Draining time based scheduling algorithm

Distributed scheduling and routing policies that perform well are increasingly being sought for multi-hop wireless infrastructure networks. The state-of-the-art max-pressure algorithms have provably optimal stability properties but in networks with cycles and loops the delay performance can be quite poor at rates that are not very close to the capacity region boundary. We propose a new scheduling and routing policy to try to address this that results in serving the longest queue but routing packets along (dynamic) shortest-path routes. For a two-node relay we prove stability for our policy using fluid limits.