In wireless networks, where each node transmits independently of other nodes in the network (the ALOHA protocol), the expected delay experienced by a packet until it is successfully received at any other node is known to be infinite for the signal-to-interference-plus-noise-ratio (SINR) model with node locations distributed according to a Poisson point process. Consequently, the information velocity, defined as the limit of the ratio of the distance to the destination and the time taken for a packet to successfully reach the destination over multiple hops, is zero, as the distance tends to infinity. A nearest neighbor distance based power control policy is proposed to show that the expected delay required for a packet to be successfully received at the nearest neighbor can be made finite. Moreover, the information velocity is also shown to be nonzero with the proposed power control policy. The condition under which these results hold does not depend on the intensity of the underlying Poisson point process.
"Achieving nonzero information velocity in wireless networks." Ann. Appl. Probab. 27 (1) 48 - 64, February 2017. https://doi.org/10.1214/16-AAP1196