Connectivity at crossroads

Motivated by studies of wireless ad hoc networks in obstructed environments, in this work we focus on the problem of establishing connectivity at an intersection of two roads, or streets, surrounded by obstacles. An instance of the problem is defined by four street segments meeting at an intersection point, a street width, a node density at each street segment and a transmission range of the communication nodes. The problem that we focus on consists in computing the probability that there is a communication path connecting all four intersecting street segments. We propose a simplified model that approximates the connectivity properties in this setting and compute a lower bound for the connectivity probability. We compare our result to a Euclidean Line-of-Sight (LoS) model and show that our model provides an accurate approximation, while greatly simplifying the analytical treatment.