On the catalyzing effect of randomness on the per-flow throughput in wireless networks

This paper investigates the throughput capacity of a flow crossing a multi-hop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, Heavy-Tailed distributions for both the nodes´ densities and the number of hops. The key contribution is to demonstrate how the per-flow throughput depends on the distribution of 1) the number of nodes N_j inside hops´ interference sets, 2) the number of hops K, and 3) the degree of spatial correlations. The randomness in both N_j´s and K is advantageous, i.e., it can yield larger scalings (as large as Θ(n)) than in non-random settings. An interesting consequence is that the per-flow capacity can exhibit the opposite behavior to the network capacity, which was shown to suffer from a logarithmic decrease in the presence of randomness. In turn, spatial correlations along the end-to-end path are detrimental by a logarithmic term.