On the Analysis of Expected Distance between Sensor Nodes and the Base Station in Randomly Deployed WSNs

Abstract

In this study, we focus on the analytical derivation of the expected distance between all sensor nodes and the base station (i.e., E[d _toBS ]) in a randomly deployed WSN. Although similar derivations appear in the related literature, to the best of our knowledge, our derivation, which assumes a particular scenario, has not been formulated before. In this specific scenario, the sensing field is a square-shaped region and the base station is located at some arbitrary distance to one of the edges of the square. Having the knowledge of E[d _toBS ] value is important because E[d _toBS ] provides a network designer with the opportunity to make a decision on whether it is energy-efficient to perform clustering for WSN applications that aim to pursue the clustered architectures. Similarly, a network designer might make use of this expected value during the process of deciding on the modes of communications (i.e., multi-hop or direct communication) after comparing it with the maximum transmission ranges of devices. Last but not least, the use of our derivation is not limited to WSN domain. It can be also exploited in any domain when there is a need for a probabilistic approach to find the average distance between any given number of points which are all assumed to be randomly and uniformly located in any square-shaped region and at a specific point outside this region.