Expected Probabilistic Detection and Sink Connectivity in Wireless Sensor Networks

Given that a finite number of object-detecting sensors are independently and uniformly distributed at random in a finite rectangular plane of which a sink is located at the center, we derive two mathematical formulae. One is for the expected detection probability at any arbitrary point, and the other is for the expected degree of sink connectivity for any sensor node that cannot directly transmit to the sink. In this paper, we assume that the sensing model is Gaussian-like and a function of distance away from the sensor node, while the connectivity model is a binary disk. With consideration of border effects, the striking accuracy of our formulae was demonstrated by the result comparisons with simulations in various scenarios. Our work here can be used to predict the levels of coverage and connectivity. It can determine the values of related parameters for specific degrees of coverage and connectivity. When examining both coverage and connectivity together, our work 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 homogeneous SNs.