Rapid Transit Interstation Spacings for Minimum Travel Time

Several factors influencing the optimal interstation spacings for line-haul passenger transportation, for example, rapid transit or commuter railroads, are analyzed with respect to the objective of minimum total passenger travel time. The study concentrates on a case in which the population of an area commutes to one central point. The number and locations of stations at which the commuters board the trains for their travel to the central terminus are to be determined so that the total time of all passengers---from their origins to the destination---is minimal. The model incorporates as parameters: passenger (“population”) distribution along the line, access speed, dynamic characteristics of the train, standing time of the train in stations, and intermodal transfer time at stations. In general, the spacings are functions of the ratio between the number of passengers traveling on the train and those wanting to board or alight. The optimal station locations satisfy a set of simultaneous difference equations. Algorithms for numerical and graphical solutions for several different sets of parameters are presented and demonstrated by examples. For uniform population along the line, spacings increase in an arithmetic progression in the direction of passenger cumulation. In all cases density and distribution of stations have high sensitivity to the access-to-station speed.