Link-Sharing Backpressure Routing In Wireless Multi-Hop Networks

Backpressure (BP) routing and scheduling is an established resource allocation method for wireless multi-hop networks, noted for its fully distributed operation and maximum queue stability. Recent advances in shortest path-biased BP routing (SP-BP) mitigate shortcomings such as slow startup and random walks, yet exclusive link-level commodity selection still causes last-packet problem and bandwidth underutilization. By revisiting the Lyapunov drift theory underlying BP, we show that the legacy exclusive commodity selection is unnecessary, and propose a Maximum Utility (MaxU) link-sharing method to expand its performance envelope without increasing control message overhead. Numerical results show that MaxU SP-BP substantially mitigates the last-packet problem and slightly expands the network capacity region.

💡 Research Summary

This paper addresses a fundamental limitation in Backpressure (BP) routing for wireless multi-hop networks by proposing a novel link-sharing approach called Maximum Utility (MaxU) selection, integrated into the state-of-the-art Shortest Path-biased BP (SP-BP) framework.

BP routing is renowned for its distributed operation and throughput optimality, guaranteeing maximum network stability within its capacity region. While SP-BP mitigates traditional BP issues like slow startup and random walks through queue-agnostic shortest-path biases, it inherits the “last-packet problem” (LPP) and bandwidth underutilization. These stem from the legacy “exclusive commodity selection” rule, where a wireless link can serve packets for only one destination (commodity) per time slot. This causes short-lived, bursty traffic flows to be starved when they lack sustained queue pressure and fails to fully utilize high-bandwidth links.

The authors’ key insight comes from revisiting the Lyapunov drift minimization problem that underpins BP’s theoretical optimality. They demonstrate that the constraint enforcing exclusive per-link commodity selection is stricter than necessary to maintain queue stability. By relaxing this constraint, multiple commodities can share a link’s capacity within a single time slot.

The proposed MaxU SP-BP algorithm operates in four steps per time slot: (1) On each link, filter commodities that have positive backpressure and available packets. (2) Sort these commodities in descending order of their backpressure value. Assign the full link rate to the top-ranked (optimal) commodity first. Then, sequentially allocate any remaining link capacity to the next commodities in the sorted list. This is the core “link-sharing” mechanism. (3) Calculate a “link utility” as the weighted sum of the allocated packets for all commodities on that link, using backpressure as the weight. Then, execute MaxWeight scheduling (e.g., solving a Maximum Weighted Independent Set problem on the conflict graph) based on these link utilities to select a non-interfering set of links for activation. (4) Apply the final schedule to transmit the pre-allocated packets.

Theoretically, the paper proves (Theorem 1) that MaxU SP-BP does not shrink the network capacity region of classic SP-BP. Because MaxU always allocates at least as many packets as the exclusive method for the optimal commodity and potentially more for others, the resulting link utilities are always greater than or equal to those under the legacy method. This leads to a weakly dominant performance, preserving the throughput optimality guarantee of SP-BP.

Numerical simulations confirm the advantages. Under identical streaming traffic, MaxU SP-BP achieves slightly higher per-flow throughput than exclusive SP-BP, empirically validating the capacity region expansion. More significantly, under mixed streaming and bursty traffic, MaxU SP-BP substantially reduces the delivery-ratio-weighted latency, especially for bursty flows at light-to-medium loads, effectively mitigating the LPP. It even outperforms a non-BP shortest-path routing baseline in this metric. These benefits are achieved without increasing control message overhead, requiring only a modest O(|C| log |C|) increase in computational complexity due to the sorting operation.

In conclusion, the MaxU link-sharing method successfully expands the practical performance envelope of backpressure routing. It alleviates the last-packet problem and improves bandwidth utilization for diverse traffic patterns while maintaining the algorithm’s desirable theoretical properties and distributed nature, making it a promising enhancement for modern wireless multi-hop networks.