Partial Connectivity of Multi-hop Two-Dimensional Finite Hybrid Wireless Networks

We consider the connectivity of finite two-dimensional wireless networks consisting of a finite number of randomly deployed nodes and sinks at fixed locations. First, we focus on the likelihood that each node is able to convey a message to at least one of the few sinks. We then consider the potential for partial network connectivity under the same configuration. We derive approximate solutions using geometric random graphs theory and evaluate their tightness through stochastic simulation of network realizations. We show the benefits of using more than one sink and provide an approximate formula for the connectivity of such networks. We show how partial connectivity with sinks improves some network metrics at the cost of having a small number of isolated nodes, a situation that would be acceptable, for example, in a large network of redundant sensors.