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Energy-Efficient Decentralized Broadcasting in Wireless Multi-Hop Networks^{ †}

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## Abstract

**:**

## 1. Introduction

- We present BTP, a practical protocol that approximates a game-theoretical model for constructing an energy-minimal broadcast tree while preserving both its convergence and Nash Equilibrium properties. To the best of our knowledge, BTP is the first protocol for energy-efficient data dissemination in wireless multi-hop networks based on a provably optimal game-theoretical model that is implemented on real hardware.
- We design and implement a discovery mechanism that allows the nodes in a wireless multi-hop network to construct a broadcast tree in a decentralized fashion using locally available information from their direct neighbors.
- We change the decision strategy of the algorithm from a weakly dominant strategy to a strictly dominant strategy to avoid ping-pong effects, in which a node may potentially continue changing its decision without further reducing the transmission power.
- We implement and evaluate three different algorithms for inhibiting graph cycles. Specifically, (1) the Path-to-Source algorithm avoids cycles by letting each node keep track of the path from the root to itself so that each node can check the consistency of the spanning tree when making decisions. (2) The Mutex algorithm avoids cycles by letting each node lock its sub-tree when connecting to a different parent node, ensuring consistency at all times. (3) The Ping-to-Source algorithm allows for cycles temporarily, but it detects and resolves such cycles immediately.
- We evaluate BTP using different tools to assess its feasibility under various conditions. First, we use Matlab simulations to compare BTP against approaches from the literature. Second, we perform NS-3 simulations to investigate the scalability of BTP. Third, we present a real-world implementation of BTP, that is evaluated on a testbed of 75 Raspberry Pis deployed in one of our university buildings to explore its practical feasibility. The evaluations show that BTP can achieve an energy reduction of up to 90% in real-world experiments compared to a simple broadcast protocol.
- The code of the NS-3 implementation and the real-world implementation has been released under a permissive open-source license. Furthermore, all code required to reproduce the experiments as well as the experimental artifacts are also been made available.

## 2. Related Work

## 3. System Model

#### 3.1. Graph Representation

#### 3.2. Transmission Power Model

## 4. Broadcast Tree Protocol

#### 4.1. Potential Game

#### 4.1.1. Design of the Potential Game

#### 4.1.2. Approximation of the Potential Game

#### 4.2. BTP

#### 4.2.1. Broadcast Tree Construction Phase

- ${p}_{{Q}_{j}}\left({C}_{{Q}_{j}}\right)$, i.e., the transmission power of ${Q}_{j}$ needed to reach all its children;
- ${p}_{{Q}_{j}}({C}_{{Q}_{j}}\setminus \left\{j\right\})$, i.e., the transmission power of ${Q}_{j}$ if j is no longer ${Q}_{j}$’s child;
- ${p}_{i}\left({C}_{i}\right)$, i.e., the transmission power of i needed to reach all its current children;
- ${p}_{i}({C}_{i}\cup j)$, i.e., the transmission power of i if j becomes i’s child.

- Path-to-Source

- Mutex

- Ping-to-Source

#### 4.2.2. Data Dissemination Phase

#### 4.3. Protocol Packets

- Neighbor Discovery

- Child Request

- Child Confirmation

- Child Rejection

- Child Revocation

- End of Construction

- Application Data

## 5. Matlab Simulation

#### 5.1. Experimental Setup for the Matlab Simulation

- Dijkstra

- BIP

- BIPSW

- PCP

- BPG

- SBP

#### 5.2. Results of the Matlab Simulation

## 6. NS-3 Simulation

#### 6.1. Experimental Setup for the NS-3 Simulation

#### 6.2. Results of the NS-3 Simulation

#### 6.2.1. Total Energy Consumption

#### 6.2.2. Protocol Overhead

#### 6.2.3. Time for Broadcast Tree Construction Phase

#### 6.2.4. Cycle Handling

#### 6.2.5. Unconnected Nodes

## 7. Real-World Implementation

`0x88DF`) and enable the reception of BTP packets in userland. Addressing was handled on the Link Layer, with each node identified according to its Wi-Fi MAC address. Neighbour Discovery packets and Application Data packets were sent as MAC-broadcasts; all other packets were unicasts.

#### 7.1. Testbed

#### 7.2. Experimental Setup for the Real-World Implementation

#### 7.3. Results of the Real-World Implementation

#### 7.3.1. Total Energy Consumption

#### 7.3.2. Energy Consumption for Tree Construction and Data Dissemination

#### 7.3.3. Successful Receptions

#### 7.3.4. Time for Broadcast Tree Construction Phase

#### 7.3.5. Contributions of Individual Nodes

## 8. Conclusions

#### 8.1. Contributions

#### 8.2. Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Notation | Description | Notation | Description |
---|---|---|---|

T | Broadcast tree consisting of nodes V and edges E | $v\in V$ | A node of the broadcast tree T |

$S\in V$ | Source node of the broadcast tree | $e\in E$ | An edge of the broadcast tree T |

${p}^{max}$ | Maximum possible Tx power | ${p}_{i}$ | Tx power of node $i\in V$ |

$|{h}_{i,j}{|}^{2}$ | Channel gain of $(i,j)\in E$ | ${\sigma}^{2}$ | Noise power |

${\gamma}_{j}$ | SNR at node j | ${\gamma}^{min}$ | Minimum required SNR |

${C}_{i}$ | All children of node $i\in V$ | ${N}_{k}$ | All neighbours of node $k\in V$ |

${p}_{i,j}$ | Tx power that node $i\in V$ must use to reach node $j\in V$ | ${p}_{i}\left({C}_{i}\right)$ | Tx power that node $i\in V$ must use to reach all its children ${C}_{i}$ |

p | Sum of Tx powers of all nodes in V | ||

$\mathcal{G}$ | Potential game | $\mathcal{P}$ | Set of rational players $V\setminus \left\{S\right\}$ |

${a}_{j}^{\left(t\right)}$ | Selected parent of destination node j at iteration t | ${\mathbf{a}}^{\left(t\right)}$ | Action profile at iteration t |

${\phi}_{j}\left({a}_{j}^{\left(t\right)}\right)$ | Cost function of destination node j for action ${a}_{j}^{\left(t\right)}$ at iteration t | ${\mathcal{A}}_{j}^{\left(t\right)}$ | Set of possible actions (parents) for node j at iteration t |

Parameter | Values |
---|---|

Protocols | BTP, BPG, BIP, BIPSW, PCP, SBP, Dijkstra |

Nodes | 10, 20, 30, 40, 50, 60, 70, 80, 90 |

Simulation Area | 500 m × 500 m |

${p}^{max}$ | 20 dBm |

$|{h}_{i,j}{|}^{2}$ | $\frac{1}{{d}^{\alpha}}$ |

$\alpha $ | 3 |

${\gamma}^{min}$ | 10 |

${\sigma}^{2}$ | −90 dBm |

Finishing Threshold | 10 |

Parameter | Values |
---|---|

Protocols | BTP, SBP |

Cycle Handling | Ping-to-Source, Path-to-Source, Mutex |

Nodes | 50, 100, 150, 200, 250, 300 |

Simulation Area | (1) 100 m × 100 m, (2) 200 m × 200 m, (3) 300 m × 300 m, (4) 400 m × 400 m, (5) 500 m × 500 m |

Data Size | 1 KiB |

Finishing Threshold | 10 |

Runs | 30 |

Parameter | Values |
---|---|

Source Nodes | 3 |

Data Sizes | 1 KiB, 4 KiB, 16 KiB |

Finishing Threshold | 5, 15, 25 |

Protocols | BTP, SBP |

Runs | 5 |

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## Share and Cite

**MDPI and ACS Style**

Sterz, A.; Klose, R.; Sommer, M.; Höchst, J.; Link, J.; Simon, B.; Klein, A.; Hollick, M.; Freisleben, B.
Energy-Efficient Decentralized Broadcasting in Wireless Multi-Hop Networks. *Sensors* **2023**, *23*, 7419.
https://doi.org/10.3390/s23177419

**AMA Style**

Sterz A, Klose R, Sommer M, Höchst J, Link J, Simon B, Klein A, Hollick M, Freisleben B.
Energy-Efficient Decentralized Broadcasting in Wireless Multi-Hop Networks. *Sensors*. 2023; 23(17):7419.
https://doi.org/10.3390/s23177419

**Chicago/Turabian Style**

Sterz, Artur, Robin Klose, Markus Sommer, Jonas Höchst, Jakob Link, Bernd Simon, Anja Klein, Matthias Hollick, and Bernd Freisleben.
2023. "Energy-Efficient Decentralized Broadcasting in Wireless Multi-Hop Networks" *Sensors* 23, no. 17: 7419.
https://doi.org/10.3390/s23177419