Impact of region-based faults on the connectivity of wireless networks

The last few years have seen considerable interest in the wireless networking research community in analyzing the connectivity of wireless ad-hoc networks formed by a set of nodes distributed in a two dimensional plane (deployment area) with a (i) uniform probability density function and (ii) uniform transmission range. Although several important and interesting results are known in this domain, most of the connectivity studies consider a fault-free scenario where all nodes are available for network formation and do not consider failures among nodes caused by one reason or another. In very few studies where faults are considered, they are usually considered to be random in nature, i.e., the probability of a node failing is independent of its location in the deployment area. However, such fault scenario is inadequate to capture many realistic situations where the faulty nodes are spatially correlated. This is particularly true in combat environment where an enemy bomb can destroy a subset of nodes confined to a region. In this paper we investigate the impact of region-based faults on the connectivity of wireless networks. Through analysis and simulation, we provide results relating the probability of a network being connected as transmission range and the size of fault-region are varied. If d_min(G) denotes the minimum node degree of the network, we provide the analytical expression for P(d_min(G) ≥ k), which represents the probability of the minimum node degree being at least k, for k = 1. Moreover, we compute P(K(G) ≥ k), where K(G) represents the connectivity of the graph G formed by the distribution of nodes in the deployment area and examine the relationship between P(dmin(G) ≥ k) and P(K(G) ≥ k) when k = 1.