The game-theoretic routing protocol GTRP for 3-D underwater acoustic sensor networks (UASNs) lets each eligible node forward a packet with a Nash-equilibrium probability derived from a forwarding-dilemma game whose participant count is estimated beacon-free from network geometry. Simulations show GTRP beats the virtual-pipeline baselines VBF and HH-VBF in received packets, packet delivery fraction, end-to-end delay, and energy per delivered packet, but consistently loses on packet collisions, because equilibrium forwarding engages more redundant transmitters than the baselines' routing pipe. The source paper's authors explicitly leave collision avoidance and cross-layer design of the protocol as their next research phase.

Background

Underwater acoustic sensor networks (UASNs) are the communication substrate of the Internet of Underwater Things (IoUT): battery-powered sensor nodes deployed throughout a three-dimensional (3-D) ocean volume that exchange data over acoustic links, since radio attenuates too quickly underwater and optical links reach only short ranges. Compared with terrestrial radio networks, the acoustic channel offers very small usable bandwidth, propagation delays roughly five orders of magnitude larger (sound travels at about 1500 m/s), frequency-dependent absorption, multipath, and Doppler effects, and transmissions dominate the nodes' energy budget. These properties make medium access control (MAC — the link-layer discipline deciding when nodes may transmit) and routing far harder than on land: carrier-sense-based contention resolution loses effectiveness over long delays, and every redundant rebroadcast wastes scarce bandwidth and energy.

For 3-D UASNs, a leading routing family is position-based geographic forwarding, exemplified by VBF (Vector-Based Forwarding) and its successor HH-VBF (Hop-by-Hop VBF). In VBF, a packet carries a vector from source to destination, and only nodes inside a virtual 'routing pipe' of fixed radius around that vector may forward; HH-VBF applies the pipe hop by hop, improving robustness in sparse regions. Confining the forwarding set keeps packet collisions (simultaneous transmissions that destroy one another at a receiver) low, but performance is sensitive to the pipe radius, which must be tuned per scenario, and overly restrictive pipes cause forwarding failures (voids) in sparse deployments.

The source paper (Wang, Li, Qi, Zhou, and Wu, IEEE Internet of Things Journal, 2020) proposes GTRP, a game-theoretic routing protocol for 3-D UASNs with three components. First, a forwarding area: a node FF that just forwarded a packet considers a neighbor II eligible only if the distance dIFd_{IF} lies between αR\alpha R and the communication radius RR (where α\alpha is a protocol parameter, set to α=0.1\alpha=0.1 in the paper's experiments) and the angle between the directions F→IF\to I and F→DF\to D (toward the destination DD) is within 90 degrees, so the neighbor makes progress toward the destination. Second, a beacon-free estimate of the number of eligible forwarders: assuming nodes are uniformly distributed in a volume of dimensions L×W×HL\times W\times H, the expected node degree in the forwarding area is NF=2(n−1)πR3(1−α3)/(3LWH)N_F=2(n-1)\pi R^3(1-\alpha^3)/(3LWH), so no periodic neighbor-discovery ('hello') broadcasts are needed. Third, a forwarding-dilemma game: each eligible node independently decides whether to forward; in game-theory terms, every node has the strategy set {forward, not forward} and a payoff structure in which a node that forwards pays a cost vv, while every node enjoys benefit uu (with u=βvu=\beta v, β>1\beta>1) if at least one eligible node forwards. The symmetric Nash equilibrium (the strategy profile in which no player gains by unilaterally deviating) is that each of the NFN_F eligible nodes forwards with probability P=1−β−1/(NF−1)P=1-\beta^{-1/(N_F-1)}, and P=1P=1 when a node is the only eligible forwarder.

In Aqua-Sim (an NS-2-based underwater network simulator) experiments over a 500 m cube with 200-400 nodes and a simple broadcast MAC and physical layer, GTRP delivered more packets, a higher packet delivery fraction (PDF — the ratio of packets received at the destination to packets generated at the source), lower end-to-end delay, and lower energy consumption per received packet than VBF and HH-VBF. However, on the paper's own fifth metric — average collisions, the total number of collisions divided by the number of received packets — GTRP is consistently worse than VBF and HH-VBF across the node-density, node-speed, and packet-sending-interval sweeps, precisely because the equilibrium forwarding probability engages more forwarders than the virtual-pipe restriction of the baselines. Collision reduction was already a recognized goal in 3-D UASN routing before GTRP (e.g., the collision-analysis-based energy-efficient routing protocol of Yang, Ssu, and Yang, 2015), and channel-aware cross-layer routing protocols that use link-quality statistics in relay selection, such as CARP, exist for underwater networks; but neither line has been combined with equilibrium-probability-based geographic forwarding.

Problem Statement

Design and integrate collision-avoidance mechanisms (for example, MAC-layer adaptations, coordinated suppression, or forwarding-timer disciplines) and cross-layer designs (forwarding decisions that exploit MAC/physical-layer state such as local channel load or link signal-to-noise ratio) into the GTRP game-theoretic forwarding framework for 3-D underwater acoustic sensor networks, such that: (1) the average collisions of the resulting protocol — total collisions divided by received packets — are no higher than those of VBF and HH-VBF on the same simulation stack and comparable scenarios, and (2) the protocol preserves GTRP's advantages over these baselines in number of received packets, packet delivery fraction, end-to-end delay, and average energy consumption per received packet.

The forwarding core that must be retained is the analytically grounded, beacon-free equilibrium decision: an eligible node's forwarding probability derived from the forwarding-dilemma game with the estimated participant count (the game model itself may be extended to account for contention, provided the decision rule remains derived from that model rather than an untethered heuristic). A complete answer specifies the full protocol — forwarding-eligibility rules, the modified forwarding probability or suppression/timing rules, any new packet fields, and the MAC/PHY interactions — and validates it by comparative simulation against GTRP, VBF, and HH-VBF under scenario sweeps at least covering node density, node mobility, and traffic rate on a common protocol stack, reporting all five metrics. Any mechanism family may be used, provided it is specified and demonstrated on this framework and comparative setup.

References

  1. Qingwen Wang, Jianghui Li, Qian Qi, Pan Zhou, Dapeng Oliver Wu, 'A Game-Theoretic Routing Protocol for 3-D Underwater Acoustic Sensor Networks', IEEE Internet of Things Journal, vol. 7, no. 10, pp. 9846-9857, 2020. DOI: 10.1109/JIOT.2020.2988503, https://doi.org/10.1109/JIOT.2020.2988503 (open-access copy: https://eprints.soton.ac.uk/441467/)
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