Characterization of a Connectivity Measure for Sparse Wireless Multi-hop Networks

The extent to which a wireless multi-hop network is connected is usually measured by the probability that all the nodes form a single connected component. We jind this measure, called connectivity, unsuitable for use with sparse networks since it is not indicative of the actual communication capability of the network, and can be unresponsive to changes in network parameters. An alternate connectivity measure that wejnd useful in sparse networks is the fraction of node pairs in the network that are connected. We call this term reachability and claim that it is more intuitive and expressive than connectivity when dealing with sparse networks. We identify reachability as growing according to the logistic growth model and present a regression model for reachability in terms of number of nodes and normalized transmission range. This can be used by a network designer to estimate the tradeoff between how connected the network is, the number of nodes, the area of operation, and transmission range of nodes.