduling protocols for 3D heterogeneous WSNs that can work with sensors without location information. Considering these limitations in the literature, we propose an approach to identify the sensors redundant for k-coverage of a FoI with the sensors deployed uniformly at random. We also propose a distributed scheduling protocol that does not require geographical information and schedule the redundant sensors to sleep without creating holes in the coverage.