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Changing Rank-Size Distributions over 24 Hrs on London Tube and Rail

Inspired by Jon Reades’ great visualizations of flows using the TfL Oyster card data, we are now starting to examine the statistical properties of the data, beginning with an analysis of what goes on in the nodes. The data yields 666 hubs or nodes which have entry and exit volumes – in graph theoretic terms the in-degrees of the sources/origins and the out-degrees of the sinks/destinations. We have this data for 20 minute time segments of the entire day, giving us 72 temporal slots defining the diurnal sequence.

Now the tube and rail are closed during the dead of night and as is characteristic of such data, all 666 nodes are never active at any one time in terms of the data set. But there are records for at last one hub in every one of the 72 segments and they build up so that for the most part, most of the 666 are in use between 7am and 11pm. More or less. What we have done so far with this data is simply examine the changing profile of the hubs in terms of their volumes and an easy way to get into this is to rank them in terms of the size for each time slice and then order them, forming a rank size distribution which we fist examine as in the video below as a Zipf plot. These change at each time slice. We start the simulation at midnight and the volumes then drop dramatically until around 5 am things begin to pick up reaching a morning peal around 8am and then falling off a bit and then picking up for the evening peak at 5pm and thence declining slowly through the evening as we move back towards midnight. Click on the image below and you will get the Vimeo link where you can see the animation. I must confess that I have forgotten how to embed the Vimeo directly into the post and someone doubtless will remind me

You can see the peaks more or less as we color the plots from white at midnight to red at midday and back down to white again in the rest of the day. The color balance can be improved and we need to do this and probably this would look really good if we used a more powerful graphics language but as a first pass, it suffices. Of course the next step is to examine the local volatility of the hubs and to put all this into the rank clocks software which in fact would be our first application where the clock where truly a clock and the diurnal cycles the dominant driver. More soon.

The idea is that we present a paper on this at the forthcoming meeting organised by the Urban Design Studies Unit of the School of Architecture in partnership with ICSS Institute of Complex System on the subject of the Evolution of Complex Transportation Networks (ECTN) Workshop to be held at University of Strathclyde, Glasgow, on 29-30 August 2011.