Testing the Gaussian approximation of aggregate traffic

ABSTRACT

We search for methods or tools to detect whether the 1-dimensional marginal distribution of traffic increments of aggregate TCP-traffic satisfy the hypothesis of approximate normality. Gaussian approximation requires a high level of aggregation in both "vertical" (source aggregation) and "horizontal" (time scale) directions. We discuss these different concepts of aggregation first separately, with an example from real data traffic, and show how to rule out cases where the level of aggregation will not be sufficient. Gaussian approximation is then quantified with the square of the linear correlation coefficient in normal-quantile plots. We propose an elementary method based on this correlation test, by looking at the behavior of the test statistic for different sample sizes, and show positive and negative examples from the example data. We use this method to look for the first time scale, where the Gaussian approximation is plausible with the example data, and then we look how much more vertical aggregation would be needed for smaller time scales in order to obtain a reasonable approximation by normal distribution.

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INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.3 Network Operations
          Subjects: Network monitoring

Additional Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.5 Local and Wide-Area Networks
          Subjects: Internet (e.g., TCP/IP)
  C.4 PERFORMANCE OF SYSTEMS
      Subjects: Performance attributes

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Gaussian quadrature

General Terms:
Management, Measurement, Performance

Keywords:
Quantile-Quantile plots, TCP/IP, aggregate traffic, correlation tests, normal plots, traffic modeling and measurements