Empirical Connectivity for Mobile Ad Hoc Networks under Square and Rectangular Covering Scenarios

In the mobile ad hoc networks (MANET), one basic problem is that some nodes are unable to communicate with certain nodes because they are disconnected at the graph level even when a strong routing protocol has been imposed. Thus, connectivity is an important factor affecting the performance of MANETs. The connectivity is related to many factors of the MANET scenario. In this paper, we investigate how the connectivity is related to the region of interest, the number of nodes, and the transmission radius of the nodes. Firstly, we propose the modeling of the MANET connectivity problem for rectangular and square covering scenarios. From these models and associated empirical rules, we present schemes to normalize these two scenarios. We also propose to use second-order polynomial equations for modeling different connectivity levels. The coefficients of these equations are explicitly estimated by the least-square method. Applications of these equations to solve typical connectivity-related problems are discussed. Finally, the precisions of these equations for estimating connectivity are evaluated, which show that the proposed empirical rules are practical and useful. These empirical rules are proposed as simple guidelines for deploying MANETs and sensor networks