Locating stations on rapid transit lines

When the alignment of a new line or section of a line of a rapid transit system has already been designed, the problem of locating stations arises. One of the measures used to predict the future utilization of the line is the coverage provided by the stations. In this paper the problem of locating a prefixed number of stations so that the weighted coverage will be maximized is considered. To evaluate the coverage of each station an estimation of the street network metric and the triangulations of the census tracts are used. Finally, a longest path type algorithm over an acyclic graph is devised in order to maximize the objective function, in which it was necessary to approximately determine the catchment area for each station.