Optimization models for comparing conventional and subscription bus feeder services

Analytic models are developed and used in comparing fixed route conventional bus and flexible route subscription bus systems for providing feeder services to a single point (such as a transportation terminal). In the mathematical models for these two systems, vehicle size and service zone size are the optimizable decision variables, and total system cost, including operator and user costs, is the objective function to be minimized. Average cost per trip is the criterion used to determine which system is preferable and how it should be optimized in various circumstances. With an approximation for subscription services, closed form solutions for optimal vehicle size and service zone area are obtained for both alternatives. The analytic results for optimized conventional services indicate that constant ratios should be maintained at all demand densities between vehicle size and route spacing and between fleet size and user wait time. Analytic solutions are extended to conditions where (1) demand and costs are time dependent, requiring multiperiod optimization and (2) the maximum load factor may differ from 1.0 to allow for standees and stochastic demand fluctuations. A method for comparing the two systems when their service levels generate different passenger volumes is also presented. Sensitivity analyses indicate that the relative advantage of subscription bus services generally increases with smaller service areas, higher speeds, lower fixed bus cost, lower incremental costs of vehicle size, higher values of access and wait time, and lower values of in-vehicle time.