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Towards a physics of Internet traffic in a geographic network

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  • Baker, R.G.V.

Abstract

A set of equations from a biased random walk are shown to describe the time-based Gaussian distributions of Internet traffic relative to the Earth’s time zones. The Internet is an example of a more general physical problem dealing with motion near the speed of light relative to different time frames of reference. The second order differential equation (DE) takes the form of ‘time diffusion’ near the speed of light or alternatively considered as a complex variable with real time and imaginary longitudinal components. Congestion waves are generated by peak global traffic from different time zones following the Earth’s revolution. The DE is divided into space and time operators for discussion and each component solution, including constants, is illustrated using data from a global network compiled by the Stanford Linear Accelerator Centre (SLAC). Indices of global and regional phase congestion for the monitoring sites are calculated from standardised regressions from the Earth’s rotation. There is also a J-curve limit to transferring information by the Internet and this is expressed as an inequality underpinned by the speed of light with examples from US and European traffic. The research returns to an often little known theme of Isaac Newton’s: mixing physics with geography. In our case, the equations define trajectories of information packets travelling near the speed of light, navigating within networks and between longitudes, relative to the Earth’s rotation.

Suggested Citation

  • Baker, R.G.V., 2012. "Towards a physics of Internet traffic in a geographic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1133-1148.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1133-1148
    DOI: 10.1016/j.physa.2011.10.002
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    References listed on IDEAS

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    1. Yong Wang & Phillip Lai & Daniel Sui, 2003. "Mapping the Internet using GIS: The death of distance hypothesis revisited," Journal of Geographical Systems, Springer, vol. 5(4), pages 381-405, December.
    2. Stéger, József & Vaderna, Péter & Vattay, Gábor, 2006. "On the propagation of congestion waves in the Internet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 134-142.
    3. Mario Maggioni & Teodora Uberti, 2009. "Knowledge networks across Europe: which distance matters?," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 43(3), pages 691-720, September.
    4. R. Baker, 2005. "Instantaneous global spatial interaction? Exploring the Gaussian inequality, distance and Internet pings in a global network," Journal of Geographical Systems, Springer, vol. 7(3), pages 361-379, December.
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    Cited by:

    1. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    2. Li, Ming & Zhao, Wei, 2012. "Quantitatively investigating the locally weak stationarity of modified multifractional Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6268-6278.
    3. Baker, Robert G.V., 2017. "The Sun–Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 508-531.

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