BUFFONS NEEDLE AND THE PROBABILITY OF INTERCEPTING SHORT-DISTANCE TRIPS BY MULTIPLE SCREEN-LINE SURVEYS

For transport planning purposes, information on origin-destination mov ements may be obtained by stopping traffic at the roadside and intervi ewing drivers. The roadside interview stations are usually located so that they lie on one of a number of lines (called screen lines) that c ross from one side of the survey area to another. In this way, all mov ements with the origin on one side of a screen line and the destinatio n on the other are intercepted. For regional surveys, a grid of screen -lines may be used. The movements intercepted are not, however represe ntative of all those in the region. That is because shorter-distance m ovements are underrepresented; the coarser the grid, the worse the eff ect. 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 unifo rm rectangular grid, and that trips of a given length are distributed over the region at random. The result is an extension to the Buffon ne edle problem. Ways in which such a result, obtained for an idealized s ituation, may be extended to apply to more realistic situations, are d iscussed: in particular it is shown how the trip-length frequency dist ribution of all trips may be estimated from that of intercepted trips, using a simple formula that is applicable to a much more general patt ern of screen lines.