Rapid Transit Interstation Spacings for Maximum Number of Passengers

Abstract

Two transportation systems, following the same alignment, serve an area from which population commutes to a central point. One system has a constant speed and can be taken at any point along the line; the other has a discrete movement and can be boarded at stations only. The study analyzes the optimal station locations of the latter system for which its patronage will be maximum, assuming that passengers select systems on the basis of shorter travel time. The optimal solution, derived analytically and shown graphically on a time-distance diagram, indicates that the interstation spacings for this objective should be increasing at a decreasing rate in the direction of cumulation. Compared with the optimal interstation spacings for minimum total passenger travel time, given in a recent paper by Vuchic and Newell, this solution has a greater density of stations and, naturally, larger travel times. Sensitivity of the two solutions to various parameters is examined. Several problems to which this model would be applicable are shown and the model's realistic validity is discussed. From the optimal solution and numerical examples, several conclusions are drawn that are directly relevant to the planning of station locations for discrete public transportation systems.