Open Access
2010 Statistical analysis and modeling of Internet VoIP traffic for network engineering
Bowei Xi, Hui Chen, William S. Cleveland, Thomas Telkamp
Electron. J. Statist. 4: 58-116 (2010). DOI: 10.1214/09-EJS473


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.


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Bowei Xi. Hui Chen. William S. Cleveland. Thomas Telkamp. "Statistical analysis and modeling of Internet VoIP traffic for network engineering." Electron. J. Statist. 4 58 - 116, 2010.


Published: 2010
First available in Project Euclid: 29 January 2010

zbMATH: 1329.62480
MathSciNet: MR2645478
Digital Object Identifier: 10.1214/09-EJS473

Primary: 62-07 , 62P30
Secondary: 62M10 , 62M15

Keywords: long-range dependence , semi-empirical models , Statistical model building , very large datasets

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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