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T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A Nonstationary Poisson View of Internet Traffic", in IEEE INFOCOM. March 2004, IEEE INFOCOM.
A Nonstationary Poisson View of Internet Traffic
Authors: T. Karagiannis
M. Molle
M. Faloutsos
A. Broido
Published: IEEE INFOCOM, 2004
URL:http://www.caida.org/publications/papers/2004/infocom/
Entry Date: 2004-02-18
Abstract: Since the identification of long-range dependence in network traffic ten years ago, its consistent appearance across numerous measurement studies has largely discredited Poissonbased models. However, since that original data set was collected, both link speeds and the number of Internet-connected hosts have increased by more than three orders of magnitude. Thus, we now revisit the Poisson assumption, by studying a combination of historical traces and new measurements obtained from a major backbone link belonging to a Tier 1 ISP. We show that unlike the older data sets, current network traffic can be well represented by the Poisson model for sub-second time scales. At multi-second scales, we find a distinctive piecewise-linear non-stationarity, together with evidence of long-range dependence. Combining our observations across both time scales leads to a time-dependent Poisson characterization of network traffic that, when viewed across very long time scales, exhibits the observed long-range dependence. This traffic characterization reconciliates the seemingly contradicting observations of Poisson and long-memory traffic characteristics. It also seems to be in general agreement with recent theoretical models for large-scale traffic aggregation.
Datasets:

We use three types of traces for our study: a) Internet backbone traces from an OC48 link, b) traces from the WIDE backbone maintained by the MAWI Working Group Traffic Archive and the WIDE project , and c) the well-known BCpAug89 and LBL-PKT-4 traces.

The WIDE backbone traces were captured in a trans-Pacific 100Mbps link. They are 15 minute traces taken daily at 14:00 local time (JST). We use traces from June 2003.The BCpAug89 trace was taken at 11:25 (EDT) on August 29, 1989 on an Ethernet at the Bellcore Morristown Research and Engineering facility. It consists of 1,000,000 packets (approximately 3142.82 seconds). Finally, the LBL-PKT-4 was captured on January 21, 1994, 14:00-15:00 (PST) at Lawrence Berkeley Laboratory (approximately 1.3M packets).

We analyze three different backbone traces captured in August 2002, January 2003 and April 2003. These were taken on CAIDA monitor located at a SONET OC48 (2.5 Gbps) link that belongs to MFN, a US Tier 1 Internet Service Provider (ISP).

Experiments:

Using various tests and statistical tools, we reexamine the Poisson traffic assumption in relation to the traffic carried within the Internet core.

Results:

We show that unlike older traffic data sets, current network traffic can be well represented by the Poisson model for sub-second time scales. At multi-second scales, we find a distinctive piecewise-linear non-stationarity, together with evidence of long-range dependence. Combining our observations across both time scales leads to a time-dependent Poisson characterization of network traffic that, when viewed across very long time scales, exhibits the observed long-range dependence. This traffic characterization reconciliates the seemingly contradicting observations of Poisson and long-memory traffic characteristics.

References:
  • L. Kleinrock. Queueing Systems, Vol. II Computer Applications. Wiley, New York, 1976.
  • W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson. On the Self-Similar Nature of Ethernet Traffic. In IEEE/ACM Transactions on Networking, 1994.
  • V. Paxson and S. Floyd. Wide Area Traffic: The Failure of Poisson Modeling. IEEE/ACM Transactions on Networking, 1995.
  • K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexors for Voice and Data. In IEEE J. Select. Areas Commun., volume 4, pages 833.846, 1986.
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