# Self-Similar Markovian Sources

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Markov Chains and the Markov Traffic Sources

#### 2.1. Special Semi-Markov Process (SSMP)

#### 2.2. Markov Modulated Poisson Process (MMPP)

- ${\lambda}^{*}$—the mean rate of the process to be modeled,
- n—number of time scales,
- d—number of active MMPPs,
- $H=1-\frac{\beta}{2}$—the Hurst parameter,
- $\rho $—lag 1 correlation.

#### 2.3. Poisson Pareto Burst Process (PPBP)

- The traffic time duration t,
- The intensity of the Poisson burst $\lambda $,
- The mean intensity of bursts $E\left(D\right)$,
- The Hurst parameter $H\in (0.5,1)$.

## 3. Experimental Results

## 4. Summary

## Author Contributions

## Funding

## Conflicts of Interest

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**Table 1.**The comparison of distances between calculated values, and the fitted values provided by the method of least squares. SSMP: special semi-Markov process; MMPP: modulated Markov Poisson process; PPBP: Poisson Pareto burst process.

Method | Max Distance | Avg Distance |
---|---|---|

SSMP4 | 1.0722 | 0.5264 |

SSMP5 | 0.8912 | 0.3974 |

SSMP6 | 0.7088 | 0.2664 |

MMPP5 | 0.3999 | 0.1087 |

MMPP22 | 0.3257 | 0.0991 |

PPBP | 0.1790 | 0.0542 |

Method | Avg Time [ms] |
---|---|

SSMP4 | 12.1257 |

SSMP5 | 12.8312 |

SSMP6 | 13.5641 |

MMPP5 | 18.1601 |

MMPP22 | 32.6147 |

PPBP | 197.1943 |

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**MDPI and ACS Style**

Domański, A.; Domańska, J.; Filus, K.; Szyguła, J.; Czachórski, T.
Self-Similar Markovian Sources. *Appl. Sci.* **2020**, *10*, 3727.
https://doi.org/10.3390/app10113727

**AMA Style**

Domański A, Domańska J, Filus K, Szyguła J, Czachórski T.
Self-Similar Markovian Sources. *Applied Sciences*. 2020; 10(11):3727.
https://doi.org/10.3390/app10113727

**Chicago/Turabian Style**

Domański, Adam, Joanna Domańska, Katarzyna Filus, Jakub Szyguła, and Tadeusz Czachórski.
2020. "Self-Similar Markovian Sources" *Applied Sciences* 10, no. 11: 3727.
https://doi.org/10.3390/app10113727