Connectivity in obstructed wireless networks: from geometry to percolation

In this work, we analyze an alternative model for obstructed wireless networks. The model is based on a grid structure of one-dimensional street segments and two-dimensional street intersections. This structure provides a realistic representation of a variety of network scenarios with obstacles and, at the same time, allows a simple enough analysis, which is partly based on percolation theory and partly based on geometric properties. We propose three different ways of modeling the geometric part of the network and derive analytical bounds for the connectivity probability and the critical transmission range for connectivity in the network. Finally, we present extensive simulations that demonstrate that our analytical results provide good approximations, especially for high density scenarios.