Optimal scaling of multicommodity flows in wireless ad hoc networks: Beyond the Gupta-Kumar barrier

We establish a tight max-flow min-cut theorem for multicommodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cut-capacity scale as Theta(n2r3(n)/k) for a random choice of k ges Theta(n) source-destination pairs, where r(n) is the communication range in the network. We exploit the fact, that the MCF in a random geometric graph equals the interference-free capacity of an ad-hoc network under the protocol model, to derive scaling laws for interference-constrained network capacity. We generalize all existing results reported to date by showing that the per-commodity capacity of the network scales as Theta(1/r(n)k) for the single-packet reception model suggested by Gupta and Kumar, and as Theta(nr(n)/k) for the multiple-packet reception model suggested by others. More importantly, we show that, if the nodes in the network are capable of multiple-packet transmission and reception, then it is feasible to achieve the optimal scaling of Theta(n2r3(n)/k), despite the presence of interference. This result provides an improvement of Theta(nr2(n)) over the highest achieved capacity reported to date. In stark contrast to the conventional wisdom that has evolved from the Gupta-Kumar results, our results show that the capacity of ad-hoc networks can actually increase with n while the communication range tends to zero!