Coverage properties of one-dimensional infrastructure-based wireless networks

We consider an infrastructure-based wireless network comprising two types of nodes, namely, relays and sinks. The relay nodes are used to extend the network coverage by providing multi-hop paths to the sink nodes that are connected to a wireline infrastructure. Restricting to the one-dimensional case, our objective is to characterize the fraction of covered region for given densities of sink and relay nodes. We first compare and contrast our infrastructure-based model with the traditional setting, where a point is said to be covered if it simply lies within the range of some node. Then, drawing an analogy between the connected components of the network and the busy periods of an M/D/oc queue, and using renewal theoretic arguments we obtain an explicit expression for the average vacancy (which is the complement of coverage). We also compute an upper bound for vacancy by introducing the notion of left-coverage (i.e., coverage by a node from the left). We prove a lower bound by coupling our model with an independent-disk model, where the sinks' coverage regions are independent and identically distributed. Through numerical work, we study the problem of minimizing network deployment cost subject to a constraint on the average vacancy. We also conduct simulations to understand the properties of a general notion of coverage, obtained by introducing hop-counts into the definition.