A justification of the fluid network model using stochastic geometry

An important topic in performance evaluation of wireless networks is the modeling of inter-cell interference, to predict the distribution of the Signal to Interference plus Noise Ratio (SINR) in the network. The classical hexagonal model is generally intractable and requires extensive numerical calculations. Two approaches have been shown to produce tractable, closed-form formulas: Poisson networks (the interfering Base Stations (BSs) locations form a Poisson process) and fluid networks (the interfering BSs are replaced by a continuum of infinitesimal interferers). Compared to network measurements, the fluid model is known to be optimistic, while the Poisson model is pessimistic. We show that fluid networks are equivalent to dense Poisson networks. We show a Central Limit Theorem (CLT)-like result: the difference of interference predicted by the two models is Gaussian for dense networks with a known mean and variance. These results provide a justification of the fluid model. Furthermore, there is an interesting duality: for dense networks, all results proven for Poisson networks hold for fluid networks and vice-versa.