Instantaneous global spatial interaction? Exploring the Gaussian inequality, distance and Internet pings in a global network

Abstract

The Internet has been publicly portrayed as a new technological horizon yielding instantaneous interaction to a point where geography no longer matters. This research aims to dispel this impression by applying a dynamic form of trip modelling to investigate pings in a global computer network compiled by the Stanford Linear Accelerator Centre (SLAC) from 1998 to 2004. Internet flows have been predicted to have the same mathematical operators as trips to a supermarket, since they are both periodic and constrained by a distance metric. Both actual and virtual trips are part of a spectrum of origin–destination pairs in the time–space convergence of trip time-lines. Internet interaction is very near to the convergence of these time-lines (at a very small time scale in milliseconds, but with interactions over thousands of kilometres). There is a lag effect and this is formalised by the derivation of Gaussian and gravity inequalities between the time taken (Δt) and the partitioning of distance (Δx). This inequality seems to be robust for a regression of Δt to Δx in the SLAC data set for each year (1998 to 2004). There is a constant ‘forbidden zone’ in the interaction, underpinned by the fact that pings do not travel faster than the speed of light. Superimposed upon this zone is the network capacity where a linear regression of Δt to Δx is a proxy summarising global Internet connectivity for that year. The results suggest that there has been a substantial improvement in connectivity over the period with R 2 increasing steadily from 0.39 to 0.65 from less Gaussian spreading of the ping latencies. Further, the regression line shifts towards the inequality boundary from 1998 to 2004, where the increased slope shows a greater proportional rise in local connectivity over global connectivity. A conclusion is that national geography still does matter in spatial interaction modelling of the Internet.