Generalizing Biased Backpressure Routing and Scheduling to Wireless Multi-hop Networks with Advanced Air-interfaces

TL;DR

This paper generalizes biased backpressure routing to wireless multi-hop networks with advanced air-interfaces by introducing a MaxU link-sharing commodity selection and an attributed capacity hypergraph (ACH) to extend MaxWeight scheduling to MIMO. The proposed LGS-MIMO scheduler performs distributed, transceiver-level scheduling while incorporating backlog reassignment to prevent detours and looping. Theoretical analysis shows MaxU SP-BP dominates classic SP-BP in the network capacity region, and numerical experiments demonstrate mitigated last-packet problems and improved resource utilization, especially under mixed streaming and bursty traffic in both SISO and MIMO contexts. The results imply substantial practical benefits for throughput, latency, and bandwidth utilization in next-generation wireless networks with SDMA/TDMA and multi-modal interfaces.

Abstract

Backpressure (BP) routing and scheduling is a well-established resource allocation method for wireless multi-hop networks, known for its fully distributed operations and proven maximum queue stability. Recent advances in shortest path-biased BP routing (SP-BP) mitigate shortcomings such as slow startup and random walk, but exclusive link-level commodity selection still suffers from the last-packet problem and bandwidth underutilization. Moreover, classic BP routing implicitly assumes single-input-single-output (SISO) transceivers, which can lead to the same packets being scheduled on multiple outgoing links for multiple-input-multiple-output (MIMO) transceivers, causing detouring and looping in MIMO networks. In this paper, we revisit the foundational Lyapunov drift theory underlying BP routing and demonstrate that exclusive commodity selection is unnecessary, and instead propose a Max-Utility link-sharing method. Additionally, we generalize MaxWeight scheduling to MIMO networks by introducing attributed capacity hypergraphs (ACH), an extension of traditional conflict graphs for SISO networks, and by incorporating backlog reassignment into scheduling iterations to prevent redundant packet routing. Numerical evaluations show that our approach substantially mitigates the last-packet problem in state-of-the-art (SOTA) SP-BP under lightweight traffic, and slightly expands the network capacity region for heavier traffic.

Figures (6)

• Figure 1: A mini example of commodity selection and link utility calculation with three devices and three commodities.
• Figure 2: (a) A MIMO ad-hoc network, (b) its capacity hypergraph after internal contention and before OTA contention, along with the maximal numbers of outgoing and incoming links of each device listed. (c) A local capacity hypergraph on device A in distributed scheduling.
• Figure 3: Average throughput per flow versus flow rate $\lambda$ in networks of 100 nodes. All flows are streaming at identical arrival rate.
• Figure 4: Results on networks of 20-110 nodes with MIMO and TDMA for $T=1000$: (a) Average end-to-end delay of delivered packets, (b) Average packet delivery ratio at the end of simulation. The bands indicate $95\%$ confidence interval. There are $0.4|\ccalV|$ commodities, flow rate $\lambda_c\in\mathbbm{U}(0.1,1)$. At a probability of $0.5$, a flow can be configured with streaming traffic or bursty traffic lasting $30$ time slots with a random start time $\mathbbm{U}(0,T-100)$.
• Figure 5: Latency weighted by delivery ratio (Latency $\times$ delivery ratio + $T$($1-$ delivery ratio)) in networks of 20-110 nodes for $T=1000$: (a) Average flows, and (b) $95$ percentile flows (y axis range tripled). The bands indicate $95\%$ confidence interval. Same test configuration as that in Figs. \ref{['fig:mimo']}.

Theorems & Definitions (1)

• Theorem 1