The delay-optimal number of hops in Poisson multi-hop networks

We study the delay and throughput in a wireless multihop network with sources that form a Poisson point process and relays which are placed equidistantly on the source-destination line. A combined TDMA/ALOHA MAC protocol with intra-route TDMA and inter-route ALOHA is employed. We give bounds on the delay-optimal number of hops and derive the asymptotic delay-throughput tradeoff as the source-destination distance R gets large. The delay includes both the service times and waiting times in the buffers of the typical route. One main finding is that when the transmission probability and number of hops are jointly optimized for minimum delay, the number of hops scales as R
^2/3
while the delay scales as R
^4over3
.