An analytical framework with border effects to estimate the connectivity performance of finite multihop networks in shadowing environments

Connectivity is one of the critical performance parameters of wireless multihop networks (WMNs) explored in detail for the last few years. The assumption, a constant communication range (CR) of sensor nodes in all possible paths taken in earlier studies may not be accurate due to many fluctuations in the received signal strength (RSS) caused by the random nature of wireless channels and the presence of obstacles in the communication environment. Studies have also ignored the border effects (BEs), rendering an overestimated and erroneous result on performance parameters. In this study, we formulate an analytical framework considering BEs to investigate and analyze the influence of shadowing environments on minimum node degree distribution (MNDD), node isolation probability (NIP), and κ -connectivity of a WMN deployed in a rectangular-shaped region (RSR). The proposed framework provides closed-form expressions for the MNDD and NIP. Simulation results validate the outcomes obtained through the proposed framework. We observed that the NIP increases and the κ -connectivity degrades severely with the rise in the shadowing effects' standard deviation.