| Abstract: | For transport planning purposes, information on origin-destination movements may be obtained by stopping traffic at the roadside and interviewing drivers. The roadside interview stations are usually located so that they lie on one of a number of lines (called screen lines) that cross from one side of the survey area to another. In this way, all movements with the origin on one side of a screen line and the destination on the other are intercepted. For regional surveys, a grid of screen-lines may be used. The movements intercepted are not, however, representative of all those in the region. That is because shorter-distance movements are underrepresented; the coarser the grid, the worse the effect. The extent of this underrepresentation is estimated in this paper by calculating the probability of intercepting a trip of given direct length, under the assumption that the screen lines constitute a uniform rectangular grid, and that trips of a given length are distributed over the region at random. The result is an extension to the Buffon needle problem. Ways in which such a result, obtained for an idealized situation, may be extended to apply to more realistic situations, are discussed: in particular it is shown how the trip-length frequency distribution of all trips may be estimated from that of intercepted trips, using a simple formula that is applicable to a much more general pattern of screen lines. |
