Throughput-Delay Trade-off for Hierarchical Cooperation in Ad Hoc Wireless Networks

Hierarchical cooperation has recently been shown to achieve better throughput scaling than classical multihop schemes under certain assumptions on the channel model in static wireless networks. However, the end-to-end delay of this scheme turns out to be significantly larger than those of multihop schemes. A modification of the scheme is proposed here that achieves a throughput-delay trade-off $D(n)=(\log n)^2 T(n)$ for T(n) between $\Theta(\sqrt{n}/\log n)$ and $\Theta(n/\log n)$, where D(n) and T(n) are respectively the average delay per bit and the aggregate throughput in a network of n nodes. This trade-off complements the previous results of El Gamal et al., which show that the throughput-delay trade-off for multihop schemes is given by D(n)=T(n) where T(n) lies between $\Theta(1)$ and $\Theta(\sqrt{n})$. Meanwhile, the present paper considers the network multiple-access problem, which may be of interest in its own right.