Longest Edge Routing on the Spatial Aloha Graph

The multihop spatial reuse Aloha (MSR-Aloha) protocol was recently introduced by Baccelli et aL, where each transmitter selects the receiver among its feasible next hops that maximizes the forward progress of the head of line packet towards its final destination. They identify the optimal medium access probability (MAP) that maximizes the spatial density of progress, defined as the product of the spatial intensity of attempted transmissions times the average per-hop progress of each packet towards its destination. We propose a variant called longest edge routing where each transmitter selects its longest feasible edge, and then identifies a packet in its backlog whose next hop is the associated receiver. The main contribution of this work (and of Baccelli et aL) is the use of stochastic geometry to identify the optimal MAP and the corresponding optimal spatial density of progress.