Analytical Models for Probabilistic Detection Coverage and Sink Connectivity in Wireless Sensor Networks

Abstract

To efficiently employ WSNs, not only should the day-to-day operations of WNs be studied and properly engineered, pre-deployment planning and design for sensor placement have been and should be investigated as well. This dissertation derives two mathematical formulae. One mathematical expression is for the expected probabilistic detection coverage, and the other is for the expected degree of sink connectivity for any sensor node (SN) that cannot directly transmit to the sink. This dissertation assumes that the sensing model and the connectivity models are different. The sensing model is Gaussian-like and a function of distance away from the sensor node, while the connectivity model is a binary disk. The two mathematical models derived in this dissertation consider a scenario where a finite number of object-detecting sensors are independently and uniformly distributed at random in a finite 2-D rectangular plane of which a sink is located at the center. With consideration of border effects, the striking accuracy of the formulae was demonstrated by comparing the numerical results from the proposed mathematical models with results from MATLAB simulations of random SN placement in uniform manner in various scenarios. To be exact, the proposed model for the expected probabilistic detection coverage is accurate within about 2.5 percent of the simulation results, while the sink connectivity model, in pragmatic scenarios, is practically exactly the same as the simulation. To efficiently employ WSNs, not only should the day-to-day operations of WNs be studied and properly engineered, pre-deployment planning and design for sensor placement have been and should be investigated as well. This dissertation derives two mathematical formulae. One mathematical expression is for the expected probabilistic detection coverage, and the other is for the expected degree of sink connectivity for any sensor node (SN) that cannot directly transmit to the sink. This dissertation assumes that the sensing model and the connectivity models are different. The sensing model is Gaussian-like and a function of distance away from the sensor node, while the connectivity model is a binary disk. The two mathematical models derived in this dissertation consider a scenario where a finite number of object-detecting sensors are independently and uniformly distributed at random in a finite 2-D rectangular plane of which a sink is located at the center. With consideration of border effects, the striking accuracy of the formulae was demonstrated by comparing the numerical results from the proposed mathematical models with results from MATLAB simulations of random SN placement in uniform manner in various scenarios. To be exact, the proposed model for the expected probabilistic detection coverage is accurate within about 2.5 percent of the simulation results, while the sink connectivity model, in pragmatic scenarios, is practically exactly the same as the simulation. The work in this dissertation can be used to predict the levels of coverage and sink connectivity of random SN placements in uniform manner for a given number of deployed SNs and a given dimension of the 2-D deployment area (DA). It can determine values of related parameters for specific degrees of coverage and sink connectivity using graphs. It is apt for scalability in clustered square WSNs. The model for the expected probabilistic detection coverage is applicable for other sensing models which are functions of the distance between an SN and the object to be detected. When examining both coverage and connectivity together, the dissertation shows that the relationship between coverage and connectivity is not straightforward. Finally, the formulae can be utilized in planning uncoordinated node scheduling schemes, analyzing the fault tolerance of networks in which the sensor nodes independently and randomly die, and optimizing the deployment cost from different sets of a finite number of homogeneous Ns that are uniformly and randomly deployed.