The uniform line density has maximum crossing factor

If straight lines of infinite length are placed at random on the plane such that the relative numbers in a range of directions is described by a continuous function then it is proved that the maximum crossings per unit area for a fixed length of line per unit area occurs when the lines are provided equally in each direction.     

Further aspects of rectangular routeing in Smeed's City

Two types of routeing on a rectangular system of roads are examined in a simple circular city where homes and workplaces are uniformly and independently distributed. Expressions for the number of vehicles crossing a given line segment, the average distance travelled by a commuter and the total number of crossings of vehicle paths in the city are derived. Comparisons are made with other routeing systems in terms of average distance travelled, expected number of crossings and average travel time.     

Calibration of large-scale transport planning models: a structured approach

Transportation - Traditionally, transport planning model systems are estimated and calibrated in an unstructured way, which does not allow for interactions among included parameters to be...     

Rectangular routeing in Smeed's city

A rectangular system of roads is examined in a simple circular city where homes and workplaces are uniformly and independently distributed. Expressions for the number of vehicles crossing a given line segment are derived.