Biased Backpressure Routing Using Link Features and Graph Neural Networks

TL;DR

Numerical experiments show that the proposed 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.

Abstract

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.

Figures (7)

• Figure 1: A flow from the red node to the blue node in a wireless multi-hop network with 60 nodes. The width of an edge is $1+\sqrt[3]{n}$, where $n$ is the number of packets sent over that link in 500 time steps; green edges indicate routes ($n>0$). (a) Basic BP routing. (b) Enhanced dynamic BP routing (EDR) neely2005dynamicgeorgiadis2006resource with a pre-defined bias given by a scaled shortest hop distance from a node to the destination.
• Figure 2: System diagram of our GNN-enhanced SP-BP scheme.
• Figure 3: The queue states at four nodes (with hop distance to the destination marked) in an exemplary case of backpressure routing with a single commodity, at time (a) $t$ and (b) $t+1$. An arrow indicates the magnitude and direction of pressure on a link, and its color encodes the choice of the edge weight. All links have an identical $\bar{r}$ rate.
• Figure 4: End-to-end delay of SP-BP routing algorithms as a function of the multiplier of minimum edge weight $\min(\delta_{e})=a\bar{r}$ on networks of $100$ nodes, simulated with unit-disk interference model, long-term link rates $r_{e} \sim \mathbb{U}(10,42)$, total time steps $T=1000$, and $100$ test instances per point. Flow rate $\lambda(f) \sim \mathbb{U}(0.2,1.0)$ for streaming traffic, $\lambda(f) \sim \mathbb{U}(2.0,10.0)$ for bursty traffic when $t<30$.
• Figure 5: Performance of BP algorithms as a function of network size under the unit-disc interference model: (a) end-to-end delay under streaming traffic, (b) end-to-end delay under bursty traffic with low flow rate $\lambda(f) \sim \mathbb{U}({2.0,10.0})$ for $t<30$, (c) end-to-end delay of bursty traffic with high flow rate $\lambda(f) \sim \mathbb{U}({6.6,33.0})$ for $t<30$, and (d) packet delivery rate of bursty traffic with high flow rate. Simulated with long-term link rates $r_{e} \sim \mathbb{U}(10,42)$, total time steps $T=1000$, and all queues are initialized to be empty. $100$ test instances per point (10 random networks $\times$ 10 realizations of random source-destination pairs and link rates). Error band indicates $95\%$ confidence interval.

Theorems & Definitions (6)

• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2
• proof