#
Fuzzy Logic and Regression Approaches for Adaptive Sampling of Multimedia Traffic in Wireless Computer Networks^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{©}AIR-AP1852E access points (APs) operating using the IEEE 802.11ac/n Wi-Fi protocol. Cisco

^{©}APs contain four external dual-band antennas. A Cisco

^{©}catalyst 3560-CX switch connected the two APs with a Session Initiation Protocol (SIP) server via 1 Giga bits per second (Gbps) wired links. The specifications of the personal computers (PCs) used in the study were as follows: Intel

^{©}Core i7-3770 processor, 3.40 GHz, 16 GB DDR3 RAM, Microsoft Windows

^{©}7 Enterprise SP1 64 bits, for 802.11ac Linksys

^{©}AC1200 Dual-Band wireless adaptor. There was no encryption activated between the APs and the PCs’ wireless adapters. As the wireless devices were close to each other, the transmission power was kept to 30 mW (15 dBm) [24].

^{©}operating system providing SIP VoIP, using a G711a coder–decoder (CODEC), and RTP was used with a packet size of 160 bytes. The queuing mechanism for all scenarios was First-In-First-Out (FIFO) chosen for its simplicity, and queue size was 50 packets.

#### Network Traffic Parameters

_{i}) was calculated by subtracting the arrival time for the packet (${R}_{i}$) from the sent time (${S}_{i}$) as indicated by Equation (1).

_{i}) was measured by determining the difference between the current packet delay (${D}_{i}$) and the delay for the previous packet (${D}_{i-1}$) as in Equation (2).

_{i}) was measured by determining the total number of received packets ($\sum}{R}_{i}(t)$) and the total number of sent packets ($\sum}{S}_{i}(t)$) at a given time (t), as illustrated in Equation (3).

- Pre- and post-sampling sections: These sections contain the traffic that needs to be sampled. The durations of these sections are kept fixed (predefined) and do not change during the sampling process.
- Inter-section interval (isi): This interval is between the pre- and post-sampling sections. Its duration is adaptively updated by the FIS.
- Regression model: The traffic parameter (i.e., delay, jitter, and percentage packet loss ratio) were represented by an n × n matrix to allow regression analysis, where n is the number of subsections in the pre- and post-sampling sections. Each subsection contained n packets.
- Euclidean distance (ED): ED was used to quantify the extent of traffic variations between the pre- and post-sampling sections.
- Fuzzy inference system: FIS was used to update the duration of the isi based on its current value and the ED measures.

_{1}, s

_{2}, …, s

_{n}), each subsection containing (n − 1) packets as shown in Figure 5; the traffic values of each subsection were represented by a row of matrix P and the associated time period of every subsection was represented by the vector T as indicated in Equation (4).

_{1}pre, S

_{2}pre, S

_{3}pre, and S

_{4}pre for the pre-sampling section and S

_{1}post, S

_{2}post, S

_{3}post, and S

_{4}post for the post-sampling section. Each subsection contained 3 data packets. This was repeated for the pre- and post-sampling sections. The general representation of the traffic matrices for pre- and post-sampling sections is shown in Equation (4).

_{1}, s

_{2}, …, s

_{n}) were represented by t

_{1}, t

_{2}, …, t

_{n}. The vector E = [e

_{1}, e

_{2}, …, e

_{n}] represents the measurement error, assumed to be zero in this study. These durations were measured by subtracting the arrival time of the last packet from the arrival time of first packet in the corresponding subsection. The regression coefficients ${c}_{1},\text{}{c}_{2},\dots {c}_{n}$ were determined by Equation (5).

_{i}and σ

_{i}are the mean and standard deviation of the ith fuzzy set A

_{i}[17].

_{i}and M are the means of the traffic parameters for the original data and its sampled population.

_{0}… a

_{N}] is a set of polynomial coefficients. The polynomial evaluation function examines a polynomial for x values and then produces a curve to fit the data based on the coefficients that were found using the curve fitting function [32,33].

## 3. Results and Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**An illustration of sampling techniques: (

**a**) Nonadaptive sampling; (

**b**) The concept of adaptive sampling [12].

**Figure 7.**Membership functions for (

**a**–

**c**) the Euclidean distance sets for delay, jitter, and percentage packet loss ratio; (

**d**) inter-sampling interval; and (

**e**) the updated inter-sampling interval.

**Figure 8.**Typical results obtained from the developed adaptive technique: (

**a**) FIS output for the inter-sampling interval (isi), (

**b**) the Euclidean distance for delay, (

**c**) original traffic delay, and (

**d**) sampled traffic delay.

**Figure 9.**Typical results obtained from the developed adaptive technique: (

**a**) measured Euclidean distance for jitter, (

**b**) measured Euclidean distance for packet loss, (

**c**) original traffic jitter, (

**d**) sampled traffic percentage jitter, (

**e**) original traffic packet loss ratio, and (

**f**) sampled traffic packet loss ratio.

**Figure 10.**Comparisons of biasness of (

**a**) delay, (

**b**) jitter, and (

**c**) %PLR between the developed technique and nonadaptive methods.

**Figure 11.**Comparisons of RSE of (

**a**) delay, (

**b**) jitter, and (

**c**) PLR between the developed technique and nonadaptive methods.

**Table 1.**Mean and standard deviation of the Gaussian fuzzy sets for inputs (Euclidian delay, Euclidian jitter, and Euclidian %PLR).

Membership Functions | (Mean, Standard Deviation (Std)) for ED Delay, ED Jitter, ED of %PLR |
---|---|

Very low | 0.1, 0 |

Low | 0.1, 0.25 |

Medium | 0.1, 0.5 |

High | 0.1, 0.75 |

Very high | 0.1, 1 |

**Table 2.**Mean and standard deviation of the Gaussian fuzzy sets for the inter-sample interval difference and output updated inter-sample interval.

Membership Functions for Current isi | Membership Functions Updated isi | (Mean, Standard Deviation) for Current and Updated isi |
---|---|---|

Very small | Decrease low (DL) | 10, 0 |

Small | Decrease High (DH) | 10, 25 |

Medium | No change (NC) | 10, 50 |

Large | Increase low (IL) | 10, 75 |

Very large | Increase high (IH) | 10, 100 |

Rule | Current isi | TD Delay | TD Jitter | TD Packet Loss Ratio | Updated isi |
---|---|---|---|---|---|

1 | Very small | Very low | Very low | None | Increase high (IH) |

2 | Very small | Very low | None | Very low | Increase high (IH) |

3 | Very small | None | Very low | Very low | Increase high (IH) |

4 | None | Very low | Very low | Very low | Increase high (IH) |

5 | None | Low | Low | Low | Increase low (IL) |

6 | Small | None | Low | Low | Increase low (IL) |

7 | Small | Low | None | Low | Increase low (IL) |

8 | Small | Low | Low | None | Increase low (IL) |

9 | Medium | Medium | Medium | None | No change (NC) |

10 | Medium | Medium | None | Medium | No change (NC) |

11 | Medium | None | Medium | Medium | No change (NC) |

12 | None | Medium | Medium | Medium | No change (NC) |

13 | None | High | High | High | Decrease low (DL) |

14 | Large | None | High | High | Decrease low (DL) |

15 | Large | High | None | High | Decrease low (DL) |

16 | Large | High | High | None | Decrease low (DL) |

17 | None | Very high | Very high | Very high | Decrease low (DH) |

18 | Very large | None | Very high | Very high | Decrease low (DH) |

19 | Very large | Very high | None | Very high | Decrease High (DH) |

20 | Very large | Very high | Very high | None | Decrease High (DH) |

**Table 4.**Measurement results for delay using different sampling methods: adaptive, systematic, random, and stratified.

Unit | Sample Fractions % | ||||
---|---|---|---|---|---|

0 | 6.1 | 10.2 | 13 | 22.9 | |

Adaptive sampling method | |||||

Mean | 146 | 147 | 147 | 147 | 147 |

Std. | 141 | 141 | 141 | 142 | 141 |

Bias | 0 | 0.875 | 0.683 | 0.067 | −0.262 |

RSE | 0 | 0.0090 | 0.0040 | 0.0030 | 0.0011 |

Systematic sampling | |||||

Mean | 147 | 145 | 146 | 148 | 143 |

Std. | 141 | 146 | 142 | 141 | 138 |

Bias | 0 | 1.9740 | 0.725 | −1.279 | 3.960 |

RSE | 0 | 0.0099 | 0.0052 | 0.0038 | 0.0019 |

Random sampling | |||||

Mean | 147 | 176 | 157 | 149 | 150 |

Std. | 141 | 165 | 152 | 149 | 142 |

Bias | 0 | −28.551 | −9.741 | −1.401 | −2.432 |

RSE | 0 | 0.0113 | 0.0050 | 0.0029 | 0.0014 |

Stratified sampling | |||||

Mean | 147 | 146 | 150 | 150 | 149 |

Std. | 141 | 143 | 149 | 142 | 139 |

Bias | 0 | 1.0932 | −2.74034 | −2.9770 | −2.1844 |

RSE | 0 | 0.0127 | 0.0046 | 0.00389 | 0.00265 |

**Table 5.**Measurement results of jitter using different sampling methods: adaptive, systematic, random, and stratified.

Unit | Sample Fractions % | ||||
---|---|---|---|---|---|

0.0 | 6.1 | 10.2 | 13 | 22.9 | |

Adaptive sampling method | |||||

Mean | 11.116 | 11.235 | 10.6386 | 11.1855 | 11.0730 |

Std. | 17.493 | 17.479 | 11.636 | 14.073 | 17.4936 |

Bias | 0 | −0.1185 | 0.478 | −0.0689 | 0.0435 |

RSE | 0 | 0.00112 | 4.31 × 10^{−4} | 2.69 × 10^{−4} | 1.5 × 10^{−4} |

Systematic sampling | |||||

Mean | 11.116 | 12.6123 | 11.133 | 12.732 | 10.855 |

Std. | 17.493 | 23.7784 | 21.049 | 26.650 | 12.120 |

Bias | 0 | −1.4956 | −0.016 | −1.615 | 0.261 |

RSE | 0 | 0.00161 | 6.97 × 10^{−4} | 7.40 × 10^{−4} | 1.66 × 10^{−4} |

Random sampling | |||||

Mean | 11.116 | 11.733 | 10.325 | 10.691 | 10.608 |

Std. | 17.493 | 23.990 | 13.723 | 21.510 | 14.770 |

Bias | 0 | −0.6166 | 0.790 | 0.425 | 0.508 |

RSE | 0 | 0.00165 | 4.53 × 10^{−4} | 4.34 × 10^{−4} | 1.55 × 10^{−4} |

Stratified sampling | |||||

Mean | 11.116 | 13.127 | 11.357 | 11.202 | 11.389 |

Std. | 17.493 | 23.601 | 19.236 | 18.428 | 18.681 |

Bias | 0 | −2.011 | −0.241 | −0.085 | −0.272 |

RSE | 0 | 0.002 | 6.08 × 10^{−4} | 5.05 × 10^{−4} | 3.5 × 10^{−4} |

**Table 6.**Measurement results of packet loss ratio using different sampling methods: adaptive, systematic, random, and stratified.

Unit | Sample Fractions % | ||||
---|---|---|---|---|---|

0.0 | 6.1 | 10.2 | 13 | 22.9 | |

Adaptive sampling method | |||||

Mean | 0.0356 | 0.035 | 0.034 | 0.036 | 0.035 |

Std. | 0.0291 | 0.0292 | 0.0290 | 0.029 | 0.029 |

Bias | 0 | 6.23 × 10^{−6} | 0.0016 | −5.96 × 10^{−4} | −7.22 × 10^{−5} |

RSE | 0 | 1.88 × 10^{−6} | 3.05 × 10^{−7} | 5.93 × 10^{−7} | 2.08 × 10^{−7} |

Systematic sampling | |||||

Mean | 0.0356 | 0.037 | 0.035 | 0.035 | 0.035 |

Std. | 0.0291 | 0.029 | 0.0290 | 0.028 | 0.029 |

Bias | 0 | −0.0014 | 5.20 × 10^{−4} | 7.95 × 10^{−6} | −2.72 × 10^{−4} |

RSE | 0 | 2.06 × 10^{−6} | 9.62 × 10^{−7} | 8.05 × 10^{−7} | 3.99 × 10^{−7} |

Random sampling | |||||

Mean | 0.0356 | 0.035 | 0.0343 | 0.034 | 0.035 |

Std. | 0.0291 | 0.029 | 0.027877 | 0.028954 | 0.029492 |

Bias | 0 | 1.65 × 10^{−5} | 0.0013 | 8.07 × 10^{−4} | −2.90 × 10^{−4} |

RSE | 0 | 1.98 × 10^{−6} | 1.03 × 10^{−6} | 7.94 × 10^{−7} | 3.30 × 10^{−7} |

Stratified sampling | |||||

Mean | 0.0356 | 0.034 | 0.035 | 0.037 | 0.036 |

Std. | 0.0291 | 0.028 | 0.029 | 0.029 | 0.0286 |

Bias | 0 | 0.0013 | 1.03 × 10^{−6} | −0.0014 | −6.45 × 10^{−4} |

RSE | 0 | 2.55 × 10^{−6} | 9.35 × 10^{−7} | 8.13 × 10^{−7} | 5.47 × 10^{−7} |

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**MDPI and ACS Style**

Salama, A.; Saatchi, R.; Burke, D. Fuzzy Logic and Regression Approaches for Adaptive Sampling of Multimedia Traffic in Wireless Computer Networks. *Technologies* **2018**, *6*, 24.
https://doi.org/10.3390/technologies6010024

**AMA Style**

Salama A, Saatchi R, Burke D. Fuzzy Logic and Regression Approaches for Adaptive Sampling of Multimedia Traffic in Wireless Computer Networks. *Technologies*. 2018; 6(1):24.
https://doi.org/10.3390/technologies6010024

**Chicago/Turabian Style**

Salama, Abdussalam, Reza Saatchi, and Derek Burke. 2018. "Fuzzy Logic and Regression Approaches for Adaptive Sampling of Multimedia Traffic in Wireless Computer Networks" *Technologies* 6, no. 1: 24.
https://doi.org/10.3390/technologies6010024