Optimal headways for multiroute transit systems

Abstract

AbstractThe problem considered is that of determining net‐benefit maximizing headways for multiroute transit systems which are subject to constraints on vehicle capacity, subsidy, and fleet size. Route demands are assumed to be independent of one another and to vary with the frequency of service, but details of route demand functions are assumed to be unknown. Conditions of optimality are derived for the unconstrained case and the various constrained cases. The relationship between conditions of optimality based on the assumption of fixed demand and those based on the assumption of variable demand is expressed by means of terms incorporating the elasticity of demand with respect to frequency of service. It is shown that the magnitude of discrepancies between the true conditions of optimality and fixed‐demand approximations of them depends on the elasticity of demand and on the distribution of ridership and cycle times among the various routes of the system. It is also shown that a trial‐and‐error search procedure based on fixed‐demand approximations should eventually converge to a stable schedule, although its use is not appropriate for all situations in which rescheduling might be considered. A case study is presented in which the maximum possible discrepancies between the variable‐demand and fixed‐demand conditions of optimality are found to be reasonable small, and an actual transit schedule is found to be generally similar to one indicated as optimal by the fixed‐demand approximation.