Cost minimizing positions, lengths and headways for parallel public transit lines having different speeds

Abstract

In this paper, a model of a transit system is built in order to find for parallel lines in a rectangular city the lengths, positions, and headways which minimize user (travel time) and operating costs in response to a general population density function and differing line speeds. It is found that, at some point, low speed lines should be cut off, this point depending upon the relative positions, headways and speeds of adjacent lines. Further, it is found that the optimum position depends upon the tributary population and the changes in operating costs due to changes in line position. The optimum headway depends upon the tributary population, the operating cost and the change in operating cost due to changes in headway. Simplifying the problem by assuming a uniform population density, it is found that the optimum headway depends upon the average headway and the deviations of the reciprocal speed from the average reciprocal speed. Furthermore, if the fleet size is constrained, the optimum headway depends not only on these, but also on the variance of the headway and the covariance of the headway and reciprocal speed among the lines.