# A Framework for Analyzing Neighbor Discovery Protocols under Non-Ideal Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Framework to Model Deterministic Algorithms

#### 3.1. Disco

#### 3.2. Quorum

#### 3.3. Hello

#### 3.4. Searchlight

#### 3.5. Stochastic Algorithms

#### 3.5.1. Birthday

#### 3.5.2. Random

## 4. Framework Validation

#### 4.1. Simulator Validation under Ideal Conditions

#### 4.2. Analytic Model Validation under Non-Ideal Conditions

## 5. Protocol Comparison under Non-Ideal Conditions

#### 5.1. Duty Cycle vs. Error

#### 5.2. Probability of Coincidence vs. Error

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ND | Neighbor Discovery |

IoT | Internet of Things |

CDF | Cummulative Distribution Function |

MAC | Medium Access Control |

## References

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**Figure 11.**Evaluation of Disco’s analytic model at 10% duty cycle. (

**a**) Analytic model vs. simulations. (

**b**) Error of the analytic model.

**Figure 12.**Evaluation of Quorum’s analytic model at 10% duty cycle. (

**a**) Analytic model vs. simulations. (

**b**) Error of the analytic model.

**Figure 13.**Evaluation of Hello’s analytic model at 10% duty cycle. (

**a**) Analytic model vs. simulations. (

**b**) Error of the analytic model.

**Figure 14.**Evaluation of Searchlight’s analytic model at 10% duty cycle. (

**a**) Analytic model vs. simulations. (

**b**) Error of the analytic model.

**Figure 15.**Evaluation of (

**a**) Random’s and (

**b**) Birthday’s analytic models vs. simulations at 10% duty cycle.

**Figure 16.**Slot where a percentage of discoveries occur given a duty cycle. (

**a**) Ninety-eight percent discoveries, 10% error. (

**b**) Eighty percent discoveries, 10% error. (

**c**) Ninety-eight percent discoveries, 50% error. (

**d**) Eighty percent discoveries, 50% error.

**Figure 17.**Slots required to achieve a percentage of discoveries given a probability of success. (

**a**) Ninety-eight percent of coincidences with 1% duty cycle. (

**b**) Eighty percent of coincidences with 1% duty cycle. (

**c**) Ninety-eight percent of coincidences with 10% duty cycle. (

**d**) Eighty percent of coincidences with 10% duty cycle.

Year | Deterministic | Stochastic | |||
---|---|---|---|---|---|

Quorum-Based | Prime Number-Based | Dynamic Listen Slot | Fixed Listen Slot | ||

1985 | Grid [2] | ||||

1997 | Cyclic [4] | ||||

1998 | Torus [3] | ||||

2001 | Birthday [14] | ||||

2003 | Quorum [22] | ||||

2005 | e-torus [23] | ||||

2008 | f-torus [24] | Disco [8] | |||

2009 | Aloha-like [16] | ||||

2010 | [5] | U-Connect [7] | |||

2011 | [17,25] | ||||

2012 | Searchlight [10] | Aloha-like [15] | |||

2014 | [9] | Blinddate [11] | Hello [13] | [18] | |

2015 | Code-base [6,26] | Todis [27] | Hedis [27] | PSBA [28] | |

2016 | Nihao [12], Q-Connect [29] | Panda [30] | |||

2018 | Panacea [31], Alano [32] | ||||

2020 | PWEND [33] |

Duty Cycle | 10% | 1% |

Random | $p=0.1$ | $p=0.01$ |

Birthday | ${p}_{t}=0.05$, ${p}_{r}=0.05$ | ${p}_{t}=0.005$, ${p}_{r}=0.005$ |

Disco | ${p}_{1}=9$, ${p}_{2}=11$ | ${p}_{1}=99$, ${p}_{2}=101$ |

Quorum | $m=20$ | $m=200$ |

Hello | $\varsigma =15$ | $\varsigma =150$ |

Searchlight | $t=20$ | $t=200$ |

% of Coincidences | Random | Birthday | Disco | Quorum | Hello | Searchlight | |
---|---|---|---|---|---|---|---|

90% | ${P}_{e}=0\%$ | 230 | 460 | 89 | 270 | 205 | 175 |

${P}_{e}=30\%$ | 475 | 960 | 350 | 613 | 760 | 637 | |

[2.06] | [2.08] | [3.93] | [2.27] | [3.7] | [3.64] | ||

${P}_{e}=50\%$ | 921 | 1831 | 795 | 1420 | 1710 | 1468 | |

[4] | [3.98] | [8.93] | [5.25] | [8.34] | [8.38] | ||

98% | ${P}_{e}=0\%$ | 394 | 770 | 96 | 221 | 339 | 195 |

${P}_{e}=30\%$ | 801 | 1589 | 579 | 1278 | 1136 | 1110 | |

[2.03] | [2.06] | [6.03] | [5.78] | [3.35] | [5.69] | ||

${P}_{e}=50\%$ | 1577 | 3126 | 1348 | 2977 | 2626 | 2603 | |

[4] | [4.05] | [14.04] | [13.47] | [7.74] | [13.34] |

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**MDPI and ACS Style**

Camacho-Escoto, J.J.; Lopez-Bolaños, E.; Arana, O.; Gomez, J.
A Framework for Analyzing Neighbor Discovery Protocols under Non-Ideal Conditions. *Sensors* **2021**, *21*, 6822.
https://doi.org/10.3390/s21206822

**AMA Style**

Camacho-Escoto JJ, Lopez-Bolaños E, Arana O, Gomez J.
A Framework for Analyzing Neighbor Discovery Protocols under Non-Ideal Conditions. *Sensors*. 2021; 21(20):6822.
https://doi.org/10.3390/s21206822

**Chicago/Turabian Style**

Camacho-Escoto, Jose Jaime, Eduardo Lopez-Bolaños, Oscar Arana, and Javier Gomez.
2021. "A Framework for Analyzing Neighbor Discovery Protocols under Non-Ideal Conditions" *Sensors* 21, no. 20: 6822.
https://doi.org/10.3390/s21206822