Optimal Spatial Reuse in Poisson Multi-Hop Networks

We consider a wireless multi-hop network with sources that are Poisson distributed and relays which are placed on the source-destination line. Given a combined TDMA/ALOHA MAC protocol, we explore the following question of optimal spatial reuse: Increasing the number of nodes that are simultaneously scheduled to transmit in a route allows nodes to transmit more often. At the same time, it results in an increase of intra-route and inter-route interference, which has a negative impact on the end-to-end delay and throughput. In a regime of large source-destination distances R, we find that it is delay-optimal for either only one node, or a number of nodes that increases linearly in R, to be scheduled in each slot, depending on the ALOHA probability. If the transmission probability is also optimized, we find that maximum spatial reuse is delay-optimal. Scaling laws for the end-to-end delay and throughput are derived in all cases.