On the Capacity of Fractal Wireless Networks With Direct Social Interactions

TL;DR

This paper analyzes the capacity limits of fractal wireless networks with direct social interactions, showing how different communication strategies impact maximum network capacity and comparing results to classical models.

Contribution

It introduces a mathematical model for fractal wireless networks with social interactions and derives capacity bounds under different communication schemes, highlighting significant improvements over classical results.

Findings

Maximum capacity with random contact is Θ(1/√(n log n)).

Capacity with distance-based communication can reach Θ(1/ log n).

Social interaction models significantly enhance network capacity.

Abstract

The capacity of a fractal wireless network with direct social interactions is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution $ P(k) $, and we capture the connection feature between two nodes with degree $ k_{1} $ and $ k_{2} $ by a joint probability distribution $ P(k_{1},k_{2}) $. It is proved that if the source node communicates with one of its direct contacts randomly, the maximum capacity is consistent with the classical result $ \Theta\left(\frac{1}{\sqrt{n\log n}}\right) $ achieved by Kumar \cite{Gupta2000The}. On the other hand, if the two nodes with distance $ d $ communicate according to the probability $ d^{-\beta} $, the maximum capacity can reach up to $ \Theta\left(\frac{1}{\log n}\right) $, which exhibits remarkable improvement compared with the well-known result in \cite{Gupta2000The}.