Impact of Region-Based Faults on the Connectivity of Wireless Networks in Log-Normal Shadow Fading Model

The traditional studies on fault-tolerance in networks assume that the faults are random in nature, i.e., the probability of a node failing is independent of its location in the deployment area. However, this assumption is no longer valid if the faults are spatially correlated. In this paper we focus on the study of the impact of region-based faults on wireless networks. Most of the studies on connectivity of wireless networks assume a unit disk graph model, i.e., links exist between two nodes if they are within a circular transmission range of one another. However, the unit disk graph model does not capture wireless communication environment accurately. The log-normal shadow fading model for communication was introduced to overcome the limitations of the unit disk graph model. In this paper we investigate connectivity issues of wireless networks in a log-normal shadow fading environment where the faults are spatially correlated. If d_min(G) denotes the minimum node degree of the network, we provide the analytical expression and method for computing P(d_min(G) ≥ 1) in a region-based fault scenario, where P(d_min(G) ≥ 1) denotes the probability of the minimum node degree being at least 1. Through extensive simulation, we find (P(κG) ≥ 1), where κ(G) represents the connectivity of the graph G formed by the distribution of nodes on a 2D plane and examine the relationship between P(d_min(G) ≥ 1) and P(κ(G) ≥ 1).