  To reduce the latency of Backpressure (BP) routing in wireless multi-hop
networks, we propose to enhance the existing shortest path-biased BP (SP-BP)
and sojourn time-based backlog metrics, since they introduce no additional time
step-wise signaling overhead to the basic BP. Rather than relying on
hop-distance, we introduce a new edge-weighted shortest path bias built on the
scheduling duty cycle of wireless links, which can be predicted by a graph
convolutional neural network based on the topology and traffic of wireless
networks. Additionally, we tackle three long-standing challenges associated
with SP-BP: optimal bias scaling, efficient bias maintenance, and integration
of delay awareness. Our proposed solutions inherit the throughput optimality of
the basic BP, as well as its practical advantages of low complexity and fully
distributed implementation. Our approaches rely on common link features and
introduces only a one-time constant overhead to previous SP-BP schemes, or a
one-time overhead linear in the network size to the basic BP. Numerical
experiments show that our solutions can effectively address the major drawbacks
of slow startup, random walk, and the last packet problem in basic BP,
improving the end-to-end delay of existing low-overhead BP algorithms under
various settings of network traffic, interference, and mobility.
