Fractal road hierarchy (02)

One definition which the Internet offers of a fractal (link) is:

“A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same “type” of structures must appear on all scales. “

 Road networks are scale-independent; they do ‘display self-similarity on all scales’.  If you use Google Earth to view the geography and road network of a country, then as you zoom further into the view you see a similar pattern of major and minor roads. Papers which discuss fractal math and road networks include (ref. 301).

The hierarchy of roads at any particular scale can be described as a ‘shallow’ road hierarchy with just two levels or types of road: through routes and link routes. With some imagination it might even be possible to see a two-level hierarchy in Eppell et al’s paper (although it is called “a four-level hierarchy for network planning and management”) (ref. 305).  For example (ref. 305 figure 1) refers to:

  • Roads (through traffic)
  • Streets (local and access traffic)

 And then

  • Roads (through traffic)
  • Arterial road
  • Sub-arterial road

Streets (local and access traffic)

  • Collector street
  • Local street

 India’s 2007 rural roads programme (ref. 282) also recognises just two types of road – it talks of a core network of rural roads which consists of through routes and link routes. Stephen Marshall, in his 2004 paper on “Marshall on Buchanan” (ref. 297) makes the point (of two road types) very clearly, when he quotes directly from the Buchanan Report “Traffic in Towns”

 “Basically, however, there are only two kinds of roads – distributors designed for movement, and  access  roads  to  serve  the  buildings” [original emphasis]

Stephen goes on to write that

 “In  effect,  this  ‘basic  principle’  is  a  division  between  a  system  of  traffic distributors,  where  the  needs  of  movement  are  prioritised,  and  a  system  of ‘environmental areas’ where environmental considerations are prioritised”.

 And in reference to scale, Stephen’s paper says:

 “The  significance  of  this  is  that  road  hierarchy  is  not  after  all  based  on  some inscrutable and unassailable ‘traffic engineering’ principles that urban designers and  planners  find  themselves  unable  to  challenge,  but  is  in  fact  based  on  a simple nesting of geographical scale, that is transparent to all”.

 And

“While the rankings (of a road hierarchy) may appear to be some kind of ‘traffic function’ ( …. ) It turns out that the ranking is actually based on the geographical scale of significance of the network to which a road belongs”

 Speed and classification

So the argument is that any road network in any country is scalar (and probably fractal) in nature, and that at a given scale there are only two types of road.

Another key feature of a road is that its physical properties – horizontal radius, gradient etc – are related to speed. With existing road vehicles and materials there are only around 12 speed values which are in use: from 0 km/hr to 120 km/hr at 10 km/hr intervals. This is generally true for all road networks, in every country. Speed could then be used to define just 12 classes of road. The measure of distributor and access functions vary with speed -for example, zero access function at 120 km/hr, zero distributor function at 10 km/hr.

Also, if you stand next to a road in a network

  • The roads in the rest of the network which have higher speeds are distributors
  • The roads in the rest of the network which have lower speeds are access roads

(the question is, is the road which you are standing next to a distributor or an access road?)

References

  • 282 / PRADHAN  MANTRI  GRAM  SADAK  YOJANA , programme guidelines (India 2012)
  • 297 / Stephen Marshall, “Marshall on Buchanan: evolving road hierarchy for today’s streets-oriented design criteria” (UK 2004)
  • 301 / Clauset and others, “Scale invariance and hierarchy in national road networks” NetSci2006 (USA 2006)
  • 305 / V.A.T. Eppell and others, “A four level hierarchy for network planning and management” (Proceedings, 20th ARRB Conference, Australia 2001)
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About roadnotes

Robert Bartlett is an international consultant with over 30 years of professional experience as a highway and traffic engineer with leading companies and organisations in several countries, including Germany, China (Hong Kong), Qatar and the UK. Specialised in urban studies, transport and the use of GIS, research has included new ideas on subjects such as the study of social justice using GIS, the dimensions of vehicles, and comparative geometrics (highways and transport).
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