Spatial aspects of traffic circulation: II. Routing patterns that exactly minimise path crossings

The total number of path crossings between vehicles following different routes on a road network can be taken as a rough proxy for congestion and accident risk. It is therefore useful to identify ways of routing traffic in the plane such that the number of crossings are minimised; these can serve as models for the design of traffic management schemes in urban areas. The authors have previously investigated a number of routing patterns; the best ones generated path crossings whose number exceeded a conjectured minimum by 33%. In this article, two configurations are put forward that achieve the minimum value. The networks required to support such routing patterns are probably not realisable in practice, but the exercise provides a useful insight into the traffic circulation problem and suggests a yardstick against which other routing patterns can be evaluated.