Self-similarity in urban wireless networks: Hyperfractals

We introduce a model of Poisson patterns of fixed and mobile nodes on lines designed for urban wireless networks. The pattern obeys to "Hyperfractal" rules of dimension larger than 2. The hyperfractal pattern is best suitable for capturing the traffic over the streets and highways in a city. We show that the network capacity under ad hoc routing algorithms scales much better than with the classic uniform Poisson shot model. The scaling effect depends on the hyperfractal dimensions. We show this results in two different routing models: nearest neighbor routing with no collision, minimum delay routing model assuming slotted Aloha and signal to interference ratio (SIR) capture condition, power-path loss and Rayleigh fading. The novelty of the model is that, in addition to capturing the irregularity and variability of the node configuration, it exploits self-similarity, a characteristic of urban wireless networks.