Multiobjective Optimal Formulations for Bus Fleet Size of Public Transit under Headway-Based Holding Control

Abstract

In recent years, with the development of advanced technologies for data collection, real-time bus control strategies have been implemented to improve the daily operation of transit systems, especially headway-based holding control which is a proven strategy to reduce bus bunching and improve service reliability for high-frequency bus routes, with the concept of regulating headways between successive buses. This hot topic has inspired the reconsideration of the traditional issue of fleet size optimization and the integrated bus holding control strategy. The traditional headway-based control method only focused on the regulation of bus headways, without considering the number of buses on the route. The number of buses is usually assumed as a given in advance and the task of the control method is to regulate the headways between successive buses. They did not consider the bus fleet size problem integrated with headway-based holding control method. Therefore, this work has presented a set of optimal control formulations to minimize the costs for the passengers and the bus company through calculating the optimal number of buses and the dynamic holding time, taking into account the randomness of passenger arrivals. A set of equations were formulated to obtain the operation of the buses with headway-based holding control or the schedule-based control method. The objective was to minimize the total cost for the passengers and the bus company in the system, and a Monte Carlo simulation based solution method was subsequently designed to solve the optimization model. The effects of this optimization method were tested under different operational settings. A comparison of the total costs was conducted between the headway-based holding control and the schedule-based holding control. It was found that the model was capable of reducing the costs of the bus company and passengers through utilizing headway-based bus holding control combined with optimization of the bus fleet size. The proposed optimization model could minimize the number of buses on the route for a guaranteed service level, alleviating the problem of redundant bus fleet sizes caused by bus bunching in the traditional schedule-based control method.