The apparent BGP4 square law relationships... and their demise

Most recent publication

A square law revisited, ACM SIGCOMM CCR, 51(3) (July 2021) 41-45

Abstract:

An earlier study observed that until 2008, the size of the BGP4 system for IPv4 appeared to have grown approximately in proportion to the square root of the host count of the globally addressable Internet. This article revisits this study by including IPv4 data until 2020 and adding IPv6 data. The results indicate that BGP4 for IPv4 is continuing to scale steadily even as IPv4 approaches its end of life, and that it is working as it should for IPv6, except for a slight concern that the number of announced routes is trending upwards faster as time goes on.

Original publication

Observed Relationships between Size Measures of the Internet, ACM SIGCOMM CCR, 39(2) (April 2009) 6-12

Abstract:

This paper reports some observations on the relationships between three measures of the size of the Internet over more than ten years. The size of the BGP4 routing table, the number of active BGP4 Autonomous Systems, and a lower bound on the total size of the Internet, appear to have fairly simple relationships despite the Internet's growth by two orders of magnitude. In particular, it is observed that the size of the BGP4 system appears to have grown approximately in proportion to the square root of the lower-bound size of the globally addressable Internet. A simple model that partially explains this square law is described. It is not suggested that this observation and model have predictive value, since they cannot predict qualitative changes in the Internet topology. However, they do offer a new way to understand and monitor the scaling of the BGP4 system.

Note that the observations concern IPv4 only. ISC domain count data are used as lower bounds on the total size of the IPv4-addressable Internet. The choice and validity of this metric are discussed in the paper.

Errata:

Cited in:

(Overtaken by events: Updated graphs based on data through July 2011)

The approximate square law relationships originally observed in data through 2008 still appeared to exist in 2011. However, there was a hint in the data of an upward inflection of the relative growth of the BGP4 system, starting in 2007.

BGP4 routes vs active AS count (1997-2011):

BGP4 routes vs square root of domain count (1994-2011):

Active AS count vs square root of domain count (1997-2011):

As always, thanks to isc.org and potaroo.net for the data.

External talks on this topic

BGP scaling revisited, (IEPG Meeting, Taipei, China, November 2011)

BGP growth over 15 years, or Is the Internet really just a star network after all? (Keynote at APRICOT 2010, March 2010)

Observed Relationships between Size Measures of the Internet, or Is the Internet really just a star network after all? (Seminar, University of Cambridge, June 2009)

Some multi-year graphs (IEPG Meeting, Dublin, Ireland, July 2008)

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