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.
['Kostas Stamatiou', 'Martin Haenggi']
Optimal Spatial Reuse in Poisson Multi-Hop Networks