On the properties of one-dimensional infrastructure-based wireless multi-hop networks

Many wireless multi-hop networks are deployed with some infrastructure support. Existing results on ad-hoc networks are inadequate to fully understand the properties of those networks. In this paper, we study the properties of 1-D infrastructure-based multi-hop networks. Specifically, we consider networks with two types of nodes, i.e. ordinary nodes and powerful nodes. Ordinary nodes are i.i.d. and Poissonly distributed in a unit interval. Powerful nodes are arbitrarily distributed within the same unit interval. These powerful nodes are inter-connected via some backbone infrastructure. The network is said to be connected if each ordinary node is connected (possibly through a multi-hop path) to at least one of the powerful nodes. We obtain analytical results for the connectivity probability and the average number of clusters in the network. We also prove for the first time that the optimum powerful node distribution that minimizes the average number of clusters, and maximizes the asymptotic connectivity probability, is to deploy these powerful nodes in an equi-distant fashion. These results are important for the design and deployment of 1-D infrastructure-based networks.