# A Statistical Performance Analysis of Named Data Ultra Dense Networks

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## Abstract

**:**

## 1. Introduction

- We present a four-way factorial design method, which is applied to generate the dataset, including various network parameters, in the ndnSIM simulator.
- We provide a background and overview of the different statistical analysis methods that can be used to evaluate or enhance the interest satisfaction rate (ISR).
- We evaluate various network parameters based on mean plots and interaction plots and use multiple comparison tests to analyze how the main effects and interaction effects influence the ISR.
- We select an adequate multiple linear regression (MLR) model to fit the ISR based on both the Akaike information criterion (AIC) [19] and the coefficient of determination ${R}^{2}$. A network may achieve a higher ISR in the final model.

## 2. Motivation: Ultra-Dense Network

- (1)
- Radio frequency (RF) coverage: The RF coverage must be the same throughout the stadium so that the users are not affected by signal fading due to signal attenuation and obstacles.
- (2)
- Multimedia support: The stadium network must support all service types, such as audio or video streaming [20].
- (3)
- Real-time and reliable connection: The stadium network should support a real-time and extremely reliable connection so that a cooperative and intelligent communication system can handle emergency scenarios in such a crowded area.
- (4)
- Hands-off management: Users in the stadium may be mobile and may change their position very often, mainly if they are outside the bowl area. Therefore, reliable hands-off strategies should be established in these areas to avoid intermittent connectivity.
- (5)
- Interference management: Interference may occur in the stadium due to the deployment of multiple wireless access points (WAP) inside and outside the stadium. Minimizing interference may increase network capacity and throughput.
- (6)
- Edge computing: A stadium network must be facilitated with the emerging technology of edge computing. Edge computing offers cloud resources closer to the end-users, thereby improving the latency requirements and reducing the backhaul traffic on cloud devices [21].
- (7)
- Bottleneck mitigation: Ultra-dense networks with single edge computing devices are cost efficient. However, bottleneck or congestion may occur [22], since many WAPs may frequently and directly access the information from the edge node, as shown in Figure 2. Therefore, a stadium network must be capable of coping with such situations to give better services to its end users.

## 3. Simulations and Dataset Generation

#### 3.1. Simulation Environment

#### 3.1.1. Phase 1: Predictors Selection

#### 3.1.2. Phase 2: Dataset Generation

#### 3.2. Four-Way Factorial Design

_{k}levels, then the size of the experiment is given by N as in Equation (2).

## 4. Statistical Methods

#### 4.1. Multiple Linear Regression

#### 4.2. Akaike Information Criterion

#### 4.3. Main and Interaction Effects

#### 4.4. Multiple Comparison Test

## 5. Results

#### 5.1. Main Effect

#### 5.2. Interaction Effects

#### 5.3. Model Selection

#### 5.3.1. Initial Model

#### 5.3.2. Step AIC

#### 5.3.3. Model with Categorical NN

#### 5.3.4. Final Model

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Named data networking (NDN) communication process. CS, content store; PIT, pending interest table; FIB, forwarding information base.

**Figure 3.**Network topologies: (

**a**) 3 wireless access points, (

**b**) 9 wireless access points, (

**c**) 15 wireless access points, and (

**d**) 21 wireless access points

**Figure 4.**Mean plot for the main effect: (

**a**) ISR as a function of the number of interest (NI), (

**b**) ISR as a function of number of nodes (NN), (

**c**) ISR as a function of router bandwidth (RB), and (

**d**) ISR as a function of router delay (RD).

**Figure 5.**Interaction effect plots: (

**a**) NN vs. NI, (

**b**) NN vs. RB, (

**c**) NN vs. RD, (

**d**) NI vs. RB, (

**e**) NI vs. RD, and (

**f**) RB vs. RD.

**Figure 6.**Residuals plots: (

**a**) residuals vs. leverage, (

**b**) NN residuals, (

**c**) NI residuals, and (

**d**) log(RB) residuals.

Factors | Levels |
---|---|

Number of Interests (NI) | 250, 500, 750, 1000 |

Number of Nodes (NN) | 9, 25, 41, 49 |

Router Bandwidth in Mbps (RB) | 1, 5, 10, 20 |

Router Delay in ms (RD) | 10, 50, 100, 200 |

Levels | 250–500 | 250–750 | 250–1000 | 500–750 | 500–1000 | 750–1000 | |

NI | p-values | 0 | 0 | 0 | 8 × 10${}^{-7}$ | 0 | 1 × 10${}^{-7}$ |

estimates | −18.01813 | −28.85063 | −40.51750 | −10.83250 | −22.49938 | −11.66688 | |

Levels | 9–25 | 9–41 | 9–49 | 25–41 | 25–49 | 41–49 | |

NN | p-values | 0.0000134 | 0.0000029 | 0.0000003 | 0.9881607 | 0.8683795 | 0.9706484 |

estimates | −9.6742188 | −10.3223438 | −11.2096875 | −0.6481250 | −1.5354687 | −0.8873437 | |

Levels | 1–5 | 1–10 | 1–20 | 5–10 | 5–20 | 10–20 | |

RB | p-values | 0 | 0 | 0 | 0 | 0 | 0 |

estimates | 34.59859 | 57.21875 | 82.51203 | 22.62016 | 47.91344 | 25.29328 | |

Levels | 10–50 | 10–100 | 10–200 | 50–100 | 50–200 | 100–200 | |

RD | p-values | 0.9995204 | 0.9997671 | 0.9952438 | 0.9999952 | 0.9992516 | 0.9987582 |

estimates | −0.2200000 | −0.1728125 | −0.4753125 | 0.0471875 | −0.2553125 | −0.3025000 |

Estimate | Std. Error | t-Value | Pr (>| t |) | |
---|---|---|---|---|

(Intercept) | 5.104 × 10${}^{1}$ | 7.348 × 10${}^{0}$ | 6.946 | 3.36 × 10${}^{-11}$ *** |

NN | −6.763 × 10${}^{-2}$ | 1.796 × 10${}^{-1}$ | −0.377 | 0.707 |

NI | −4.744 × 10${}^{-2}$ | 9.360 × 10${}^{-3}$ | −5.068 | 7.93 × 10${}^{-7}$ *** |

RD | −4.195 × 10${}^{-3}$ | 4.372 × 10${}^{-2}$ | −0.096 | 0.924 |

RB | 4.402 × 10${}^{0}$ | 4.372 × 10${}^{-1}$ | 10.069 | <2 × 10${}^{-16}$ *** |

NN:NI | −1.716 × 10${}^{-4}$ | 2.117 × 10${}^{-4}$ | −0.810 | 0.419 |

NN:RD | −2.298 × 10${}^{-4}$ | 8.328 × 10${}^{-4}$ | −0.276 | 0.783 |

NN:RB | −7.338 × 10${}^{-3}$ | 8.328 × 10${}^{-3}$ | −0.881 | 0.379 |

NI:RD | 1.281 × 10${}^{-5}$ | 4.577 × 10${}^{-5}$ | 0.280 | 0.780 |

NI:RB | −1.501 × 10${}^{-4}$ | 4.577 × 10${}^{-4}$ | −0.328 | 0.743 |

RD:RB | 1.194 × 10${}^{-4}$ | 1.800 × 10${}^{-3}$ | 0.066 | 0.947 |

Estimate | Std. Error | t-Value | Pr (>| t |) | |
---|---|---|---|---|

(Intercept) | 56.879840 | 3.074145 | 18.503 | <2 × 10${}^{-16}$ *** |

NN | −0.261602 | 0.058563 | −4.467 | 1.2 × 10${}^{-5}$ *** |

NI | −0.052954 | 0.003219 | −16.452 | <2 × 10${}^{-16}$ *** |

RB | 4.091370 | 0.126599 | 32.317 | <2 × 10${}^{-16}$ *** |

Estimate | Std. Error | t-value | Pr (>| t |) | |
---|---|---|---|---|

(Intercept) | 46.677446 | 2.535294 | 18.411 | <2 × 10${}^{-16}$ *** |

factor(newNN)1 | −10.402083 | 1.732878 | −6.003 | 6.72 × 10${}^{-9}$ *** |

NI | −0.052954 | 0.002685 | −19.725 | <2 × 10${}^{-16}$ *** |

log(RB) | 27.051692 | 0.675387 | 40.054 | <2 × 10${}^{-16}$ *** |

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**MDPI and ACS Style**

Rehman, M.A.U.; Kim, D.; Choi, K.; Ullah, R.; Kim, B.S.
A Statistical Performance Analysis of Named Data Ultra Dense Networks. *Appl. Sci.* **2019**, *9*, 3714.
https://doi.org/10.3390/app9183714

**AMA Style**

Rehman MAU, Kim D, Choi K, Ullah R, Kim BS.
A Statistical Performance Analysis of Named Data Ultra Dense Networks. *Applied Sciences*. 2019; 9(18):3714.
https://doi.org/10.3390/app9183714

**Chicago/Turabian Style**

Rehman, Muhammad Atif Ur, Donghak Kim, Kyungmee Choi, Rehmat Ullah, and Byung Seo Kim.
2019. "A Statistical Performance Analysis of Named Data Ultra Dense Networks" *Applied Sciences* 9, no. 18: 3714.
https://doi.org/10.3390/app9183714