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**Statistical analysis and modeling of Internet VoIP traffic for network engineering.**
*(English)*
Zbl 1329.62480

Summary: Network engineering for quality-of-service (QoS) of Internet voice communication (VoIP) can benefit substantially from simulation study of the VoIP packet traffic on a network of routers. This requires accurate statistical models for the packet arrivals to the network from a gateway. The arrival point process is the superposition, or statistical multiplexing, of the arrival processes of packets of individual calls. The packets of each call form a transient point process with on-intervals of transmission and off-intervals of silence. This article presents the development and validation of models for the multiplexed process based on statistical analyses of VoIP traffic from the Global Crossing (GBLX) international network: 48 hr of VoIP arrival times and headers of 1.315 billion packets from 332018 calls. Statistical models and methods involve point processes and their superposition; time series autocorrelations and power spectra; long-range dependence; random effects and hierarchical modeling; bootstrapping; robust estimation; modeling independence and identical distribution; and visualization methods for model building. The result is two models validated by the analyses that can generate accurate synthetic multiplexed packet traffic. One is a semi-empirical model: empirical data are a part of the model. The second is a mathematical model: the components are parametric statistical models. This is the first comprehensive modeling of VoIP traffic based on data from a service provider carrying a full range of VoIP applications. The models can be used for simulation of any IP network architecture, wireline or wireless, because the modeling is for the IP-inbound traffic to an IP network. This is achieved because the GBLX data, collected on an IP link, are very close to their properties when they entered the GBLX network.

### MSC:

62P30 | Applications of statistics in engineering and industry; control charts |

62-07 | Data analysis (statistics) (MSC2010) |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62M15 | Inference from stochastic processes and spectral analysis |

90B20 | Traffic problems in operations research |

### Keywords:

statistical model building; very large datasets; semi-empirical models; long-range dependence### References:

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